cross the river problem solving game

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The PE Specialist

Awesome Resources for Physical Education Teachers

PE Games: Cross The River

This week I’m coming to you with a CLASSIC game that I play every year with my kids. Like most activities – I only play it once a year so kids love it when they walk in and see the game setup. I usually save it for a time when students are coming back from a break and kids would benefit from some team building and cooperative activities.

Aside from the fact that it’s an awesome activity, I think my students love it so much because I present the game in a gamified format by creating different levels for each increasingly difficult or complex extension of the game (I do this with most activities, for more examples check out Hula Hut Relays , Pass the Frog , or Fire and Ice .

Check out the video below for an example of me teaching the game to a 3rd grade class at my school:

If you don’t have time for the video check out the summary of the game below, or download the free lesson plan at the bottom of this post.

Cross The River

I shoot for about 5-7 kids on each team, but you can modify and adjust for different situations. The setup below is for one class, for double classes I would simply double the equipment. To start the game, I give my K-2 students 1 more dot than the members of their team, with 3-5th they get the same number of dots as team members.

No sliding or throwing the PE equipment
If any part of your body touches the “water” your entire team must start over

Level 1: Get to the “Island”

In this level students will learn how to get across the river with their team and attempt to make it to the island (gymnastics mats folded up)

Level 2: Cross the River

In this level students will attempt to cross the ENTIRE river. If they make it to the island, it acts as a “Checkpoint” where they can “Save their game”. If they fall in after saving their game, they can start over at the island.

Level 3: You Lost a Rock

In this level students once again, attempt to get their entire team to the island – However, you have some bad news for all the teams… The water has picked up and they’ve lost one of their rocks! They must use creativity and brainstorm a way to get to the island with one less rock. One hint I give kids on this level is “You need to think outside the Box!” 😉 , you can see an example in the instagram post below :

View this post on Instagram Kids: This is totally impossible…???? . Me (for the 3,00th time): Think outside the BOX and use all of your resources… . Kids: ???????????? USE the BOX!!!! . Me: ???????????????? . Details and lesson plan for this team building game “cross the river” are linked up on our resources page ???????? . #physicaleducation #physed #pegeeks #iteachpe #pe #peteacher #elempe #primarype #teamwork #teachersofinstagram A post shared by Ben Landers (@thepespecialist) on Jan 9, 2020 at 6:07am PST

Level 4: Cross the River Again

Same as level 2, but with one less rock this time. Checkpoint stays the same.

Level 5: Double Up

In this level I combine my 4 teams into 2 teams and have them attempt to make it to the island and then combine all of their equipment to go all the way across the river together.

That’s the basic outline, but there are tons of variations and different ways to present the game (different equipment, blindfolds, add obstacles to the river, create mines with bowling pins, change the scenario or add more restrictions).

I really love watching the kids play and there are TONS of teachable moments that will happen throughout the game that you can explore with the kids after each level.

I also use this game as one of my Field Day stations each year. The classroom teachers enjoy watching the kids use teamwork and attempt to be the first group to “cross the river”

If you want specifics and a more detailed list of ideas, strategies and variations – you can download my lesson plan for free below:

It’s so fun watching kids complete a challenge for the first time – check out the post below to see what I mean 🙂

View this post on Instagram Going into Friday like… . ???????? . #physicaleducation #physed #pegeeks #iteachpe #pe #peteacher #elempe #primarype A post shared by Ben Landers (@thepespecialist) on Jan 10, 2020 at 7:04am PST

Got some cool variations of the game not included in the lesson plan? Leave them in the comments below.

Have fun and teach on.

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Reader Interactions

May 21, 2024 at 12:58 pm

I love your games! I am a special ed teacher. I typically work with children in Early Intervention and preschool special ed. I am now working in an after school program with children in Grades K-8. Most are 2nd/3rd and 5th grade. We have a small group. The kids get to use the “gym” area. It’s called a Dojang as this is a martial arts center that teaches tae kwon do. Typically the middle schoolers and elementary kids have separate times in the Dojang. Then, there is a group time. How would you modify this for the older kids? Also, what other games would you recommend? They are so bored at times with the same games like gaga.

Thank you so much!

May 22, 2024 at 6:52 am

Thanks for reaching out!

Do you have any equipment? If so, you can do activities as stations. Check out the link below for ideas on stations:

https://www.thepespecialist.com/stationteaching/

If there is no equipment, you may want to organize the activities for fun games. Check out the link below to fun games and activities we like to do in PE class:

Physical Education Games and Activities

Hope this helps!

February 4, 2023 at 2:19 am

The object of the activity is to get all members of the group safely across the river. this a great game.

February 6, 2023 at 3:24 pm

Glad you’re enjoying the activity Rebecca!

May 18, 2021 at 1:50 pm

I just had my students play Cross the River. I needed a break from our Field Day fun prep and some inclement weather so I went on the website looking for something new. I have played a similar game that I call “Rescue Island” with my 3-5th graders that uses a scooter board (boat) substituted for the step (log) to the spots and the island played across the width of the gym. Anyway, Ben I sure appreciate your ideas and resources! I will definitely be adding this to my cooperative games unit. Teach on!

May 18, 2021 at 4:18 pm

Sounds like such a cool game Nathan! Thanks for sharing!

April 8, 2021 at 10:57 am

Hi! this is great fun with the kids, tried yesterday 🙂 but i am having trouble downloading the lesson plan. Not sure if it’s on my end or yours! 🙂 Loryn

April 8, 2021 at 3:25 pm

Sorry about the issue!

Usually, this issue is related to a school filter, pop-up blocker, or browser caching issue – so we’d recommend trying from another computer, switching browsers, clearing your cache and making sure all pop up blockers have been turned off.

As a another option you can also find some of our products on our Teachers Pay Teachers Page Here: https://www.teacherspayteachers.com/Store/The-Pe-Specialist

Just search “Cross the River”

March 14, 2021 at 8:03 pm

Exactly what I’ve been looking for! Can’t download the lesson plans though:/

March 15, 2021 at 3:45 pm

April 1, 2020 at 1:28 pm

It was a good game for the children to learn how to work together

April 2, 2020 at 12:16 pm

CTR is one of our favorites!

October 14, 2019 at 2:25 pm

Do you play until one team finishes the level or until 5 minutes are up or do you give all the students 5 minutes to finish and teams that finish first sit and watch?

October 16, 2019 at 4:52 pm

I stop the music about 20 seconds after the first team finishes and have all the teams reset – we talk about strategies and refinements and then play the next level. DO what works for you though!

October 3, 2019 at 9:39 am

I’m not able to download the lesson plan above. Is there another way to retrieve it?

October 7, 2019 at 6:14 pm

March 11, 2019 at 3:09 pm

I love the idea of this game but I am unable to download the lesson plan…

March 12, 2019 at 3:06 pm

Hey Rochelle, sorry about the issue, but it’s working on our end.

As a another option you can also find this product on our Teachers Pay Teachers Page Here: https://www.teacherspayteachers.com/Store/The-Pe-Specialist

January 9, 2019 at 8:23 am

Thank you! Fun reminder of some renditions of this classic!

January 6, 2019 at 10:13 pm

This sounds like a super fun game to kick off second semester! We do not have any Aerobic Steps. Trying to think of an alternative? I am going to rummage through our equipment room tomorrow.

January 9, 2019 at 5:21 pm

Anything works – yoga mats, scrap pieces of wood, pieces of cardboard…

January 6, 2019 at 2:15 pm

How can I get access to your Cross the River Download? When I click on “checkout” there is nothing in my cart.

January 9, 2019 at 5:20 pm

Sorry about the issue – Usually, this issue is related to a school filter, pop-up blocker, or browser issue – so we’d recommend trying from another computer, switching browsers and making sure all pop up blockers have been turned off.

As a last resort you can also find this download on our Teachers Pay Teachers Page Here: https://www.teacherspayteachers.com/Store/The-Pe-Specialist

January 5, 2019 at 12:20 pm

Thanks looks fun.

May 15, 2018 at 8:07 am

Hi Ben, I saw the modifications you make for Grades K-2. Even with grades K-2 you still use the “LOG”? How does that work with K passing and moving the “LOG”? Is it something they struggle with physically? Just was curious before I teach it to my younger students.

May 16, 2018 at 3:18 pm

K usually doesn’t pass the log (even though it’s there if they thought of it). They usually don’t need to use the log because I always give them one extra spot.

1st and up can pass the log without any issues – although, yes it’s harder for them than it would be for a 4th grade student.

August 9, 2017 at 8:49 pm

Thanks so much! I used it for VBS and the kids loved it! It was so fun to see them work together and think. The 1st graders did better than the 4th graders, too many chiefs in the older group. LOL!

Thanks for sharing!

August 14, 2017 at 4:02 pm

Haha – perfect. I’ve used it for a church camp as well – it’s always a hit 🙂

May 22, 2017 at 9:36 am

What could I use instead of the aerobic steps as the logs?

May 22, 2017 at 4:27 pm

Go to home depot or Lowes and by a few 2x4s and have them cut it into smaller pieces and use those. Or you could get 1 x 6s if you want to have a wider “log” for the kids to make it easier.

Or you could use any other flat object in your equipment room that can be stepped on – or just don’t use logs, use scooters instead as “boats”

May 3, 2017 at 11:18 am

Ben have you ever used Cross the River as a Field Day station? I was thinking Of playing it with my 2nd-3rd grades. My field day stations are 15 min. each. Do you think we could play 2 levels in that time? Just wanted your opinion.

Thanks, Doug

May 8, 2017 at 8:56 am

Yep – we use cross the river for Field Day every year with K-5th, our stations are 7 minutes each, but I think 15 would work as well if you had the different levels.

February 21, 2017 at 2:43 pm

I play this game using floatation devices (pinnies, poly spots) instead of rocks. Students must ALWAYS be touching (with some body part) the floatation device or it will float away and the team will have one less device to get across with. I like how you added levels.

February 22, 2017 at 7:11 pm

Nice! I’ve heard of that variation with the floating objects, but never tried it – sounds fun though. Thanks for sharing!

February 15, 2017 at 4:06 pm

I did this today with third and fourth graders. They really enjoyed it. Presenting it in a “gamified” format really resonated with a lot of them. I had a number of students ask me after class when we could do this again. Ben Landers for the win!

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River Crossing

June 29, 2018

This particular game focuses on cooperation and coordination. It is a great way to enhance group efforts in the pursuit of a common goal. It favors the bonding of individuals and builds an environment where people become more inclined to help one another, as part of a team.

“ Cross the River” Game Objective

The basic aim of the game is quite simple: all participants must safely cross the river and reach the other side together , in order to win.

What is Needed to Play “Cross the River”

The materials that are required for the game are few in number and easy to come across. First of all, you need a rope that acts as a marker for the imaginary river. Second of all, the players need some sort of material such as paper or cardboard, that will be cut into pieces. Those will represent the rocks that will carry each member to the other side of the river.

“ Cross the River” Game Setup

Since this is a game that relies heavily on the imagination of the participants, it is suitable for both the indoors and the outdoors. It is preferred, however, to be played on a leveled ground. On a relaxing day, there can be a single team that will work together towards the goal of the game. But, if a challenge is what you are after, there can be two ( or more ) equally-divided groups that will compete together.

How to Play “Cross the River”

Step 1. .

All players will position themselves on one side of the river. Each team will receive an equal amount of “rocks”.

Each team will analyze the situation at hand ( e.g. the distance of the river ) and will come up with a strategy ( e.g. how the “rocks” will be placed / how the members will make their movements ) in the given amount of time.

Each member of the team will be assigned a “rock” which won’t be interchangeable between players. The “rocks” can be placed in the water and moved only by their owner. One or more members can, however, step on a “rock” when river crossing.

All players are required to walk only on the “rocks” available to them. No part of a person’s clothing or skin may touch the water. If someone falls, the whole team needs to start from the beginning.

How to Win at “Cross the River”

This type of game focuses a lot on communication between players. Reaching the goal takes planning and precise execution and for this purpose, the team must come together for success. It is crucial for all members to be on the same page regarding the strategies taken and to willingly offer their help to their fellow teammates when the situation requires them to.

The Benefits of Playing “Cross the River”

The key aspect that makes this game ideal for team building activities is the fact that it breaks down barriers between individuals. Victory can be achieved only through solidarity and cohesiveness . It makes people share, not only their personal space but also their thoughts and ideas in hopes of reaching their common objective.

Moreover, it creates a space where leadership may take place. The developmental stage of the game, when tactics are being initiated is essential. It presents the players with the opportunity to showcase their skills and ability to quickly come up with solutions. The sense of urgency imposed by the time limit pushes the players to resort to their default behavior in a crisis, which is highly relevant for understanding how performance patterns form in the workplace.

In the end, this team building game offers quite a lot in bringing about harmony and consensus between participants and it is a great tool for observing how people may act in certain situations.

2 thoughts on “River Crossing”

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Cross the River Game

During the game, members are required to safely move across a Cross the River. Everybody who is on the team, is not allowed to touch the water or river and must utilize platforms in order to cross the river safely.

Required Resources :

Either a small piece of wood, tire, milk crate, carpet square or rubber baseball base per person or even a piece of paper
To mark off the activity area, use 2 pieces of rope (or 4 cones)
Blindfolds (optional)

Space Required: Medium. Indoors or outdoors.

Group Size: 8 to 12 ideally, but can be done with 6 to 15 participants. For larger groups split them into teams and get them to race against each other.

Total Time: 25-30 minutes

5 minutes to brief and setup
15-20 minutes to achieve outcome
5 minutes to review and debrief

Running the Cross the River Activity

Create the Cross the River by marking two river banks with the rope. Make the Cross the River wide enough to be a challenge for the group to get from one side to the other (aim for 5 – 8 meters). Distribute the platforms – one per person.

Introduce the resources to the team/s and explain that the objective of the activity is to get all team members safely across the Cross the River.

Give them a total of fifteen to twenty minutes to complete the challenge. If you have a larger group and opt for two teams instead of one, then the team that crosses the river the quickest wins the challenge.

Rules of Crossing the River Game

Players are not allowed to touch the imaginary rive, which is the floor or grass and they must use the platforms (piece of wood etc.) provided. Platforms can include tires or anything else available.
All players must be on the banks (demarcated roped area) before anyone can start to move to safety on the other side.
When crossing the River on the platforms and somebody falls off, the team must then go back and start the challenge over again.
The platforms must remain in contact with each person all the time, otherwise everyone will be swept away. During the game, there is a chosen leader, this leader must ensure everybody is following the rules. If the rule is broken, they are then instructed to remove platforms.
All participants cannot step in-between platforms and are not permitted to jump over the platforms.

Safety Precautions

Keep your eyes open, as players could easily slip or fall off the platforms. This is definitely a safety issue and underlines the difference between team work and individual effort.

Suggested Learning Outcomes

The activity highlights the necessity for team work
Communication plays a major role for the success of the team
Helps to improve leadership qualities
Problem solving skills are required

Guidance and Notes for Facilitators

During the activity, some may find the task a bit too easy, one way to remedy this, is to take away a few of the platforms. Another way to make it more challenging, would be to blindfold participants. This will increase the need for team work and listening skills. To make the challenge even more interesting, introduce a rule whereby all players must always remain in contact with each other. In other words, team members must connect with each other via their hands or feet etc.

Come up with a mission for teams, their mission could be to retrieve an item on the other side and then return it safely back again. Have them carry the item back again and if they drop the it, then the team must begin over with the mission from the start.

Change the idea up a bit, you don’t always have to have a Cross the River. Instead, you can imagine a volcano of sorts, if they or their objects falls into the river, they will be swept away.

Debriefing and Review of Cross the River Game

Here are some questions to ask, this will help the group process their experience of Cross the River:

Was there any planning involved before you began the activity?
What strategy did you come up with?
Was everybody involved with the planning?
Did the plan work and what delayed your steps forward?
Were there problems during the activity?
Was there a definite leader chosen amongst you?
Was there any leadership shown during the activity?
What part did each member of the team play? And did everyone agree with their particular role?
Did players communicate clearly during the activity?
Did you gain anything from participating in the activity?

View other Group Team Building Activities .

Cross the River Group Team Building Activity

Can You Solve This River Crossing Puzzle?

By chris higgins | nov 5, 2016.

River crossing puzzles are a classic form of logic puzzle. In them, you're provided with a scenario—some number of entities trying to cross a river using a raft or boat—and a set of constraints (typically, some of the entities might eat each other under certain circumstances).

In the TED-Ed video below , we tackle a variant of the puzzle in which a group totaling six, three lions and three wildebeest, need to cross a river using a raft. Only two animals can go at once. The problem is, if the lions ever outnumber the wildebeest, they'll eat them. How can they all cross the river?

The larger question of this puzzle is how should we solve such puzzles? In the video, the narrator walks through this solution, but explains how it can be generalized by drawing up decision trees. At each step of the puzzle, you lay out all the possible options, then cross out any that don't work. As you proceed, the set of possibilities dwindle until you're left with only a few viable paths.

Here are the conditions for this puzzle (also listed in the video):

1. The raft needs at least one animal to paddle it across the river, and it can hold at most two animals. 2. If the lions ever outnumber the wildebeest on either side of the river (including the animals in the boat if it's on that side), they'll eat the wildebeest. 3. The animals can't just swim across, and there are no tricks; the animals have to use the boat as described.

Tune in to see how it's done:

For more on this puzzle, check out this TED-Ed page which explains its relationship to the The Missionaries and Cannibals Problem .

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River crossing.

Classic team puzzle that focuses on critical thinking.

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Develops critical thinking
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Step-by-step instructions.

Form small teams of 2 to 5 people.
Challenge each team to solve an imaginary puzzle:
Using a small rowboat, how can they transport a chicken, a fox and a bag of corn to the other side of the river in as few moves as possible.
To govern fair-play, the solution must acknowledge three critical parameters: – The rowboat can only carry one person and one item at any point in time. – The fox and chicken cannot be left alone; and – The chicken and the bag of corn cannot be left alone.
Describe the step-by-step solution to get all three items safely to the other side of the river.
Allow ample time for discussion and trial-and-error.

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Add your Comments...

Have you played this activity? What worked, what didn't work? What type of group? Do you have useful advice for other users? Do you know a fun variation?

Comments (2)

This is interesting and i will use it very soon!

Yes, I agree. A solution does not normally take too long, but the process of how each small group sorts through their solution is the most interesting. Ideal for many teachable moments.

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River Crossings

Combining story telling with preposterous scenarios (and the potential to create your own) makes for a great problem for engaging students.
As students reason through the possible solutions, they develop their communication and logical reasoning skills.
The activity is low-floor in that every student can get started by the simple act of trying something, yet gets progressively more difficult.
Students are naturally pushed towards developing their own notation structures that help them strategize and discover patterns .

Why do YOU like this activity? Try it out and let us know at [email protected]!

Make sense of problems and persevere in solving them. ccss.math.practice.mp1

River crossings is a low-floor problem, in that any student can get started by the simple act of trying something and seeing what happens. And then trying something else. This allows the student to focus on the mathematical process and helps develop the problem-solving skill of looking ahead, which is the ability to anticipate the results of the next few steps. From there, the students can start thinking about the solution as a pathway and think about what might hinder or help their progress. And when they successfully solve one problem, there is always another problem to challenge and engage them.

Construct viable arguments and critique the reasoning of others. ccss.math.practice.mp3

This activity is great for getting students to explain their thinking because it’s framed as a story. This provides starting points for their arguments like “We need to bring the wolf, because…” or “We can’t leave the cabbage, because three moves from now…”, which encourages them to practice their mathematical communication skills.

Model with mathematics. ccss.math.practice.mp4

This idea of working with constraints is an important idea in mathematics and river crossing puzzles make readily apparent the need to develop an organized and readable way of representing them. This notation will vary between students but they should be encouraged to develop some kind of tracking system that makes sense to them. It will also help with logical reasoning as well as students explain their model.

Look for and make use of structure. ccss.math.practice.mp7

Tracking their moves helps here as students may recognize cases or dead ends they have already encountered. This helps them move from trial and error and into sense-making and pattern recognition. It provides the tool to help them reason through more challenging problems.

Problem History

River crossing puzzles are a genre of logic puzzles often attributed to Alcuin of York (735-804) although versions of this puzzle have been found throughout Europe and Africa. In our sequences, we have retained two of the classics – wolf-goat-cabbage and adult-child puzzles – and added two more. Zombies and Humans is our spin on the dated cannibal-missionary puzzles and Monsters is our fun, novel puzzle that adds an arithmetic aspect.

Mathematical Theory

State Transition Graphs

At the heart of every river crossing puzzle is a collection of legal arrangements (or states) and transitions from one state to another. A natural way to represent a puzzle is as a graph , taking these states as vertices and transitions as edges . In the classic wolf-goat-cabbage puzzle, there are 16 possible states, divided into legal and illegal:

We can then examine the 10 legal states and diagram the possible transitions:

The far left vertex is the starting state and the far right is the desired end state, so solving the puzzle now amounts to finding a path from the start to end following the edges. We can see there are two shortest paths (the upper path and the lower path), each requiring 7 crossings.

Vertex Covers

In a generalized version of the wolf-goat-cabbage problem, imagine that you have a large collection of objects where each pair can either be left together unsupervised or not. If there are n objects, then the puzzle can always be solved if there are n spaces in the boat, since the ferry person can keep an eye on all of them with a single trip. However, the puzzle may not be solvable if the boat only has room for a single item. There is a smallest boat that can be used to solve the puzzle, and the number of items this boat can ferry is called the Alcuin number. By the above discussion, the Alcuin number is always between 1 and n , inclusive.

For more details on the history and theory behind River Crossings puzzles, see here !

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River Crossing Riddles

The farmer is the only one who can steer the raft. He can only take one passenger (The tiger, The Sheep, or the carrot) in addition to himself.
If the tiger and the sheep are alone on the same riverbank, the tiger will eat the sheep.
If the sheep and the Carrot are alone on the same bank, the sheep will eat the carrot.
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River Crossing

1 Objectives
2 Group Size
3 Materials
5 Directions
6 Variations
7 Debrief Questions
1’ x 1’ squares of cardboard or foam or rubber baseball bases work well also(half to two-thirds as many squares as people in the group)
You can also substitute 8.5" x 11" pieces of paper
2 pieces of rope (or masking tape or 4 cones)
Several Blindfolds (optional)

Create a river by marking two river banks with the rope. Make the river wide enough to be a challenge for the group to get from one side to the other (look at about 15 – 25 ft.). Distribute the cardboard squares – 1 piece for every 2 people.

The object of the activity is to get all members of the group safely across the river. They must go as one big group, not multiple smaller ones. Also stress that everyone must be on the river before anyone can get off the river, forcing the entire group to be engaged at once. Participants cannot touch the water (floor/grass) and therefore must use rafts (cardboard squares) to cross. The water is filled with piranhas. Therefore if someone loses their balance and touches a hand in the water it gets eaten(put behind the back). Same goes for a foot. If a person completely comes off the raft they are gone and since this is a team exercise everyone must start over. I recommend using this motto with the group, "start as a team end as a team." You can also be creative and add challenges in as the group crosses. For instance you can say a fish jumped up and tail slapped someone in the eyes so now they cannot see(blindfolded). Tell them the river is acidic and when two people share a raft it tipped and now their legs are fused together(tie ankles together). Use these tools to help take away the natural leaders or more outspoken participants and it forces the others to step up and take on more substantial roles. No scooting or sliding on the squares. This can be a safety issue and it emphasizes individual work versus teamwork. Rafts must be in contact with a human at all times or they will be swept away with the current. Once the group has started the process, your role is to take cardboard squares that are “swept away by the current” and to watch for safety issues. Use this to your advantage as well. The participants will invariably slip up and leave some rafts here or there with no one contacting them, those you should steal. When the first group members get to the other side immediately start to encourage them to hurry and get off the river. Nearly every time the first few people will rush off the rafts leaving them unattended for you to steal and stranding some of their team-mates. Work this into your debrief, when working with a team you can't forget about your mates. just because you have made it to the finish line someone else may not have.

Participants must stay in constant contact
Each raft represents a symbol named by participants
River Sections
The tiles can only go forward. They cannot move backwards
No one can finish until everyone has left the “bank” of the river
Choose to add challenges like muting individuals, using only 1 arm, eyes closed/blindfolded, no one can talk, others can be "gators" in the river and try to impede those crossing the river, stand in front of the group with arms outstretched to simulate tree they must go around.
Give group an object that they need to carry with them to safety and discuss what that might represent
Create situations for them to draw from that are connected directly to their group

Debrief Questions

What happened during the process? What worked? What didn’t or what hindered the process?
What leadership was demonstrated during the process? How so? What did you observe?
What were the individual roles people played? Were members comfortable with their roles?
Who knew what the process for crossing was? Who didn’t? How did you communicate the plans to group members?
What might the different aspects of the exercise represent in your group: the squares, the river, the loss of squares, the facilitator, etc?
When the first people rushed off the river and stranded some of you how did that feel?
Communication
Collaboration
Team Strategy

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14 Best Team Building Problem Solving Group Activities For 2024

The best teams see solutions where others see problems. A great company culture is built around a collaborative spirit and the type of unity it takes to find answers to the big business questions.

So how can you get team members working together?

How can you develop a mentality that will help them overcome obstacles they have yet to encounter?

One of the best ways to improve your teams’ problem solving skills is through team building problem solving activities .

“86% of employees and executives cite lack of collaboration or ineffective communication for workplace failures.” — Bit.AI

These activities can simulate true-to-life scenarios they’ll find themselves in, or the scenarios can call on your employees or coworkers to dig deep and get creative in a more general sense.

The truth is, on a day-to-day basis, you have to prepare for the unexpected. It just happens that team building activities help with that, but are so fun that they don’t have to feel like work ( consider how you don’t even feel like you’re working out when you’re playing your favorite sport or doing an exercise you actually enjoy! )

Team Building Problem Solving Group Activities

What are the benefits of group problem-solving activities?

The benefits of group problem-solving activities for team building include:

Better communication
Improved collaboration and teamwork
More flexible thinking
Faster problem-solving
Better proactivity and decision making

Without further ado, check out this list of the 14 best team-building problem-solving group activities for 2024!

Page Contents (Click To Jump)

2. Problem-Solving Templates

Problem-Solving Templates are popular problem-solving activities that involve a group of people working together to solve an issue. The challenge generally involves members of the team utilizing pre-made templates and creating solutions for a given problem with the help of visual aids.

This activity is great for teams that need assistance in getting started on their problem-solving journey.

Why this is a fun problem-solving activity: Problem-Solving Templates offer teams an easy and stress-free way to get the creative juices flowing. The visual aids that come with the templates help team members better understand the issue at hand and easily come up with solutions together.

	🎯 Help your team incorporate mindfulness into the workday
	🪐 Use the force to collect valuable feedback
	🦈 Pitch your million dollar idea
	🌮 Sync with your team on Tuesday!
	🗣 Ignite engaging conversations to kick off your next meeting

This activity is great for teams that need assistance in getting started on their problem-solving journey, as it provides an easy and stress-free way to get the creative juices flowing.

Problem Solving Group Activities & Games For Team Building

3. coworker feud, “it’s all fun and games”.

Coworker Feud is a twist on the classic Family Feud game show! This multiple rapid round game keeps the action flowing and the questions going. You can choose from a variety of customizations, including picking the teams yourself, randomized teams, custom themes, and custom rounds.

Best for: Hybrid teams

Why this is an effective problem solving group activity: Coworker Feud comes with digital game materials, a digital buzzer, an expert host, and a zoom link to get the participants ready for action! Teams compete with each other to correctly answer the survey questions. At the end of the game, the team with the most competitive answers is declared the winner of the Feud.

How to get started:

Sign up for Coworker Feud
Break into teams of 4 to 10 people
Get the competitive juices flowing and let the games begin!

Learn more here: Coworker Feud

4. Crack The Case

“who’s a bad mamma jamma”.

Crack The Case is a classic WhoDoneIt game that forces employees to depend on their collective wit to stop a deadly murderer dead in his tracks! Remote employees and office commuters can join forces to end this crime spree.

Best for: Remote teams

Why this is an effective problem solving group activity: The Virtual Clue Murder Mystery is an online problem solving activity that uses a proprietary videoconferencing platform to offer the chance for employees and coworkers to study case files, analyze clues, and race to find the motive, the method, and the individual behind the murder of Neil Davidson.

Get a custom quote here
Download the app
Let the mystery-solving collaboration begin!

Learn more here: Crack The Case

5. Catch Meme If You Can

“can’t touch this”.

Purposefully created to enhance leadership skills and team bonding , Catch Meme If You Can is a hybrid between a scavenger hunt and an escape room . Teammates join together to search for clues, solve riddles, and get out — just in time!

Best for: Small teams

Why this is an effective problem solving group activity: Catch Meme If You Can is an adventure with a backstory. Each team has to submit their answer to the puzzle in order to continue to the next part of the sequence. May the best team escape!

The teams will be given instructions and the full storyline
Teams will be split into a handful of people each
The moderator will kick off the action!

Learn more here: Catch Meme If You Can

6. Puzzle Games

“just something to puzzle over”.

Puzzle Games is the fresh trivia game to test your employees and blow their minds with puzzles, jokes , and fun facts!

Best for: In-person teams

Why this is an effective problem solving group activity: Eight mini brain teaser and trivia style games include word puzzles, name that nonsense, name that tune, and much more. Plus, the points each team earns will go towards planting trees in the precious ecosystems and forests of Uganda

Get a free consultation for your team
Get a custom designed invitation for your members
Use the game link
Dedicated support will help your team enjoy Puzzle Games to the fullest!

Learn more here: Puzzle Games

7. Virtual Code Break

“for virtual teams”.

Virtual Code Break is a virtual team building activity designed for remote participants around the globe. Using a smart video conferencing solution, virtual teams compete against each other to complete challenges, answer trivia questions, and solve brain-busters!

Why this is an effective problem solving group activity: Virtual Code Break can be played by groups as small as 4 people all the way up to more than 1,000 people at once. However, every team will improve their communication and problem-solving skills as they race against the clock and depend on each other’s strengths to win!

Reach out for a free consultation to align the needs of your team
An event facilitator will be assigned to handle all of the set-up and logistics
They will also provide you with logins and a play-by-play of what to expect
Sign into the Outback video conferencing platform and join your pre-assigned team
Lastly, let the games begin!

Learn more here: Virtual Code Break

8. Stranded

“survivor: office edition”.

Stranded is the perfect scenario-based problem solving group activity. The doors of the office are locked and obviously your team can’t just knock them down or break the windows.

Why this is an effective problem solving group activity: Your team has less than half an hour to choose 10 items around the office that will help them survive. They then rank the items in order of importance. It’s a bit like the classic game of being lost at sea without a lifeboat.

Get everyone together in the office
Lock the doors
Let them start working together to plan their survival

Learn more here: Stranded

9. Letting Go Game

“for conscious healing”.

The Letting Go Game is a game of meditation and mindfulness training for helping teammates thrive under pressure and reduce stress in the process. The tasks of the Letting Go Game boost resiliency, attentiveness, and collaboration.

Why this is an effective problem solving group activity: Expert-guided activities and awareness exercises encourage team members to think altruistically and demonstrate acts of kindness. Between yoga, face painting, and fun photography, your employees or coworkers will have more than enough to keep them laughing and growing together with this mindfulness activity!

Reach out for a free consultation
A guide will then help lead the exercises
Let the funny videos, pictures, and playing begin!

Learn more here: Letting Go Game

10. Wild Goose Chase

“city time”.

Wild Goose Chase is the creative problem solving activity that will take teams all around your city and bring them together as a group! This scavenger hunt works for teams as small as 10 up to groups of over 5000 people.

Best for: Large teams

Why this is an effective group problem solving activity: As employees and group members are coming back to the office, there are going to be times that they’re itching to get outside. Wild Goose Chase is the perfect excuse to satisfy the desire to go out-of-office every now and then. Plus, having things to look at and see around the city will get employees talking in ways they never have before.

Download the Outback app to access the Wild Goose Chase
Take photos and videos from around the city
The most successful team at completing challenges on time is the champ!

Learn more here: Wild Goose Chase

11. Human Knot

“for a knotty good time”.

The Human Knot is one of the best icebreaker team building activities! In fact, there’s a decent chance you played it in grade school. It’s fun, silly, and best of all — free!

Why this is an effective group problem solving activity: Participants start in a circle and connect hands with two other people in the group to form a human knot. The team then has to work together and focus on clear communication to unravel the human knot by maneuvering their way out of this hands-on conundrum. But there’s a catch — they can’t let go of each other’s hands in this team building exercise.

Form a circle
Tell each person to grab a random hand until all hands are holding another
They can’t hold anyone’s hand who is directly next to them
Now they have to get to untangling
If the chain breaks before everyone is untangled, they have to start over again

Learn more here: Human Knot

12. What Would You Do?

“because it’s fun to imagine”.

What Would You Do? Is the hypothetical question game that gets your team talking and brainstorming about what they’d do in a variety of fun, intriguing, and sometimes, whacky scenarios.

Best for: Distributed teams

Why this is an effective group problem solving activity: After employees or coworkers start talking about their What Would You Do? responses, they won’t be able to stop. That’s what makes this such an incredible team building activity . For example, you could ask questions like “If you could live forever, what would you do with your time?” or “If you never had to sleep, what would you do?”

In addition to hypothetical questions, you could also give teammates some optional answers to get them started
After that, let them do the talking — then they’ll be laughing and thinking and dreaming, too!

13. Crossing The River

“quite the conundrum”.

Crossing The River is a river-crossing challenge with one correct answer. Your team gets five essential elements — a chicken, a fox, a rowboat, a woman, and a bag of corn. You see, the woman has a bit of a problem, you tell them. She has to get the fox, the bag of corn, and the chicken to the other side of the river as efficiently as possible.

Why this is an effective group problem solving activity: She has a rowboat, but it can only carry her and one other item at a time. She cannot leave the chicken and the fox alone — for obvious reasons. And she can’t leave the chicken with the corn because it will gobble it right up. So the question for your team is how does the woman get all five elements to the other side of the river safely in this fun activity?

Form teams of 2 to 5 people
Each team has to solve the imaginary riddle
Just make sure that each group understands that the rowboat can only carry one animal and one item at a time; the fox and chicken can’t be alone; and the bag of corn and the chicken cannot be left alone
Give the verbal instructions for getting everything over to the other side

14. End-Hunger Games

“philanthropic fun”.

Does anything bond people quite like acts of kindness and compassion? The End-Hunger Games will get your team to rally around solving the serious problem of hunger.

Best for: Medium-sized teams

Why this is an effective problem solving group activity: Teams join forces to complete challenges based around non-perishable food items in the End-Hunger Games. Groups can range in size from 25 to more than 2000 people, who will all work together to collect food for the local food bank.

Split into teams and compete to earn boxes and cans of non-perishable food
Each team attempts to build the most impressive food item construction
Donate all of the non-perishable foods to a local food bank

Learn more here: End-Hunger Games

Q: What kind of skills do group problem solving activities & games improve?

A: Group problem solving activities and games improve collaboration, leadership, and communication skills.

Q: What are problem solving based team building activities & games?

A: Problem solving based team building activities and games are activities that challenge teams to work together in order to complete them.

Q: What are some fun free problem solving games for groups?

A: Some fun free problem solving games for groups are kinesthetic puzzles like the human knot game, which you can read more about in this article. You can also use all sorts of random items like whiteboards, straws, building blocks, sticky notes, blindfolds, rubber bands, and legos to invent a game that will get the whole team involved.

Q: How do I choose the most effective problem solving exercise for my team?

A: The most effective problem solving exercise for your team is one that will challenge them to be their best selves and expand their creative thinking.

Q: How do I know if my group problem solving activity was successful?

A: In the short-term, you’ll know if your group problem solving activity was successful because your team will bond over it; however, that should also translate to more productivity in the mid to long-term.

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Team Building Workshop Strategy: River Crossing Activity Guide

River crossing activities are a popular team building exercise used in cross selling workshops and retreats.

The purpose of a river crossing activity is to foster collaboration, problem-solving, communication and leadership skills – especially within a cross functional group .

Participants must work together to “cross a river” using limited “resources” provided by the facilitator.

This activity requires groups to strategize, innovate, cooperate, and build relationships within training workshops in order to be successful.

Alternative activities include the trivia questions for team bonding workshops , and the from me to you game .

Instructions for Completing the River Crossing Activity

Here are the steps for running a river crossing activity:

The facilitator divides participants into groups of 4-8 people.
The facilitator outlines a scenario, for example: “Your group must cross a 100-foot wide fast flowing river. You may only use the resources provided.”
The facilitator provides each group with resources such as rope, wood planks, tape, boxes, etc. The resources are limited and will not be enough to simply build a bridge across.
Groups are given 15-20 minutes to strategize and use the resources to cross the “river” (which can be marked with tape on the floor).
The facilitator observes each group’s collaboration process, communication, leadership, creativity and problem-solving.
After attempting the crossing, the facilitator leads a reflection, asking questions about each group’s strategy, challenges, solutions and teamwork.

Costs, Resources and Time Required

Costs are low, under $50 for materials. Rope, wood planks, tape, boxes and other spare items can be used.
Allow 15-20 minutes for the activity and 15-20 minutes for debriefing and discussion.
Have at least 4 participants, ideal group size is 6-8 people. This activity an accommodate up to 40 participants if split into groups. We hear this from customers that regularly download our training course materials .

Best Suited For

Teams, departments, youth groups, students, nonprofits, corporate retreats. Most suitable for ages 12 and up.

Facilitator and Participant Roles

Facilitator outlines the scenario, provides resources, observes the process and leads reflection.
Participants strategize, problem-solve, collaborate, communicate and implement solutions.

Reflection Strategies and Questions

What was your group’s strategy? What approach did you take?
What role did you play? How did you contribute?
What challenges did you face? How did you overcome them?
What did you learn about your team’s strengths and weaknesses?
How can you apply this experience to your real work?

River crossing team building activities foster collaboration, innovation, communication and problem-solving in a group.

This engaging activity provides insights into team dynamics and helps build trust and relationships.

With proper facilitation and debriefing, a river crossing activity can lead to significant “a-ha” moments and learning for participants.

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30 Fun Trivia Questions For Team Bonding Workshops

Training Game: From Me To You

The Essential Principles For Successful Virtual Facilitation

Mindfulness Activities In Team Building Workshops: A Guide

Team building activities: making connections to build stronger teams.

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River Crossing Challenge - Level 3

Can you get all six creatures across the river safely?

A maximum of two creatures are allowed in the boat for each crossing. The munchkins must never be outnumbered by the monsters. The boat will not move if there is no creature in it. Click on the creatures and boat to move them.

Try other river crossing puzzles.

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Leadership Activities: For Groups River Crossing

Description

River Crossing is a competitive fast-paced game that requires teamwork, coordination and speed. This game can help improve team dynamics within a group.

10-16 players; the more the merrier!

Materials Required

About 10-16 pieces of cardboard, each about the size of your palm

Time Required

Instructions

This game should be played in a large indoor open space.
Using the tape, two parallel lines are created about 10-15 metres apart. The space in between these two lines represents the river.
This river is infested with man-eating piranhas so no player is can ‘touch’ the river.
The players are split into 2 equal teams: Team A and Team B. Both teams start together on one side of the river.
The teams are given out equal pieces of cardboard (about 6-7 each).
When the round starts, each team must use these cardboard pieces to get across the river. The cardboard pieces can be placed on the river as stepping stones and can be moved around.
The team must therefore share the cardboard pieces and attempt to get the whole team across to the other side of the river.
If anyone makes contact with the river (the floor space between the two tape), then he/she is considered eaten up and has to go back to the starting point.
The team that gets its team members across in the fastest time wins.

Debriefing Notes

How did your team plan to cross the river in the shortest time possible.
Who took leadership in this fast-paced, high-stress situation? How did he/she do?

Icons made by Freepik from www.flaticon.com is licensed under CC BY 3.0

List of Leadership Icebreakers

Make a Shape This game Make a Shape is a game about communication between individuals using different kinds of communication modes all the way from speech to gestures.

Hosts and Guests Hosts and Guests is a game about taking the initiative. It tests individuals in their ability to take lead in any relationship in a casual or business setting.

Alphabetic Introductions Alphabetic Introductions is a simple game you can play for strangers in a room to get acquainted with one another.

Balloon Fight Balloon Fight is a physical leadership icebreaker game that can be used to break the ice for a group of strangers or used for observing group dynamics of a team in a competitive setting.

Blow Wind, Blow! “Blow Wind, Blow!” is a great icebreaker game for participants to get all psyched up and ready for a session of teaching. It helps build the atmosphere of a session and fosters bonding through fun.

Master Architects Master Architects demonstrate the importance of planning, teamwork, problem solving and it is a great exercise to observe any team’s group dynamics.

Newspaper Hop Newspaper Hop is a game of teamwork to explain the importance of planning, collaboration and communication in the workplace.

Truth or Lie Truth or lie is another simple icebreaker that you can play for the participants to get to know each other better with ‘wow’ facts about themselves.

Who am I? Who Am I is a simple icebreaker that you can play to get the participants to do quick self-introductions with each other. It’s used in groups where participants are generally strangers.

Word Scramble Word scramble’s purpose is to demonstrate the importance of cooperation in the team, and is useful for you to observe you team’s group dynamics as they work together in to solve a problem.

Whacko! Whacko! is a classic team building game that helps new strangers to get to know each other’s names and also to have a lot of fun at the same time.

Charades Charades is a classic game for participants of all ages, whether you’re 5 or 50, it’s a fun filled game that can engage the players fully and bring them closer together through lots of acting and drama fun!

Money Machine Money Machine is a interactive group game that requires a lot of moving around with lots of shouts and laughter that will help your team bond or help your participants ice break!

Cat and Mouse Cat and Mouse is a fast-paced, exciting team bonding game that will bring your participants closer together through lots of laughter, screams and protests as the ‘Cat’ chases the ‘Mouse’!

River Crossing River Crossing is a competitive fast-paced game of cooperation that requires teamwork, coordination and speed. It is a great leadership icebreaker that will help to cultivate the team dynamics within a group.

Pull the Tail! Pull the Tail is a free for all frenzy that brings down a lot of chaos, fun and laughter in the crowd! It’s a great physical team bonding exercise that will bring your participants closer together.

Indian Poker Indian Poker is a team building game for new friends to know each other or just for old friends to have a good time together. It is a simple, easy-to-understand game for everyone to have a good time together.

MORE LEADERSHIP ICEBREAKERS

Human Bingo People Bingo is a game that can fosters communication and great for getting a group of new friends to know each other deeper after going through the game.

Name Grid Name Grid is a game where it fosters communication between the groups in a quick reaction and fast thinking game. This game will take only a short time but will bring out excitement and passion as the participants compete in a fast paced word game.

Line Up Line Up is an icebreaking game where everyone has to communicate without speaking and line up in a straight line according to a pre-determined characteristic. It is game that will illustrate the power of communication and at the same time, have a group of new friends have a lot of fun together.

Pass the Objects Pass the Objects is an icebreaking game where objects have to be passed down a line of people holding spoons with their mouth! It is a game of communication, teamwork and strategy that will be sure to bring out lots of energy and laughter from the participants.

Entangle Entangle is an icebreaker where participants’ hands are all entangled up in the center and they have to communicate in an attempt to disentangle themselves.

Toilet Paper Game Toilet Paper Game is an icebreaking game where participants have to introduce themselves in an innovative way: the more toilet paper they choose to tear off, the more they have to share about themselves.

Words from Strings Word from Strings is a game that fosters communication, coordination and teamwork within the group to complete the task. Participants have to cooperate by controlling a marker with their strings to write a full word.

Blindfold Maze Blindfold Maze is a team icebreaker where all participants will be blindfolded and they have to get through an obstacle course with only instructions from one leader. It is a game of communication and trust that will also ensure your participants have a great time together.

Human Scissors Paper Stone Human Scissors Paper Stone is a fun-filled action packed game where two groups will have to strategize, communicate, and act in order to outsmart their opponents. There is quite a bit of physical activity like making funny actions, chasing your opponents and getting chased by them.

Ping Pong Knockout Ping Pong Knockout is a fun icebreaker that will guarantee lots of laughter as a few unlucky participants will have to attempt to knock down cups by swinging their bodies.

Human Checkers Human Checkers is an icebreaker game that requires good communication and strategy to win. In this game, participants have to play checkers, but with themselves as the chess pieces.

Shrinking Island Shrinking Island is an icebreaker game that literally fosters togetherness and teamwork in order to achieve the goal of standing on a ‘shrinking’ island. Participants have to attempt to keep afloat on a piece of newspaper as it becomes smaller and smaller.

Ha-ha-ha Game Ha-ha-ha Game is a game that will be a great ice-breaking game and one requires a lot of focus, concentration and coordination in order to succeed. Participants will literally laugh at themselves through this fun filled physical activity.

Animal Farm Animal Farm is an icebreaker game that is guaranteed to bring out lots of laughter and fun as participants have to mimic animal sounds in order to find one another. It is a simple and fun game that can help participants warm up to one another as they let loose.

Jones Jones is an icebreaker game that gets people blindfolded and then have them communicate with one another with this unique word “Jones”.

Body Water Relay Body Water Relay is an intense, competitive icebreaker game that requires participants to get physical by using their body parts to transport water with a sponge. Participants might a little wet from the activities but you can be sure you will have an energetic and breathless bunch of participants after the activity!

Hula Hoop Chain Team Building Ice Breakers: Hula Hoop Chain is an icebreaker game where participants have to attempt to weave a Hoola hoop through a series of connected bodies in the shortest time possible.

Human Value Human Value is an icebreaker game where all participants get a value attached to them, and they have to combine with other participants to form a certain dollar value. It’s a fun and exciting game with lots of running around, smiles and laughter.

Captain on Deck Captain on Deck is an icebreaker game for a big group. It’s a game that requires each participant to form groups according to the captain’s commands and it is bound to create much joy, laughter, and bring the participants closer together.

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Humans, Zombies, & Other Problems crossing the river

By spencer bowen.

This activity takes a couple of classic logic puzzles and adapts them to better suit K-12 audiences. It was designed in the Desmos Activity Builder , so it can be played online and easily given to a classroom of students. The activity as presented was developed at the San Francisco Math Circle , and was recently featured on MathCommunities.org’s Math Monday Live program.

A town has recently been plagued by an epidemic of zombies! Luckily, the virus has just started to spread and the infected are able to stave off their hunger for human brains… for now. In fact, they’re willing to work alongside the remaining humans to help them get across a river to safety.

But it’s not so easy. Rules will be needed to keep the humans safe.

The boat can only carry two people (humans or zombies) across at a time.
At least one human or zombie has to be in the boat for it to sail.
Keep all hands and legs in the boat. The river is too dangerous to swim.
If the zombies on one side of the river ever outnumber the humans, even for a moment, they will give into their hunger and attack the delicious humans.

Is it possible to get all the humans safely across the river? If the humans can solve this problem, they will be rewarded with fantastic news — the town on the other side of the river is able to cure the virus! This leads to a new question: Is it possible to get all the humans and zombies safely across the river?

Watch students attempting to solve the problem during Math Monday Live.

exploring further:

Three humans and two zombies may be a good place to get started with the problem, but the problem can be explored with many different starting set-ups. Additionally, once students find a solution to the problem, challenge them them to keep track of how many trips it took them and find the fewest number of trips needed to cross the river. (When dealing with zombies, time is of the essence!) Older students can then record this minimum as a function of the number of humans and the number of zombies.

And this isn’t even the only type of problem you can run into when crossing rivers! Readers and students may be familiar with the wolf, goat, and cabbage problem:

Once upon a time a farmer went to a market and purchased a wolf, a goat, and a cabbage. On his way home, the farmer came to the bank of a river and rented a boat. But crossing the river by boat, the farmer could carry only himself and a single one of his purchases: the wolf, the goat, or the cabbage. If left unattended together, the wolf would eat the goat, or the goat would eat the cabbage. The farmer's challenge was to carry himself and his purchases to the far bank of the river, leaving each purchase intact. How did he do it? Wikipedia

Some Notes on Narratives in problem posing

There is a rich history of interesting math and logic problems students today can puzzle over and learn from, and they often come with striking narratives. However, it is important to consider any cultural connotations associated with how the narratives are presented. For example, s ome readers may have seen this activity previously as the “missionaries and cannibals” problem, or may be familiar with the the similar “jealous husbands” problem. We chose to reframe the problem as “humans and zombies” to make the narrative more relatable and, more importantly, to remove the unfortunate colonialist and sexist references that are irrelevant to the actual problem.

In addition, when presenting problems to students, take the opportunity to consider what rules of the problem can be naturally explained through narrative. As an example, when I first presented this activity to second grade students, they immediately asked why the humans couldn’t simply swim across. As opposed to telling them “because those are the rules” and shutting down their question posing, I worked within the story we were telling to find a justification: The river was too dangerous.

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Solving River-Crossing Puzzles with R

02 Nov 2016 • 28 min. read • Comments

River-Crossing Puzzles are a popular class of puzzles in the field of AI. Many flavours of these puzzles exist. Here we use R to provide a somewhat generic framework to model and solve these type of puzzles.

River-Crossing puzzles

River-crossing puzzles are a type of puzzle where the objective is to move a set of pieces (objects, animals or people) across a river, from one bank of the river to the opposite bank, using a boat or a bridge. What makes these puzzles interesting are the set of rules and conditions that apply. Typically the boat is only able to carry a limited number of pieces at any one go. And normally there are rules and constraints that forbid having certain combination of pieces on the bank river and/or the boat.

Let’s look at an example.

The Farmer-Wolf-Goat-Cabbage riddle

Once upon a time, there was a Farmer who had a tiny boat. The boat was so tiny that it could only take the Farmer himself and one additional passenger. He wanted to move a Wolf, a Goat and a Cabbage across a river with his tiny boat.

When the Farmer is around, everyone is safe, the Wolf will not eat the Goat, the Goat will not eat the Cabbage.

But he can’t leave the Wolf alone with the Goat because the Wolf will eat the Goat. He can’t leave the Goat alone with the Cabbage because the Goat will eat the Cabbage.

And of course he can only fit one more object with him on the boat (either the Wolf, the Goat or the Cabbage).

The question is: How can he safely transport the three of them to the other side of the river?

The Solution

Solving river-crossing riddles entails starting with all pieces on one side of the river (typically the left bank). This is the start state . Then one considers all possible valid moves that can be done given the start state. These possible moves create a set of new states. The process repeats itself with the new states until we eventually arrive at the goal state , i.e., having all the pieces safe and sound on the other side of the river.

In the table below I have listed a set of moves for the Farmer-Wolf-Goat-Cabbage riddle. We are using the symbols F, W, G, and C to stand for the Farmer, Wolf, Goat, and Cabbage respectively.

move	left river bank	right river bank
Start state	F W G C	_ _ _ _
Farmer takes the Goat to the right river bank	_ W _ C	F _ G _
Farmer returns alone with the boat back	F W _ C	_ _ G _
Farmer takes the Wolf to the right river bank	_ _ _ C	F W G _
Farmer returns back with the Goat	F _ G C	_ W _ _
Farmer takes the Cabbage across the river	_ _ G _	F W _ C
Farmer returns back alone	F _ G _	_ W _ C
Farmer takes the goat across. Exit state reached!	_ _ _ _	F W G C

As can be seen from the above table, this puzzle can be solved in 7 steps.

But is this the only solution there is?

To answer the above question we must build a graph of all possible valid moves. Thus we represent (model) the problem in terms of graph theory .

Then we can apply a graph search algorithm to find all possible paths from the start node to the goal node, the shortest path (smallest number of moves needed), etc. See the following video in order to apreciate the usefulness of this graph theoretic approach.

And talking of graphs, the R language has some great packages for solving graph related problems and performing graph analytics. One such package that I have used a lot is igraph . And I will be using this package in this blog to provide a solution to the river-crossing problems.

Generalising the solution

But before we start working on the solution, it is worthwhile remembering that River-Crossing puzzles come in many flavours and varieties.

This website lists many of these. For example, there is the Farmer-Fox-Chicken-Spider-Caterpillar-Lettuce puzzle where the farmer has to transfer 5 objects, but luckily for the farmer the boat is a bit larger (can carry 3 pieces). There are variants where a particular piece is repeated. For example, in the Farmer-2 Wolves-Dog-Goat-Bag of Grain puzzle we have 2 Wolves and they can eat both the Dog and the Goat.

Then there is the Japanese Family River-Crossing puzzle with its extremely complex rules. Also worth noting is the popular Missionaries-and-Cannibals problem , found in many AI text books.

Actually river-crossing puzzles are in themselves just a subset of the class of wider puzzles called the Transport Puzzles . But this is beyond the scope here - we will just concentrate solely on river-crossing puzzles.

R (igraph) solution

Keeping the above in mind, I opted to try and write as generic a solution as much as possible. After all, the ‘game’ mechanics are nearly the same for all puzzles. It’s only the rules and conditions that change. We will codify the rules separately from the rest of the code.

Defining the Conflict Graph

The rules and conditions that define the incompatibilites (conflicts) between the pieces can themselves be represented using a graph structure. For example in the Farmer-Wolf-Goat-Cabbage, the following graph encodes the rules:

Wolf eats (conflicts with) Goat
Goat eats Lettuce

The following R code builds this conflict graph gr . Note that in order to simplify the puzzle solving code, we add all the pieces, even if they do not conflict with any other piece (F for the Farmer in this case.)

Also note that the conflict graph is a directed graph . Wolf eats Goat, but Goat does not eat Wolf - thus we define this as a directed edge (or directed arc in graph theory-speak).

Configuring the State Space graph

We now move on to the creation of the state space. This is the graph that will contain all valid states (states where no piece ends up as food and all rules of the game are observed).

We start with some configuration for this particular puzzle, and then create the empty graph gss that will store the state space. Note that we created gss as a directed graph - actually using an undirected graph is also valid for a state space graph.

We have to define which of the pieces is the Farmer. Reason is that the code that generates the state space needs to know who will be rowing (handling) the boat. Only the Farmer can operate the boat.

We now create the graph node representing the start state as shown below and add it to the state space graph gss :

We adopt the following node structure for representing a state: each node consists of a list with 3 elements, bank.l , bank.r , and boat.pos . bank.l is a vector containing the pieces that are on the left-hand side of the river, bank.r is contains those pieces that are on the right-hand side, and boat.pos indicates where the boat is (1 for left-hand side, 2 for right-hand side). In the case of the starting state, all pieces are on the left bank ( bank.l ) and the right bank is empty ( bank.r is an empty vector).

We must make a call to the function make.state.name for each state we create. This function constructs a string that serves as a label to uniquely identify that state. For the start state, the string label is: CFGWb| . The pipe symbol ( | ) represents the river and the symbols are placed on the left-hand side or the right-hand side of the pipe symbol according to where they are located. The lower-case character b indicates where the boat is. To ensure consistent labelling of nodes, the symbols for the pieces are sorted in alphabetical order.

Creating the State Space graph

Once we have the initial state defined, generating the full state space can be done via a simple call:

Function solve is defined in an R source file called solve_river_crossing_puzzles.R that can be downloaded from here . I won’t go over the code contained in this source file - I think that one can use it as it is without changes for the majority of river-crossing puzzles. Also, there are inline comments for those brave enough to venture in.

After generating the state space graph, we make a call to igraph ’s simplify() function. This removes any duplicate links that might be created by the state space generation code. We also change the colour of the exit node and display the graph.

And here is the state space graph for the Farmer-Wolf-Goat-Cabbage puzzle:

The Farmer-Wolf-Goat-Cabbage state space

Note that a cursory glance at the above graph shows that there are 2 different solutions for this puzzle, both of length 7. But let’s use igraph ’s pathfinding functions in order to get these programmatically.

Finding solution paths

igraph has a function get.all.shortest.paths() that, given some node A and another node B, it finds all the shortest paths that connect node A to B. In our case, we apply it to the start node and the goal node as shown below:

The output gives the required two paths:

If you find it a hassle to type in the labels of the start node and the goal node, you can use the following code instead. Although longer, this works for all puzzles, regardless of the symbols used and number of symbols.

As one can notice, the hardest part in R is creating the state space. Finding the solutions leverages the power of the igraph package. Let’s apply our code to some other more complex river-crossing puzzles.

The Farmer-Fox-Chicken-Spider-Caterpillar-Lettuce puzzle

This puzzle is similar to the previous one except that we now have 6 pieces and the boat can carry 3 pieces (the Farmer and any two other pieces).

The conflict graph for this puzzle is given below. Note that we are using the following symbols: M = farmer, F = fox, C = chicken, S = spider, K = caterpillar, and L = lettuce.

The Farmer-Fox-Chicken-Spider-Caterpillar-Lettuce conflict graph

We then create the state space graph as follows:

The Farmer-Fox-Chicken-Spider-Caterpillar-Lettuce state space graph

Note how complex (connected) the state space graph is! If we find all shortest paths, we get a total of 40 possible solutions, all of length 7. Only the first few are reproduced below:

The Farmer-Fox-Chicken-Spider-Caterpillar-Lettuce solutions

The 2 Wolves-Dog-Goat-and-Bag of Grain puzzle

This puzzle has a slightly more complex conflict graph as shown below. The symbols used are: F for Farmer, W for Wolf, D for Dog, G for Goat, and B for the Bag of Beans (Note that lower-case b represents the boat).

The 2 Wolves-Dog-Goat-and-Bag of Grain conflict graph

This puzzle has a total of 4 possible solutions, again all of length 7.

The 2 Wolves-Dog-Goat-and-Bag of Grain solutions

The Missionaries and Cannibals puzzle

Now we come to a famous river-crossing puzzle that has different style of rules than the ones we have seen so far. Because of this we need to override some of the logic contained in the source file solve_river_crossing_puzzles.R .

This puzzle is made up of 3 cannibals and 3 missionaries. A boat can carry at most 2 persons (anyone can operate the boat). If the number of cannibals on either side of the river outnumber the missionaries, then they will make a meal of the missionaries.

For this puzzle we need to consider counts of objects rather than conflicts between object types. Thus we will override the function is.bank.valid() that is called to check whether the pieces on a bank’s river are according to the rules or not. We do the following:

table() computes a histogram of the number of cannibals and missionaries on this side of the river. We have to handle NA ’s for the cases where there are no missionaries or cannibals on this particular river bank.

We also override the state transition checking in order to relax its strictness - anyone can operate the boat; the only rule is that the boat can not be empty.

The code for creating the state space is similar to that of the previous puzzles:

The resulting state space graph is below:

The Missionaries and Cannibals state space graph

Note that here we have 4 possible paths, all of length 11. Compare the above state space graph with the one shown on this page .

The Japanese Family River-Crossing puzzle

The final puzzle we will look at is the Japanese Family River-Crossing puzzle , which has some complex conflict rules. We have the Mom (M), Dad (D), 2 Daughters (D), 2 Sons (S), a Policeman (P), and a Thief (T). The rules of this puzzle are:

The raft can carry no more than 2 people
Only the Adults (Mom, Dad, Policeman) can operate the raft
Dad can not be in the presence of the 2 Daughters without their Mom
Mom can not be in the presence of the 2 Sons without their Dad
The Thief can not be alone with any of the family without the Policeman

It’s difficult to represent the above conflicts with a single graph (at least I could not think of a way). Instead we will override the state generation logic as we did for the Missionaries and Cannibals problem. We end up with the following:

We also need to override the state transition checks, since multiple persons can operate the boat:

The state space generation code is similar to that used in solving previous problems:

And the state space graph is shown below:

In this puzzle we have 2 possible shortest paths, both of lenth 17. Note also the number of side branches that terminate with a dead-end. A graph searching algorithm will have to use backtracking a number of times here.

Code repository

The code snippets used on this page can be found on github . There is also an R notebook that shows code usage, very similar to what has been done here.

Concluding Thoughts

I think that the given code provides a somewhat generalised solution to the river-crossing type of puzzles. It can be improved much further and also can benefit from improved packaging - something on my To-do list.

If you use the code, please acknowledgeb the source. Any improvements to the code are most welcome.

And for those that think that these puzzles are not really useful, there is a good book by Dr. Dave Moursund, titled Introduction to Using Games in Education: A Guide for Teachers and Parents . Also came across the following PhD on Games, Puzzles, and Computation , which shows the deep link between puzzles and mathematics and computing.

But perhaps the most important aspect is that they are fun to solve!

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River Crossing Challenges
Choose a river crossing puzzle above. Each puzzle requires you to get all of the characters across a river in a small boat. The boat can cross the river many times to get everyone across. Can you solve the puzzle in the smallest number of moves? You can earn a Transum trophy for each puzzle you complete.
PE Games: Cross The River
The classroom teachers enjoy watching the kids use teamwork and attempt to be the first group to "cross the river". If you want specifics and a more detailed list of ideas, strategies and variations - you can download my lesson plan for free below: Free - Cross the River Lesson Plan. It's so fun watching kids complete a challenge for ...
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The Benefits of Playing "Cross the River". The key aspect that makes this game ideal for team building activities is the fact that it breaks down barriers between individuals. Victory can be achieved only through solidarity and cohesiveness. It makes people share, not only their personal space but also their thoughts and ideas in hopes of ...
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Cross the River Game During the game, members are required to safely move across a Cross the River. Everybody who is on the team, is not allowed to touch the water or river and must utilize platforms in order to cross the river safely.Required Resources:Either a small piece of wood, tire, milk crate, carpet square or rubber baseball base per person or even a piece of paperTo mark off the ...
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Can you get all four across the river safely? Only the man and at most one other item are allowed in the boat for each crossing. Only the man is able to operate the boat. Do not leave the goat alone with the carrots or the wolf unsupervised with the goat.
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Here are the conditions for this puzzle (also listed in the video): 1. The raft needs at least one animal to paddle it across the river, and it can hold at most two animals. 2. If the lions ever ...
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Try your best, work as quickly as you can, and keep your number of moves low to earn more stars. Your total number of stars will help you access more advanced levels. If you like playing chess and solving logic puzzles, then you are all set for new challenges. But unlike chess, you can play this game alone and have a lot of fun.
River Crossing Team Puzzle
Step-by-Step Instructions. Form small teams of 2 to 5 people. Challenge each team to solve an imaginary puzzle: Using a small rowboat, how can they transport a chicken, a fox and a bag of corn to the other side of the river in as few moves as possible. To govern fair-play, the solution must acknowledge three critical parameters:
River Crossings
River crossings is a low-floor problem, in that any student can get started by the simple act of trying something and seeing what happens. And then trying something else. This allows the student to focus on the mathematical process and helps develop the problem-solving skill of looking ahead, which is the ability to anticipate the results of ...
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River Crossing is an easy to learn, minimal equipment phys ed game that can be played with upper elementary aged students to adults. With plenty of modificat...
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River Crossing Riddles are online problem logic challenges to solve. Use arrow up/down to read the instructions of each challenge. INSTRUCTIONS: A farmer wants to cross river and take with him a tiger, a sheep and a carrot. Rules: The farmer is the only one who can steer the raft. He can only take one.
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Create a river by marking two river banks with the rope. Make the river wide enough to be a challenge for the group to get from one side to the other (look at about 15 - 25 ft.). Distribute the cardboard squares - 1 piece for every 2 people. Directions. The object of the activity is to get all members of the group safely across the river.
14 Brain-Boosting Problem Solving Group Activities For Teams
Crossing The River is a river-crossing challenge with one correct answer. Your team gets five essential elements — a chicken, a fox, a rowboat, a woman, and a bag of corn. You see, the woman has a bit of a problem, you tell them. ... Some fun free problem solving games for groups are kinesthetic puzzles like the human knot game, which you can ...
Cross the River Game
Cross the River is an all-time favourite with children, and they are sure to be excited to play this game in your class. You can use Cross the River for a lesson plan for your PE classes. This game is a brilliant challenge for team building in the classroom as well. Children are required to work in teams to make decisions and develop a strategy ...
River Crossing Challenge
Level 1 Level 3 Level 4. The solutions to this and other Transum puzzles, exercises and activities are available here when you are signed in to your Transum subscription account. If you do not yet have an account and you are a teacher, tutor or parent you can apply for one by completing the form on the Sign Up page. A Transum subscription also ...
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River crossing activities are a popular team building exercise used in cross selling workshops and retreats. The purpose of a river crossing activity is to foster collaboration, problem-solving, communication and leadership skills - especially within a cross functional group. Participants must work together to "cross a river" using ...
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Can you get all six creatures across the river safely? A maximum of two creatures are allowed in the boat for each crossing. The munchkins must never be outnumbered by the monsters. The boat will not move if there is no creature in it.
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Cat and Mouse. Cat and Mouse is a fast-paced, exciting team bonding game that will bring your participants closer together through lots of laughter, screams and protests as the 'Cat' chases the 'Mouse'! River Crossing. River Crossing is a competitive fast-paced game of cooperation that requires teamwork, coordination and speed.
Crossing The River With Dogs
Crossing The River With Dogs. 'Crossing the River With Dogs' is a logic-based river-crossing puzzle based on the textbook of the same title. The idea of any river-crossing problem is simple: get all of the people or items from Side A to Side B. The problem-solving aspect comes into play when there is limited room on the 'boat', and the actors ...
River Crossing Lateral Thinking Puzzle
Solve The River Crossing Puzzle and Improve Lateral Thinking. Give children the tools to improve lateral thinking by getting them to solve this river crossing puzzle. This activity gives your child a scenario and some cut-outs of characters and items in the scenario. They will need to read the clues carefully and work out how to solve the problem.
River Crossing
The river crossing game is one of many simple games that gives your group the chance to sharpen their problem-solving skills while having a bit of fun. Participants need to cross an imaginary river as a team and they need to get all members of the group safely there.
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Rules will be needed to keep the humans safe. The boat can only carry two people (humans or zombies) across at a time. At least one human or zombie has to be in the boat for it to sail. Keep all hands and legs in the boat. The river is too dangerous to swim. If the zombies on one side of the river ever outnumber the humans, even for a moment ...
Solving River-Crossing Puzzles with R
River-crossing puzzles are a type of puzzle where the objective is to move a set of pieces (objects, animals or people) across a river, from one bank of the river to the opposite bank, using a boat or a bridge. What makes these puzzles interesting are the set of rules and conditions that apply. Typically the boat is only able to carry a limited ...
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PE Games: Cross The River

Cross The River

Level 1: Get to the “Island”

Level 2: Cross the River

Level 3: You Lost a Rock

Level 4: Cross the River Again

Level 5: Double Up

Got some cool variations of the game not included in the lesson plan? Leave them in the comments below.

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