logical problem solving games

Logic Games

Laser overload new, flip-flop new, pik cells new, frog corral new, bounce ball new, building sort new, new logic games.

Laser Overload

Frog Corral

Bounce Ball

Building Sort

Circle Puzzle

Popular logic games.

Escape from Castle Claymount

Poly Roller

Fat Slice 2

Tube Master

Cut & Dunk

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Logic games are the games that you really have to put your thinking cap on for. They involve taking in knowledge and using it to make informed decisions on what to do next. A great example is Sudoku, where players are forced to use the process of elimination to determine what number to put in each box. While logic games may look boring on the surface, once players start to understand them they often realize just how much fun they are. 

One of the best parts of our Logic Games Playlist is the variety that is offered here. There are platforming games, drawing, building, physics, the list goes on. Logic games have such a wide variety, so we recommend exploring them to your heart’s content.  

Logic Puzzles

Try these logic puzzles:

Logic Games

Logic Games constitute a captivating and intellectually stimulating category of online games that test players' problem-solving, analytical, and strategic thinking abilities. These games challenge the mind and offer a welcome break from the more action-packed genres, appealing to players who enjoy mental gymnastics and puzzle-solving. The defining feature of logic games is their focus on logical reasoning and deduction. They often present players with intricate puzzles, riddles, and conundrums that require a methodical approach to unravel. Whether it's navigating mazes, solving mathematical problems, or arranging objects in a specific order, these games push players to think critically and logically.

One of the primary appeals of logic games is their diversity. Within this category, players can encounter a wide range of subgenres, each with its unique challenges. Sudoku enthusiasts can immerse themselves in number puzzles, while fans of word games can tackle crossword puzzles or anagrams. For those who prefer spatial challenges, there are games that involve fitting shapes into predefined spaces or connecting dots to form coherent images. Logic games often employ minimalist aesthetics, focusing on clarity and simplicity in design. This visual style allows players to concentrate solely on the task at hand, free from distracting embellishments.

Many logic games have single-player modes that enable players to enjoy a solitary cerebral experience, but they also frequently include multiplayer options that foster healthy competition and social interaction. Solving puzzles collaboratively or competing against friends adds an extra layer of enjoyment to these games. Some logic games incorporate storytelling elements, immersing players in narrative-driven challenges where their decisions impact the plot's progression. These narrative puzzles encourage players to use their logic and critical thinking skills to shape the story's outcome.

Logic games are not only entertaining but also offer cognitive benefits. They enhance problem-solving skills, boost memory, and promote logical reasoning, making them a valuable addition to both leisure and educational gaming. Logic games on Silvergames.com provide a welcome mental workout in the world of online gaming. They cater to a broad audience, from puzzle aficionados to those seeking a cerebral challenge. With their focus on logical thinking and problem-solving, these games are an excellent choice for players looking to engage their minds while having fun.

Most Played Games

What are the TOP 5 Logic Games?

• Chess Online
• Crack the Code
• Chess Against Computer
• Tic Tac Toe 2 Player
• Draw to Smash!

What are the best Logic Games on tablets and mobile phones?

What are the newest logic games on silvergames.

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• Rope Puzzle
• Connect the Dots with One Line
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Logic Games

What are the best free Logic Games online?

• Logic Master 1
• Car Parking Jam
• Little Alchemy 2
• Water Color Sort
• Brain Test: Tricky Puzzles
• Brain For Monster Truck
• Word Chains
• It's Story Time!

What are the most popular Logic Games for the mobile phone or tablet?

Welcome To Daydream Puzzles!

We’re here to share our passion for logic puzzles!

Our collection of logic grid puzzles for adults and teens are free to play online using our interactive grids. There is no need to create an account – just start playing. Your answers will be checked automatically when you have completed the grid.

You can browse all of our puzzles here: Logic Grid Puzzles .

If you would like to learn more about solving logic problems, check out our guide Solving Logic Puzzles For Beginners . For the initiated, improve your skills with our tips in Advanced Logic Puzzle Techniques !

We have a free Logic Puzzle Grid Printables section for downloading blank grids you can print and use to work on grids with a pen or pencil. You could also use them to create your own puzzle for fun or to distribute to a class.

Logic puzzles are a great challenge (and often relaxation method) for those who enjoy deductive reasoning puzzles, practicing logical or analytical thinking, or are simply drawn to the type of puzzle that has a single solution with no guesswork!

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Problem Solving Games, Activities & Exercises for Adults

By: Angela Robinson | Updated: February 13, 2024

Here is our list of the best problem solving games, activities and exercises for adults.

Problem solving games are activities that require players to use critical thinking skills to solve puzzles. Example activities include escape rooms, Sudoku, and murder mysteries. The purpose of these exercises is to sharpen reasoning and decision-making skills in group settings and to do team building with employees.

These activities are a subset of remote team games , found in problem solving books , and are similar to team puzzles , team building brain teasers and team riddles .

This article contains:

• team building problem solving activities for employees
• free problem solving games for adults
• virtual problem solving activities for students
• group problem solving activities
• problem solving team builders

Here we go!

List of problem solving games & activities

From word and number puzzles to role-playing games, here is a list of inexpensive and free problem solving team builders that help groups practice the art of critical thinking and compromise.

1. Espionage! (Team Favorite)

For an exciting game of social deduction, check out Espionage! This thrilling experience will put your team’s wits and instincts to the test.

Espionage! offers the following:

• a 90-minute session led by an experienced host
• undercover teams of agents and spies
• challenging puzzles, tasks, and maneuvers
• team conversations to help uncover secret identities

The best part is we will bring all the necessary game materials to your preferred location. If you are interested in boosting communication and critical-thinking skills within your team, then consider Espionage!

Learn more about Espionage!

2. Art Heist: The Vanishing of Van Gogh (Hosted)

You can turn your team into skilled detectives with Art Heist: The Vanishing of Van Gogh! In this captivating mystery, participants will locate the stolen artwork, The Bedroom .

Key features of this experience include:

• a 90-minute adventure led by a world-class host
• detailed puzzles, clues, and mysteries to unravel
• trails of evidence and hidden secrets
• group discussions to find the art

Additionally, you can include a cocktail kit to spice up your event. Through Art Heist, you will enhance your team’s ingenuity and problem-solving skills!

Learn more about Art Heist: The Vanishing of Van Gogh .

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3. War of the Wizards (Popular)

With War of the Wizards, teams roleplay as minions of powerful wizards to vanquish forces of evil. Participants will play thrilling games and go on a quest to restore harmony to the realm!

War of the Wizards offers the following:

• a 90-minute journey guided by a distinguished host
• immersive storytelling that transports players into a magical realm
• engaging activities like world-building, role-playing games, and storytelling
• opportunities for forming alliances, facing challenges, and going on quests

Through the power of imagination and teamwork, your team can overcome tasks and participate in an epic fantasy battle. To improve communication and bonds, include War of the Wizards in your agenda!

Learn more about War of the Wizards .

Sudoku is one of the most popular free problem solving games for adults. The objective of this game is to fill each box of a 9×9 grid so that every row, column, and letter contains each number from one to nine. The puzzle makes a great team challenge. To play Sudoku on Zoom, screen share the game board. Then, turn on the annotation features. Using the add text functions, participants can fill in the numbers on the grid.

We made a starter puzzle you can use in your next meeting or virtual team bonding session:

Here are more online Sudoku puzzles .

5. Crossword puzzles

Crossword puzzles are word games that ask players to fill in words based on clues. Words interconnect, and players must think critically about the surrounding words to select the right phrase for the space.

You can use an online crossword puzzle maker to create a custom puzzle. Here are a few themes you may want to consider:

• teammates’ tastes and interests
• company knowledge and history
• industry terms and trends

Or, create a miscellaneous puzzle just for fun.

We made a sample puzzle you can use for your game:

To complete puzzles during online meetings, you can use the share screen function and add text through annotations.

Or, subscribers can play the New York Times’ daily crossword puzzle virtually . Dictionary.com also offers a free daily online crossword puzzle .

Check out more vocabulary games .

6. Online Escape Rooms

Escape rooms are timed games that get groups working together to solve puzzles. Traditionally, players enter a locked room and must complete all puzzles in an hour or two to unlock the door. However, groups can also play escape rooms online.

Digital escape rooms typically come in one of two forms: in a Zoom room and led by a host, or in a choose-your-own adventure format via Google Forms or websites. To play escape rooms virtually, enter a video meeting and follow the prompts, or screen share the Google Form and work out the puzzles together.

Check out our full list of online escape rooms .

7. Murder Mysteries

Murder Mysteries are story-based games that ask players to take on the roles of suspects or detectives while trying to identify a killer. These games often involve reading lines from a script, searching for clues, and occasionally solving puzzles to get hints.

These games make participants pay attention to conversations, analyze other characters’ behavior, and search for hidden meaning in the script. Players must use their powers of observation and logic to unravel the mystery.

Check out our list of Zoom murder mystery games .

8. Treasure Hunts

Treasure hunts are scavenger hunts with intention. While virtual scavenger hunts often ask players to collect random items, treasure hunts require participants to locate clues that lead to other prompts and hints. The game typically ends with players finding a treasure or solving a mystery, sometimes both.

The treasure hunt can have a specific theme such as secret agent missions or a hunt for pirate treasure, or you can run a more general hunt. Teammates can either compete simultaneously via Zoom call, or can play the hunt on an app individually and compete to beat each other’s scores.

Check out our list of treasure hunt apps .

9. Poem or story challenge

Most team building problem solving activities for employees revolve around science, math, and logic. Poem/story challenges rely on writing skills and are sure to appeal to the language lovers on your team.

Each player receives a limited word bank to use to create a story or poem. Then, players have a few minutes to craft their pieces. Afterward, everyone reads out or screen shares their creations.

Here are a few word challenge activities you can do remotely:

• Found poems or stories : Participants make poems or stories out of words they find by visiting websites, searching emails, glancing out the window, or taking a walk or drive around the neighborhood.
• Random word generators : Teammates use a random word generator to populate a word bank, and must use each word in the poem or story.
• Poetry magnets : Group members make poems using poetry magnets. You can send poetry magnet sets to employees and assemble the verses on a cookie pan during a Zoom call. Or, teammates can play with poetry magnets online .
• Page poems: Participants receive one page of a book or magazine, and must make a poem or story by blocking out other words so only the chosen text remains visible. This activity is part storytelling, part art, since story crafters can illustrate the pages as part of the design.
• Ransom note stories or poems : Players cut out letters from magazines and must form new words to make poems and stories. Or, players can receive a mix of random letters, form words, and run the text through a ransom note generator .

These activities are suitable for teams and individual players.

10. Moral challenge

Some problems are ethical rather than factual. Moral judgment plays just as important a role in the decision-making process as technical prowess. Players can flex their moral problem-solving skills by tackling ethical dilemmas or social puzzles.

Here are some social problem solving games online:

• Moral machine
• Scruples – the game of moral dilemmas
• Morality play

To play these games, either download the apps, or pull up the website and then screen share the prompts. These games are best played when discussed as a group, because the more belief systems and opinions, the harder an issue is to resolve. These exercises provide practice for real-life conflict resolution.

You can find similar challenges on our list of online personality tests .

11. Frostbite

Frostbite is a group game that hones team leaders’ communication skills while sharpening teammates’ listening and cooperation skills. The premise behind the game is that a group of explorers gets caught in a snowstorm and must build a shelter. Frostbite has paralyzed the leaders’ hands and snow-blinded the rest of the team. The leader must give the team instructions to build a tent that can resist arctic winds.

To play Frostbite, each teammate wears a blindfold. Then, the leader gives directions. Once the structures are complete, players turn on a fan to test whether tents can withstand the wind.

Frostbite is usually an in-person game, however you can also play virtually. In the remote version of the game, teammates construct tents out of cards and tape, while the leader surveys the scene on screen.

This exercise demonstrates the challenges of leading remotely, as teams need to operate with minimal oversight or supervisor observation. Therefore, instructions need to be clear and direct to be effective.

Check out more team building games .

12. Virtual Hackathons

Hackathons are events where participants have a set amount of time to design and pitch a new product or solution. This type of event originated in the programming world and is often used to create new apps, however you can apply the game to any industry or school subject.

Virtual hackathons are online versions of the event. Teams enter the competition, then work with each other via virtual meeting software or remote work communication platforms to design the solution. At the end of the competition, teams pitch ideas to a panel of judges and a winner is decided.

To run a virtual hackathon, first announce the theme of the event and collect sign-ups. So that no teams work ahead, hint at the general idea of the issue, and only explain the precise problem when the event begins. Then, give teams anywhere from a few hours to a few days to complete the project.

Discover more virtual hackathon ideas .

13. Improv games

Improv games are excellent problem solving activities. These exercises force participants to think and respond quickly to keep scenes moving in a logical and entertaining way.

Here are some good problem solving improv games:

Banned words : Performers cannot say certain words. Scene partners will conceive of situations that encourage the actors to use those words, and the actors must find alternatives, such as using synonyms or taking the scene in a new direction.

Scenes from a chat : Audience gives a suggestion for a scene, and players act the scene out. Though it’s a fictional and often ridiculous scenario, actors must react to the situation and solve the problem in order for the scene to end.

Miracle cure : Miracle cure is a quick-moving exercise that follows a simple format. One player declares, “I have a problem.” Another player responds, “I have a….[random object.]” The first player then replies, “great! I can use the [random object] to….” and describes how they will solve the problem.

Check out more problem-solving improv games .

14. Spaghetti Tower

The spaghetti tower is a classic team building game. Participants gather uncooked spaghetti and marshmallows, and must construct the tallest freestanding tower.

During the in-person version, players must construct one tall freestanding tower. However, for the virtual version of the game, players construct individual towers. You can send groups to breakout rooms for the build, then reconvene in the main room for judging. Teams are judged on three main factors: number of towers, height, and uniformity.

This version of the game not only tests the structural integrity of the tower, but also consistency and quality control. This exercise teaches teams to align and collaborate remotely, and produce a consistent product even when far apart.

15. What Would You Do?

What Would You Do? is a simple situational game that challenges participants to react to different circumstances. To play this game, read prompts one by one, and then ask participants to respond with gameplans. You can use the polling or raise hand feature to vote for the best option.

Here are some problem solving scenarios for adults or kids to use in the game:

• Zombies attack and you have to find a place to hide.
• You are at the zoo and the animals escape. Which one do you try to corral back into the pen first?
• After waiting in line for hours, someone cuts in front of you last minute. The person appears to be visually and hearing impaired, and doesn’t notice your protests. An official announces that due to diminishing supply, this individual will be the last in line to be served.
• You are eating a meal with important clients and/or your partner’s parents, and you want to impress. The individuals make you a dish that does not fit within your dietary restrictions, but you do not speak the same language and cannot explain why you do not want to eat.
• An imposter has infiltrated the organization, who looks, speaks, and behaves exactly like you. How do you convince your peers that you are the original?

For similar dilemmas, check out this list of Would You Rather? questions.

16. Desert Island Survival

Desert Island Survival is a game that challenges players to prioritize. The premise is that players have been stranded on an island, and must decide what order to perform survival steps.

Here are the possible actions:

• Set up shelter
• Explore the island
• Try to signal for help
• Make weapons for self-defense
• Build a raft to escape the island
• Start a fire
• Choose a group leader
• Search for other survivors

All group members must agree on the order of the steps. Players should explain the reasoning for the order of each step while ranking the actions.

Another version of the game involves players receiving a list of 15 to 20 items, and selecting five or so to bring to the island. You can also vary the location of the game, substituting remote islands for destinations like outer space or the distant past.

17. Choose Your Own Adventure

Choose Your Own Adventure stories enable readers to determine the outcome of the story by making decisions. Each action has a consequence that takes the tale in a different direction. Participants can try to guess how the story may unfold by talking through the different choices. When completing the activity in a group setting, the majority of the team must agree on an action before moving forward in the story.

There are a few ways to facilitate these activities online:

• Play an online role playing video game
• Watch an interactive movie like Black Mirror: Bandersnatch
• Read from a Choose Your Own Adventure book on Zoom
• Click through a Choose Your Own Adventure platform
• Create your own story using a Google Form

Whichever way you choose to do the exercise, you can use the screen share feature in your virtual meeting software so that listeners can more easily follow along.

18. MacGyver

MacGyver is a show where the hero escapes sticky situations by improvising tools out of unlikely materials. For example, in one episode the hero makes a telescope out of a newspaper, magnifying lens, and a watch crystal.

To play MacGyver, you can either list three to five objects participants can use, or challenge players to use items that are within arms reach.

Simply state a desired end result, such as “a way to open a locked door,” or “a getaway vehicle,” and then ask teams to explain what they will build and how they will build it. To make the activity more collaborative, you can give teams five or ten minutes in breakout rooms to strategize and design a prototype.

19. Dungeons & Dragons

Dungeons & Dragons is a roleplaying game where players pretend to be magical figures and creatures. One player serves as the dungeon master, who guides the game, while the other players pick characters and make decisions to move the story forward. Upon choosing a course of action, players roll a twenty-sided die to determine whether or not the plan succeeds. The game is story-based, the possibilities are nearly limitless, and truly creative problem solving options arise. Also, since gameplay is mostly verbal, Dungeons & Dragons is an easy activity to do over Zoom.

Here are the basic rules for Dungeons & Dragons .

20. Pandemic

Pandemic is a game that pits players against the forces of nature in a race to contain and control disease outbreaks. At the beginning of the game, each player receives a role such as containment specialist or operations expert. Participants must carry out the duties of their roles by choosing appropriate actions. Pandemic is a great game for groups because each team member has a clear part to play, and players must collaborate and work together instead of competing against each other.

To play the game online, you can use a Pandemic game app , or talk through the exercise while one attendee moves and displays pieces on the board.

Note: The subject of this game might hit too close to home for some players, considering recent history. You can find games with similar mechanics that deal with different subject matter, such as Forbidden Island.

Check out more team building board games .

21. Model UN

Model UN is one of the best virtual problem solving activities for students. This exercise casts participants in the role of international diplomats who must negotiate to solve realistic problems. Each player assumes the role of a country ambassador and must form alliances and propose solutions to solve crises.

Here are some sample Model UN scenarios:

• Human rights violation by powerful country
• Food shortage
• Disease epidemic
• Technology privacy violations
• Civil war branching into surrounding countries
• Natural disasters

Depending on the size of the group, participants either take on the part of an entire government of a country, or play a certain role within the government. To carry out the activity on Zoom, players can take turns giving speeches, message other countries privately via the chat, meet in breakout rooms to form alliances or have more intimate discussions, and use the polling feature to vote on propositions.

If politics does not resonate with your group, then you can alter the exercise by applying the same activity structure to a different theme, such as the Justice League, movie characters, business board members, or reality TV stars.

The main purpose of the exercise is to research, talk through problems, and compromise. As long as these elements are present, then the specifics of the setup do not matter.

There are many types of problem solving activities for adults. You can do online problem solving games, which require a different skill set than in-person problem solving. For instance, communication must be much clearer and more abundant when group members are far apart and unable to demonstrate or pick up physical cues.

Though many problem solving games include props and in-person elements, there are many games you can play together online. These exercises work well as educational tools as well as team bonding accelerators. Upon completion, participants are likely to feel a sense of accomplishment and increased confidence. These games are also great practice for real life conflict resolution, creative thinking and team building.

Next check out this list of connection games , this collection of crime-solving games , and this post with conflict resolution games .

We also have a list of the best decision making books and a list of team building problems for work .

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FAQ: Problem solving activities

Here are common answers to questions about group problem solving activities.

What are problem solving games?

Problem solving games are challenges that ask players to think critically and use logic to overcome issues or answer riddles. Examples include sudoku, murder mysteries, and spaghetti towers. These games are also known as “problem solving exercises”, “problem and solution games” and “group problem solving activities.”

What are the best problem solving games for groups?

The best problem solving games for groups include online escape rooms, moral challenges, and improv games.

What are some good problem solving team building activities for students?

Some good problem solving activities for students include crossword puzzles, choose your own adventure stories, and model UN.

How do you play problem solving games online?

The best way to play problem solving games online is to join a video call meeting to talk through the issue. Using the screen sharing and digital whiteboard features helps participants visualize the problem more clearly. Breakout rooms give teams the chance to discuss the issue more intimately.

Author: Angela Robinson

Marketing Coordinator at teambuilding.com. Angela has a Master of Fine Arts in Creative Writing and worked as a community manager with Yelp to plan events for businesses.

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Marketing Coordinator at teambuilding.com.

Angela has a Master of Fine Arts in Creative Writing and worked as a community manager with Yelp to plan events for businesses.

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20 Tough Riddles for Adults That Will Have You Scratching Your Head

Put your logic and math skills to the test. No cheating!

Gear-obsessed editors choose every product we review. We may earn commission if you buy from a link. Why Trust Us?

So go grab a pencil and a piece of scratch paper and prepare to rip your hair out (and we really do mean that in the best way possible). When you think you’ve got the right answer, click the link at the bottom of each riddle to find the solution. Got it wrong? No worries, you have 19 other riddles to test out.

Navigate Through Our Riddles:

Puzzmo / The King’s Orders / How Many Eggs? / The Gold Chain / Pickleball / Circuit Breaker / Two Trains, Two Grandmas / Ant Math / Peppermint Patty / Great American Rail Trail / A Cruel SAT Problem / Movie Stars Cross a River / Tribute to a Math Genius / One Belt, One Earth / Elbow Tapping / Whiskey Problem / Doodle Problem / Stumping Scientists / What ’ s On Her Forehead? / Keanu for President / Who Opened the Lockers?

Riddle No. 1: The King’s Orders Make for One Hell of a Brain Teaser

Difficulty: easy.

King Nupe of the kingdom Catan dotes on his two daughters so much that he decides the kingdom would be better off with more girls than boys, and he makes the following decree: All child-bearing couples must continue to bear children until they have a daughter!

But to avoid overpopulation, he makes an additional decree: All child-bearing couples will stop having children once they have a daughter! His subjects immediately begin following his orders.

After many years, what’s the expected ratio of girls to boys in Catan?

The likelihood of each baby born being a girl is, of course, 50 percent.

Ready for the solution? Click here to see if you’re right .

Riddle No. 2: How Many Eggs Does This Hen Lay?

This problem is in honor of my dad, Harold Feiveson. It’s due to him that I love math puzzles, and this is one of the first problems (of many) that he gave me when I was growing up.

A hen and a half lays an egg and a half in a day and a half. How many eggs does one hen lay in one day?

Riddle No. 3: The Gold Chain Math Problem Is Deceptively Simple

Difficulty: moderate.

You’re rummaging around your great grandmother’s attic when you find five short chains each made of four gold links. It occurs to you that if you combined them all into one big loop of 20 links, you’d have an incredible necklace. So you bring it into a jeweler, who tells you the cost of making the necklace will be $10 for each gold link that she has to break and then reseal.

How much will it cost?

Riddle No. 4: Try to Solve This Pickleball Puzzle

Difficulty: 🚨hard🚨.

Kenny, Abby, and Ned got together for a round-robin pickleball tournament, where, as usual, the winner stays on after each game to play the person who sat out that game. At the end of their pickleball afternoon, Abby is exhausted, having played the last seven straight games. Kenny, who is less winded, tallies up the games played:

Kenny played eight games

Abby played 12 games

Ned played 14 games

Who won the fourth game against whom?

How many total games were played?

Riddle No. 5: Our Circuit Breaker Riddle Is Pure Evil. Sorry.

The circuit breaker box in your new house is in an inconvenient corner of your basement. To your chagrin, you discover none of the 100 circuit breakers is labeled, and you face the daunting prospect of matching each circuit breaker to its respective light. (Suppose each circuit breaker maps to only one light.)

To start with, you switch all 100 lights in the house to “on,” and then you head down to your basement to begin the onerous mapping process. On every trip to your basement, you can switch any number of circuit breakers on or off. You can then roam the hallways of your house to discover which lights are on and which are off.

What is the minimum number of trips you need to make to the basement to map every circuit breaker to every light?

The solution does not involve either switching on or off the light switches in your house or feeling how hot the lightbulbs are. You might want to try solving for the case of 10 unlabeled circuit breakers first.

Riddle No. 6: Two Trains. Two Grandmas. Can You Solve This Tricky Math Riddle?

Jesse’s two grandmothers want to see him every weekend, but they live on opposite sides of town. As a compromise, he tells them that every Sunday, he’ll head to the subway station nearest to his apartment at a random time of the day and will hop on the next train that arrives.

If it happens to be the train traveling north, he’ll visit his Grandma Erica uptown, and if it happens to be the train traveling south, he’ll visit his Grandma Cara downtown. Both of his grandmothers are okay with this plan, since they know both the northbound and southbound trains run every 20 minutes.

But after a few months of doing this, Grandma Cara complains that she sees him only one out of five Sundays. Jesse promises he’s indeed heading to the station at a random time each day. How can this be?

The trains always arrive at their scheduled times.

Riddle No. 7: Here’s a Really F@*#ing Hard Math Problem About Ants

Max and Rose are ant siblings. They love to race each other, but always tie, since they actually crawl at the exact same speed. So they decide to create a race where one of them (hopefully) will win.

For this race, each of them will start at the bottom corner of a cuboid, and then crawl as fast as they can to reach a crumb at the opposite corner. The measurements of their cuboids are as pictured:

If they both take the shortest possible route to reach their crumb, who will reach their crumb first? (Don’t forget they’re ants, so of course they can climb anywhere on the edges or surface of the cuboid.)

Remember: Think outside the box.

Riddle No. 8: This Peppermint Patty Riddle Is Practically Impossible

You’re facing your friend, Caryn, in a “candy-off,” which works as follows: There’s a pile of 100 caramels and one peppermint patty. You and Caryn will go back and forth taking at least one and no more than five caramels from the candy pile in each turn. The person who removes the last caramel will also get the peppermint patty. And you love peppermint patties.

Suppose Caryn lets you decide who goes first. Who should you choose in order to make sure you win the peppermint patty?

First, solve for a pile of 10 caramels.

Riddle No. 9: Can You Solve the Great American Rail-Trail Riddle?

This problem was suggested by the physicist P. Jeffrey Ungar.

Finally, the Great American Rail-Trail across the whole country is complete! Go ahead, pat yourself on the back—you’ve just installed the longest handrail in the history of the world, with 4,000 miles from beginning to end. But just after the opening ceremony, your assistant reminds you that the metal you used for the handrail expands slightly in summer, so that its length will increase by one inch in total.

“Ha!” you say, “One inch in a 4,000 mile handrail? That’s nothing!” But … are you right?

Let’s suppose when the handrail expands, it buckles upward at its weakest point, which is in the center. How much higher will pedestrians in the middle of the country have to reach in summer to grab the handrail? That is, in the figure below, what is h ? (For the purposes of this question, ignore the curvature of the Earth and assume the trail is a straight line.)

Pythagoras is a fascinating historical figure.

Riddle No. 10: This Riddle Is Like an Especially Cruel SAT Problem. Can You Find the Answer?

Amanda lives with her teenage son, Matt, in the countryside—a car ride away from Matt’s school. Every afternoon, Amanda leaves the house at the same time, drives to the school at a constant speed, picks Matt up exactly when his chess club ends at 5 p.m., and then they immediately return home together at the same constant speed. But one day, Matt isn’t feeling well, so he leaves chess practice early and starts to head home on his portable scooter.

After Matt has been scooting for an hour, Amanda comes across him in her car (on her usual route to pick him up), and they return together, arriving home 40 minutes earlier than they usually do. How much chess practice did Matt miss?

Consider the case where Amanda meets Matt exactly as she’s leaving their house.

Riddle No. 11: Can You Get These 3 Movie Stars Across the River?

Three movie stars, Chloe, Lexa, and Jon, are filming a movie in the Amazon. They’re very famous and very high-maintenance, so their agents are always with them. One day, after filming a scene deep in the rainforest, the three actors and their agents decide to head back to home base by foot. Suddenly, they come to a large river.

On the riverbank, they find a small rowboat, but it’s only big enough to hold two of them at one time. The catch? None of the agents are comfortable leaving their movie star with any other agents if they’re not there as well. They don’t trust that the other agents won’t try to poach their star.

For example, Chloe’s agent is okay if Chloe and Lexa are alone in the boat or on one of the riverbanks, but definitely not okay if Lexa’s agent is also with them. So how can they all get across the river?

There isn’t just one way to solve this problem.

Riddle No. 12: This Ludicrously Hard Riddle Is Our Tribute to a Late Math Genius. Can You Figure It Out?

On April 11, John Horton Conway , a brilliant mathematician who had an intense and playful love of puzzles and games, died of complications from COVID-19. Conway is the inventor of one of my favorite legendary problems (not for the faint of heart) and, famously, the Game of Life . I created this problem in his honor.

Carol was creating a family tree, but had trouble tracking down her mother’s birthdate. The only clue she found was a letter written from her grandfather to her grandmother on the day her mother was born. Unfortunately, some of the characters were smudged out, represented here with a “___” . (The length of the line does not reflect the number of smudged characters.)

“Dear Virginia,

Little did I know when I headed to work this Monday morning, that by evening we would have a beautiful baby girl. And on our wedding anniversary, no less! It makes me think back to that incredible weekend day, J___ 27th, 19___ , when we first shared our vow to create a family together, and, well, here we are! Happy eighth anniversary, my love.

Love, Edwin”

The question: When was Carol’s mother born?

This problem is inspired by Conway’s Doomsday Rule .

Riddle No. 13: To Solve This Twisty Math Riddle, You Just Need One Belt and One Earth

Imagine you have a very long belt. Well, extremely long, really … in fact, it’s just long enough that it can wrap snugly around the circumference of our entire planet. (For the sake of simplicity, let’s suppose Earth is perfectly round, with no mountains, oceans, or other barriers in the way of the belt.)

Naturally, you’re very proud of your belt. But then your brother, Peter, shows up—and to your disgruntlement, he produces a belt that’s just a bit longer than yours. He brags his belt is longer by exactly his height: 6 feet.

If Peter were also to wrap his belt around the circumference of Earth, how far above the surface could he suspend the belt if he pulled it tautly and uniformly?

Earth’s circumference is about 25,000 miles, or 130 million feet … but you don’t need to know that to solve this problem.

Riddle No. 14: This Elbow Tapping Riddle Is Diabolical. Good Luck Solving It.

In some future time, when the shelter-in-place bans are lifted, a married couple, Florian and Julia, head over to a bar to celebrate their newfound freedom.

They find four other couples there who had the same idea.

Eager for social contact, every person in the five couples enthusiastically taps elbows (the new handshake) with each person they haven’t yet met .

It actually turns out many of the people had known each other prior, so when Julia asks everyone how many elbows they each tapped, she remarkably gets nine different answers!

The question: How many elbows did Florian tap?

What nine answers did Julia hear?

Riddle No. 15: You’ll Need a Drink After Trying to Solve This Whisky Riddle

Alan and Claire live by the old Scottish saying, “Never have whisky without water, nor water without whisky!” So one day, when Alan has in front of him a glass of whisky, and Claire has in front of her a same-sized glass of water, Alan takes a spoonful of his whisky and puts it in Claire’s water. Claire stirs her whisky-tinted water, and then puts a spoonful of this mixture back into Alan’s whisky to make sure they have exactly the same amount to drink.

So: Is there more water in Alan’s whisky, or more whisky in Claire’s water? And does it matter how well Claire stirred?

The size of the spoon does not matter.

Riddle No. 16: The Doodle Problem Is a Lot Harder Than It Looks. Can You Solve It?

This week’s riddle is relatively simple—but sinister all the same.

The question: Can you make 100 by interspersing any number of pluses and minuses within the string of digits 9 8 7 6 5 4 3 2 1? You can’t change the order of the digits! So what’s the least number of pluses and minuses needed to make 100?

For instance, 98 - 7 - 6 + 54 - 32 shows one way of interspersing pluses and minuses, but since it equals 107, it’s not a solution.

I call this a “doodle problem”: one that’s best worked on during meetings where you might be doodling otherwise.

You might want to start looking for solutions that use a total of seven pluses and minuses (although there are ways to use fewer).

Ready for the solution? Click here to see if you’re right.

Riddle No. 17: This Math Puzzle Stumped Every Scientist but One. Think You Can Crack It?

Difficulty: hard.

In honor of Freeman Dyson, the renowned physicist who died last month , here’s a legendary tale demonstrating his quick wit and incredible brain power.

One day, in a gathering of top scientists, one of them wondered out loud whether there exists an integer that you could exactly double by moving its last digit to its front. For instance, 265 would satisfy this if 526 were its exact double—which it isn’t.

After apparently just five seconds , Dyson responded, “Of course there is, but the smallest such number has 18 digits.”

This left some of the smartest scientists in the world puzzling over how he could have figured this out so quickly.

So given Dyson’s hint, what is the smallest such number?

My second grader has recently learned how to add a 3-digit number to itself using the classic vertical method:

18-digit numbers, of course, can be added in the same way.

Riddle No. 18: Figure Out What’s on Her Forehead

Cecilia loves testing the logic of her very logical friends Jaya, Julian, and Levi, so she announces:

“I’ll write a positive number on each of your foreheads. None of the numbers are the same, and two of the numbers add up to the third.”

She scribbles the numbers on their heads, then turns to Jaya and asks her what her number is. Jaya sees Julian has 20 on his forehead, and Levi has 30 on his. She thinks for a moment and then says, “I don’t know what my number is.” Julian pipes in, “I also don’t know my number,” and then Levi exclaims, “Me neither!” Cecilia gleefully says, “I’ve finally stumped you guys!”

“Not so fast!” Jaya says. “Now I know my number!”

What is Jaya’s number?

Jaya could be one of two numbers, but only one of those numbers would lead to Julian and Levi both not knowing their numbers. Why?

Riddle No. 19: Can You Get Keanu Reeves Elected As President?

It’s 2024, and there are five candidates running in the democratic primary: Taylor Swift, Oprah Winfrey, Mark Cuban, Keanu Reeves, and Dwayne Johnson. (Hey, it could happen.) As usual, the first primary is in Iowa.

In an effort to overcome its embarrassment after the 2020 caucus debacle , the Iowa Democratic Party has just announced a new, foolproof way of finding the best candidate: there will be four consecutive elections.

First, candidate 1 will run against candidate 2. Next, the winner of that will run against candidate 3, then that winner will run against candidate 4, and finally the winner of that election will run against the final candidate. By the transitive property, the winner of this last election must be the best candidate ... so says the Iowa Democratic Party.

Candidate Keanu has been feeling pretty low, as he knows he is ranked near the bottom by most voters, and at the top by none. In fact, he knows the Iowa population is divided into five equal groups, and that their preferences are as follows:

Keanu is childhood friends with Bill S. Preston, Esq., the new head of the Iowa Democratic Party. Preston, confident that the order of the candidates doesn’t matter for the outcome, tells Keanu he can choose the voting order of the candidates.

So what order should Keanu choose?

How would Keanu fare in one-to-one races against each candidate?

Riddle No. 20: Who Opened All These Damn Lockers?

There are 100 lockers that line the main hallway of Chelm High School. Every night, the school principal makes sure all the lockers are closed so that there will be an orderly start to the next day. One day, 100 mischievous students decide that they will play a prank.

The students all meet before school starts and line up. The first student then walks down the hallway, and opens every locker. The next student follows by closing every other locker (starting at the second locker). Student 3 then goes to every third locker (starting with the third) and opens it if it’s closed, and closes it if it’s open. Student 4 follows by opening every fourth locker if it’s closed and closing it if it’s open. This goes on and on until Student 100 finally goes to the hundredth locker. When the principal arrives later in the morning, which lockers does she find open?

Make sure you pay attention to all of the factors.

Laura Feiveson is an economist for the government, a storyteller, and a lifelong enthusiast of math puzzles.  She lives in Washington, DC with her husband and two daughters. 

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Logical Puzzles

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• Andrew Hayes

A logical puzzle is a problem that can be solved through deductive reasoning. This page gives a summary of the types of logical puzzles one might come across and the problem-solving techniques used to solve them.

Elimination Grids

Truth tellers and liars, cryptograms, arithmetic puzzles, river crossing puzzle, tour puzzles, battleship puzzles, chess puzzles, k-level thinking, other puzzles.

Main Article: Propositional Logic See Also: Predicate Logic

One of the simplest types of logical puzzles is a syllogism . In this type of puzzle, you are given a set of statements, and you are required to determine some truth from those statements. These types of puzzles can often be solved by applying principles from propositional logic and predicate logic . The following syllogism is from Charles Lutwidge Dodgson, better known under his pen name, Lewis Carroll.

I have a dish of potatoes. The following statements are true: No potatoes of mine, that are new, have been boiled. All my potatoes in this dish are fit to eat. No unboiled potatoes of mine are fit to eat. Are there any new potatoes in this dish? The first and third statements can be connected by a transitive argument. All of the new potatoes are unboiled, and unboiled potatoes aren't fit to eat, so no new potatoes are fit to eat. The second statement can be expressed as the equivalent contrapositive. All of the potatoes in the dish are fit to eat; if there is a potato that is not fit to eat, it isn't in the dish. Then, once again, a transitive argument is applied. New potatoes aren't fit to eat, and inedible potatoes aren't in the dish. Thus, there are no new potatoes in the dish. \(_\square\)

Given below are three statements followed by three conclusions. Take the three statements to be true even if they vary from commonly known facts. Read the statements and decide which conclusions follow logically from the statements.

Statements: 1. All actors are musicians. 2. No musician is a singer. 3. Some singers are dancers.

Conclusions: 1. Some actors are singers. 2. Some dancers are actors. 3. No actor is a singer.

Answer Choices: a) Only conclusion 1 follows. b) Only conclusion 2 follows. c) Only conclusion 3 follows. d) At least 2 of the conclusions follows.

Main Article: Elimination Grids

Some logical puzzles require you to determine the correct pairings for sets of objects. These puzzles can often be solved with the process of elimination, and an elimination grid is an effective tool to apply this process.

An example of an elimination grid

Elimination grids are aligned such that each row represents an object within a set, and each column represents an object to be paired with an object from that set. Check marks and X marks are used to show which objects pair, and which objects do not pair.

Mr. and Mrs. Tan have four children--three boys and a girl-- who each like one of the colors--blue, green, red, yellow-- and one of the letters--P, Q, R, S.

• The oldest child likes the letter Q.
• The youngest child likes green.
• Alfred likes the letter S.
• Brenda has an older brother who likes R.
• The one who likes blue isn't the oldest.
• The one who likes red likes the letter P.
• Charles likes yellow.

Based on the above facts, Darius is the \(\text{__________}.\)

Main Article: Truth-Tellers and Liars

A variation on elimination puzzles is a truth-teller and liar puzzle , also known as a knights and knaves puzzle . In this type of puzzle, you are given a set of people and their respective statements, and you are also told that some of the people always tell the truth and some always lie. The goal of the puzzle is to deduce the truth from the given statements.

20\(^\text{th}\) century mathematician Raymond Smullyan popularized these types of puzzles.

You are in a room with three chests. You know at least one has treasure, and if a chest has no treasure, it contains deadly poison.

Each chest has a message on it, but all the messages are lying .

• Left chest: "The middle chest has treasure."
• Middle chest: "All these chests have treasure."
• Right chest: "Only one of these chests has treasure."

Which chests have treasure?

There are two people, A and B , each of whom is either a knight or a knave.

A says, "At least one of us is a knave."

What are A and B ?

\(\) Details and Assumptions:

• A knight always tells the truth.
• A knave always lies.

Main Article: Cryptograms

A cryptogram is a puzzle in which numerical digits in a number sentence are replaced with characters, and the goal of the puzzle is to determine the values of these characters.

\[ \begin{array} { l l l l l } & &P & P & Q \\ & &P & Q & Q \\ + && Q & Q & Q \\ \hline & & 8 & 7 & 6 \\ \end{array} \]

In the sum shown above, \(P\) and \(Q\) each represent a digit. What is the value of \(P+Q\)?

\[ \overline{EVE} \div \overline{DID} = 0. \overline{TALKTALKTALKTALK\ldots} \]

Given that \(E,V,D,I,T,A,L\) and \(K \) are distinct single digits, let \(\overline{EVE} \) and \( \overline{DID} \) be two coprime 3-digit positive integers and \(\overline{TALK} \) be a 4-digit integer, such that the equation above holds true, where the right hand side is a repeating decimal number.

Find the value of the sum \( \overline{EVE} + \overline{DID} + \overline{TALK} \).

Main Articles: Fill in the Blanks and Operator Search

Arithmetic puzzles contain a series of numbers, operations, and blanks in order, and the object of the puzzle is to fill in the blanks to obtain a desired result.

\[\huge{\Box \times \Box \Box = \Box \Box \Box}\]

Fill the boxes above with the digits \(1,2,3,4,5,6\), with no digit repeated, such that the equation is true.

Enter your answer by concatenating all digits in the order they appear. For example, if the answer is \(1 \times 23 = 456\), enter \(123456\) as your final answer.

Also try its sister problem.

\[ \LARGE{\begin{eqnarray} \boxed{\phantom0} \; + \; \boxed{\phantom0} \; &=& \; \boxed{\phantom0} \\ \boxed{\phantom0} \; - \; \boxed{\phantom0} \; &=& \; \boxed{\phantom0} \\ \boxed{\phantom0} \; \times \; \boxed{\phantom0}\; &=& \; \boxed{\phantom0} \\ \boxed{\phantom0} \; \div \; \boxed{\phantom0} \; &=& \; \boxed{\phantom0} \\ \end{eqnarray}} \]

Put one of the integers \(1, 2, \ldots , 13\) into each of the boxes, such that twelve of these numbers are used once for each (and one number is not used at all) and all four equations are true.

What is the sum of all possible values of the missing (not used) number?

Main Article: River Crossing Puzzles

In a river crossing puzzle , the goal is to find a way to move a group of people or objects across a river (or some other kind of obstacle), and to do it in the fewest amount of steps or least amount of time.

A famous river crossing problem is Richard Hovasse's bridge and torch problem , written below.

Four people come to a river in the night. There is a narrow bridge, but it can only hold two people at a time. They have one torch and, because it's night, the torch has to be used when crossing the bridge. Person A can cross the bridge in one minute, B in two minutes, C in five minutes, and D in eight minutes. When two people cross the bridge together, they must move at the slower person's pace. The question is, can they all get across the bridge in 15 minutes or less? Assume that a solution minimizes the total number of crosses. This gives a total of five crosses--three pair crosses and two solo crosses. Also, assume we always choose the fastest for the solo cross. First, we show that if the two slowest persons (C and D) cross separately, they accumulate a total crossing time of 15. This is done by taking persons A, C, D: D+A+C+A = 8+1+5+1=15. (Here we use A because we know that using A to cross both C and D separately is the most efficient.) But, the time has elapsed and persons A and B are still on the starting side of the bridge and must cross. So it is not possible for the two slowest (C and D) to cross separately. Second, we show that in order for C and D to cross together that they need to cross on the second pair cross: i.e. not C or D, so A and B, must cross together first. Remember our assumption at the beginning states that we should minimize crosses, so we have five crosses--3 pair crossings and 2 single crossings. Assume that C and D cross first. But then C or D must cross back to bring the torch to the other side, so whoever solo-crossed must cross again. Hence, they will cross separately. Also, it is impossible for them to cross together last, since this implies that one of them must have crossed previously, otherwise there would be three persons total on the start side. So, since there are only three choices for the pair crossings and C and D cannot cross first or last, they must cross together on the second, or middle, pair crossing. Putting all this together, A and B must cross first, since we know C and D cannot and we are minimizing crossings. Then, A must cross next, since we assume we should choose the fastest to make the solo cross. Then we are at the second, or middle, pair crossing, so C and D must go. Then we choose to send the fastest back, which is B. A and B are now on the start side and must cross for the last pair crossing. This gives us, B+A+D+B+B = 2+1+8+2+2 = 15. It is possible for all four people to cross in 15 minutes. \(_\square\)

Main Article: Tour Puzzles See Also: Eulerian Path

In a tour puzzle , the goal is to determine the correct path for an object to traverse a graph. These kinds of puzzles can take several forms: chess tours, maze traversals, eulerian paths , and others.

Find the path that leads from the star in the center back to the star in the center. Paths can only go in the direction of an arrow. Image Credit: Eric Fisk Show Solution The solution path is outlined in red below.

Determine a path through the below graph such that each edge is traversed exactly once . Show Solution There are several possible solutions. One possible solution is shown below, with the edges marked in the order they are traversed.

A chess tour is an interesting type of puzzle in its own right, and is explained in detail further down the page.

Main Article: Nonograms

A nonogram is a grid-based puzzle in which a series of numerical clues are given beside a rectangular grid. When the puzzle is completed, a picture is formed in the grid.

The puzzle begins with a series of numbers on the left and above the grid. Each of these numbers represents a consecutive run of shaded spaces in the corresponding row or column. Each consecutive run is separated from other runs by at least one empty space. The puzzle is complete when all of the numbers have been satisfied. The primary technique to solve these puzzles is the process of elimination. If the puzzle is designed correctly, there should be no guesswork required.

Complete the nonogram: Show Solution

One of the many logical puzzles is the Battleship puzzle (sometimes called Bimaru, Yubotu, Solitaire Battleships or Battleship Solitaire). The puzzle is based on the Battleship game.

Solitaire Battleships was invented by Jaime Poniachik in Argentina and was first featured in the magazine Humor & Juegos.

This is an example of a solved Battleship puzzle. The puzzle consists of a 10 × 10 small squares, which contain the following:

• 1 battleship 4 squares long
• 2 cruisers 3 squares long each
• 3 destroyers 2 squares long each
• 4 submarines 1 square long each.

They can be put horizontally or vertically, but never diagonally. The boats are placed so that no boats touch each other, not even vertically. The numbers beside the row/column indicate the numbers of squares occupied in the row/column, respectively. ⬤ indicates a submarine and ⬛ indicates the body of a ship, while the half circles indicate the beginning/end of a ship.

The goal of the game is to fill in the grid with water or ships.

Main Article: Sudoku

A sudoku is a puzzle on a \(9\times 9\) grid in which each row, column, and smaller square portion contains each of the digits 1 through 9, each no more than once. Each puzzle begins with some of the spaces on the grid filled in. The goal is to fill in the remaining spaces on the puzzle. The puzzle is solved primarily through the process of elimination. No guesswork should be required to solve, and there should be only one solution for any given puzzle.

Solve the sudoku puzzle: Puzzle generated by Open Sky Sudoku Generator Each row should contain the each of the digits 1 through 9 exactly once. The same is true for columns and the smaller \(3\times 3\) squares. Show Solution

Main Article: Chess Puzzles See Also: Reduced Games , Opening Strategies , and Rook Strategies

Chess puzzles take the rules of chess and challenge you to perform certain actions or deduce board states.

One kind of chess puzzle is a chess tour , related to the tour puzzles mentioned in the section above. This kind of puzzle challenges you to develop a tour of a chess piece around the board, applying the rules of how that piece moves.

Dan and Sam play a game on a \(5\times3\) board. Dan places a White Knight on a corner and Sam places a Black Knight on the nearest corner. Each one moves his Knight in his turn to squares that have not been already visited by any of the Knights at any moment of the match.

For example, Dan moves, then Sam, and Dan wants to go to Black Knight's initial square, but he can't, because this square has been occupied earlier.

When someone can't move, he loses. If Dan begins, who will win, assuming both players play optimally?

This is the seventeenth problem of the set Winning Strategies.

Due to its well-defined ruleset, the game of chess affords many different types of puzzles. The problem below shows that you can even deduce whose turn it is from a certain boardstate (or perhaps you cannot).

Whose move is it now?

Main Article: K-Level Thinking See Also: Induction - Introduction

K-level thinking is the name of a kind of assumption in certain logic puzzles. In these types of puzzles, there are a number of actors in a situation, and each of them is perfectly logical in their decision-making. Furthermore, each of these actors is aware that all other actors in the situation are perfectly logical in their decision-making.

Calvin, Zandra, and Eli are students in Mr. Silverman's math class. Mr. Silverman hands each of them a sealed envelope with a number written inside.

He tells them that they each have a positive integer and the sum of the three numbers is 14. They each open their envelope and inspect their own number without seeing the other numbers.

Calvin says,"I know that Zandra and Eli each have a different number." Zandra replies, "I already knew that all three of our numbers were different." After a brief pause Eli finally says, "Ah, now I know what number everyone has!"

What number did each student get?

Format your answer by writing Calvin's number first, then Zandra's number, and finally Eli's number. For example, if Calvin has 8, Zandra has 12, and Eli has 8, the answer would be 8128.

Two logicians must find two distinct integers \(A\) and \(B\) such that they are both between 2 and 100 inclusive, and \(A\) divides \(B\). The first logician knows the sum \( A + B \) and the second logician knows the difference \(B-A\).

Then the following discussion takes place:

Logician 1: I don't know them. Logician 2: I already knew that.

Logician 1: I already know that you are supposed to know that. Logician 2: I think that... I know... that you were about to say that!

Logician 1: I still can't figure out what the two numbers are. Logician 2: Oops! My bad... my previous conclusion was unwarranted. I didn't know that yet!

What are the two numbers?

Enter your answer as a decimal number \(A.B\). \((\)For example, if \(A=23\) and \(B=92\), write \(23.92.)\)

Note: In this problem, the participants are not in a contest on who finds numbers first. If one of them has sufficient information to determine the numbers, he may keep this quiet. Therefore nothing may be inferred from silence. The only information to be used are the explicit declarations in the dialogue.

Of course, the puzzles outlined above aren't the only types of puzzles one might encounter. Below are a few more logical puzzles that are unrelated to the types outlined above.

You are asked to guess an integer between \(1\) and \(N\) inclusive.

Each time you make a guess, you are told either

(a) you are too high, (b) you are too low, or (c) you got it!

You are allowed to guess too high twice and too low twice, but if you have a \(3^\text{rd}\) guess that is too high or a \(3^\text{rd}\) guess that is too low, you are out.

What is the maximum \(N\) for which you are guaranteed to accomplish this?

\(\) Clarification : For example, if you were allowed to guess too high once and too low once, you could guarantee to guess the right answer if \(N=5\), but not for \(N>5\). So, in this case, the answer would be \(5\).

You play a game with a pile of \(N\) gold coins.

You and a friend take turns removing 1, 3, or 6 coins from the pile. The winner is the one who takes the last coin.

For the person that goes first, how many winning strategies are there for \(N < 1000?\)

\(\) Clarification: For \(1 \leq N \leq 999\), for how many values of \(N\) can the first player develop a winning strategy?

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The 20 Best Puzzle Games on Steam

Is there anything better than a great puzzle game on PC? These games are perfect for those of us who like to take our time to solve problems and plan out their moves well in advance.

If you love puzzles and games, Steam has plenty of great options to choose from.

These titles require players to work out complex problems in order to progress through the game and often present unique challenges that will keep you entertained for hours.

These games will keep your brain busy with logic and problem-solving in some very creative ways, from block-sliding puzzlers to pipe-solving adventures.

Here are 20 of the best puzzle games on Steam you can play right now.

Trine originally debuted in 2009 and took players to a colorful fantasy world where they could fight monsters, rescue fairies, and solve puzzles. It is a side-scrolling fantasy action platformer starring three characters who offer different skills to solve the problems presented in each stage.

This is a brilliant and beautiful franchise that came up with a single concept, you need teamwork. In Trine, you switch characters as you wish to overcome different challenges by using the unique strengths of each hero.

In Trine, you control one character at a time. So you might play with either Zoya the thief, Pontius knight, or Amadeus wizard as they work together to progress through levels.

For instance, you might need Amadeus to lift objects, Zoya to swing and climb, and Pontius to break stuff and fight.

Trine is a generally well-received franchise by both critics and players. To this day, it remains one of Frozenbyte’s most popular titles.

The Talos Principle

This is one of my favorite puzzle games due to its sci-fi philosophical concept and themes where you explore a rich and captivating setting.

You’ll solve puzzles by manipulating robots and utilizing in-game physics. Although they are fun, the puzzles are just one of the things that make this game good.

This is not a game that is all about its gameplay. If that’s what you are looking for, The Talos Principle might still be fun, but you will only be enjoying half of what it offers. This game dives deeply into existential questions and gets you thinking about what it means to be human.

Although it isn’t as flashy as other puzzle games, it does offer challenges that can keep players engaged for many hours. Still, I was mostly interested to see how the narrative would hit me again with some other mind-bending thought exercise.

I would highly recommend any gamer interested in puzzles or philosophy to pick up The Talos Principle. If that’s the kind of thing you are into, this game is a must-play.

The Swapper

A unique puzzle game, The Swapper, has players exploring a space station using the main character’s ability to clone himself to solve puzzles. This is a stylish, well-designed puzzler that is worth your time. The puzzles are never too challenging, but you will be spending a lot of time with them.

The story is a bit complex, but it is very well written. It is really interesting and engaging, making for one of the most memorable experiences in gaming. There’s a fair amount of questions about humanity, existence, and consciousness for all fans of the usual kind of philosophical discussions seen in sci-fi stories.

I can definitely recommend The Swapper to anyone looking for a fun puzzle game on Steam.

It may not be everyone’s cup of tea, but it’s something everyone should play at least once. The Swapper is a quite unique, well-thought-out puzzle game. Besides, it is fun even without the fascinating story behind it.

The Witness

The Witness is a puzzle game that surprised me. It is by far one of the most pleasant experiences I’ve ever had with the genre.

In this game, filled with beautiful and mysterious but calm scenarios, you must solve the puzzles you find in panels and direct beams of light to the top of the Island.

The colorful, quiet setting emanates a sense of tranquility while you explore the Island. It gives The Witness a lack of urgency that is refreshing and calming when you are surrounded by puzzles to solve.

This game is not easy. It can cause you to roam lost, desperately looking for answers. This can happen to the fact that the Island is large, and the game doesn’t really lock you in any area.

There is a chance you will face puzzles you might not be ready to solve. If you do, you can just go to a different area and try something else. The Witness will introduce new mechanics and symbols that slowly make the puzzles more challenging and engaging.

This is an intelligently designed puzzle game that is easy to recommend to any fan of the genre.

Portal is a mind-bending game that will force you to think outside your comfort zone. The plot is a bit unorthodox in the best of ways, and it might sometimes feel really over the top, but it’s a game that never takes itself seriously.

When it first came out, Portal was mind-blowing. The Portal Gun makes you think about space-time and physics in ways that would not make sense in any other context.

Thanks to Portal, the portal gun became one of the most popular items in pop culture. The game’s puzzles are inventive and original and take the game’s mechanics to the limit.

Considering that the concept of the game itself was original, it was expected to see many unusual puzzles to solve in Portal. However, the mechanic is pretty much the same until the end of the game, and it is never dull, so it says a lot about the level design.

Portal has a great sense of humor, a story with a dark twist, and a primary tool that might require a certain degree of patience and logic to master. It’s good for quick bursts when you have time to kill or for intense gaming sessions that will keep you busy for hours at a time.

Portal 2 feels much more like a reboot than a sequel to the original Portal game. In fact, it does feel like they’re the same game in many ways until it doesn’t.

Although Portal is a funny game, its dark humor and creepy twists are a big part of its identity. However, Portal 2 takes a different road, being unapologetically silly and directing its comedy to something less dark.

There are enough tweaks and changes in gameplay and storytelling to make Portal 2 something else once you pass through the Portal gun and mouse lab intro. Portal 2 has many different mechanics and easier puzzles with several mechanics that are not present in the first game.

It is argued among fans that Portal 2’s puzzles are never fully fleshed out or explored to their limit, as it happens in the first game. Gameplaywise, this is when the games start feeling completely different. The first game extracts all it can from physics puzzles using the Portal Gun. In contrast, the second game introduces many things that change the rules and moves on to an entirely different mechanic right after.

Despite the fact that Portal 2 lacks the heavier tone of its predecessor, it is nonetheless a well-written game, but a different one, which is why both are on the list.

If you like the original Portal, there’s a good chance you’ll like Portal 2 as well. It makes no difference whether you think the first one is better than the second or vice versa. Both games are fantastic, and I’m sure that any PC puzzle games fan will have a blast playing either.

Braid is a puzzle-platformer where you rewind time to solve puzzles. It’s also one of those games that makes you feel really smart when you figure out how to beat it—which is exactly what we want from puzzle games.

There are tons of little details and secrets in Braid, and each level gets increasingly more complex as you progress through its complex, metaphorical story.

Braid is simple enough for almost anyone to play and understand at first but deep enough for hardcore players looking for challenging brain teasers with multiple levels of completion.

As the game progresses, the way your time rewind ability interferes with the world changes as new mechanics appear in the different phases of the game. Each world has a unique characteristic that is differently affected by time, time reward, or even by how you move your main character.

Due to those new concepts constantly being introduced, Braid ends up being an incredible experience that keeps you playing for hours.

When it comes to puzzle games, Limbo’s unique brand of hand-drawn black and white graphics stands out from its rivals. The game has players take control of a boy who must traverse hellish environments in search of his sister.

For a 2D platformer, Limbo’s atmosphere can be a bit dark. Limbo has levels that are filled with puzzles and obstacles for players to overcome, forcing them to use their brains instead of brute force.

It’s not the most challenging puzzle game out there, but it is entertaining enough to be remarkable. Although it was originally released in 2010, Limbo remains one of the top puzzle games on Steam.

Limbo is not a long game, but by playing through its world, you’ll see why so many people have fallen in love with it. Even if you’re not typically into puzzle games, I recommend giving Limbo a try; perhaps you’ll find yourself pleasantly surprised by what you discover.

Valiant Hearts: The Great War

Valiant Hearts: The Great War is a puzzle game set during World War I that follows several characters from different sides of the conflict.

The game features puzzles to solve with help from your canine companion and follow narratives based on real-life letters and journals of men and women who lived during that time.

It’s a heartfelt and touching adventure for people looking for a historical setting for their puzzle games or anyone curious about life in France during World War I.

This game is a beautifully crafted artistic expression of a harsh and difficult era of human history. Its story has a few ups and serious downs. It might not be for everyone, and it is a hard story to tell, but it’s told brilliantly.

World of Goo

World of Goo is a charming game with a simple but cute art style and an attractive enough. This award-winning physics-based puzzle game is a favorite among fans.

Players are tasked with creating bridges and towers out of balls of goo, guiding other balls to their goals, and escaping each level before they fall off. As you solve puzzles and make your way through increasingly challenging levels, you’ll be kept entertained by adorable sound effects and a minimalist aesthetic.

World of Goo is a game for kids as well as adults. It is easy to pick up but hard to put down. World of Goo was made by 2D Boy, an indie gaming duo consisting of Kyle Gabler and Ron Carmel. Its graphics were designed to resemble beloved construction toys, making the game both familiar and charming.

This is a fun game that can be pretty entertaining to play casually, but it can also be addictive if you’re fond of puzzle games on PC. Give it a shot; you might be surprised at how challenging and addicting it can be.

Baba is You

This game is so much fun! It may not look like it, but Baba Is You actually has some of the most mentally engaging gameplay in any puzzle game I’ve ever played. It’s a game that is constantly forcing you to think outside the box because the puzzles involve changing the fundamental laws of how the game works in the first place.

I know it sounds weird and a bit crazy, but that’s pretty much how the game is. The more you play, the more you want to see what kind of weird things you have to come up with to progress.

Even though Baba is You might be a really unusual game in many ways, you don’t really feel frustrated since every puzzle somehow feels doable. When it comes to unique puzzle gameplay, it’s hard to be as unique as Baba is You.

This is a fantastic game with an unusual concept that managed to work against all odds. I definitely recommend you to try this game out, even if you don’t like puzzle games just for their uniqueness.

That is a game that will easily please fans of the genre. Hoa is a puzzle-platforming game with a lot of personalities due to its emotionally charged music and hand-painted art style.

Hoa is the ideal game for when you want to be entertained by your favorite genre, but you also want to relax and admire a beautiful work of art as opposed to getting disappointed or frustrated after spending an hour on the same puzzle.

The world of the game is diverse and beautifully designed with breathtaking art. Besides, Hoa is relatively simple. The game’s mechanics are not complicated, so you get to enjoy it easily.

There’s no question that Hoa has a lot of charm and identity. This game is so captivating that it is nearly impossible not to give it a shot. That’s how they make people play, by causing them to check a beautiful, hand-drawn game. I checked Hoa out of curiosity, and I was hooked right from the start.

In my honest opinion, Biped is a game that does not receive as much attention as it deserves. This game is a puzzle-platformer with a lot of heart. Its cute design and fun gameplay are more than enough for me to recommend it. 

Biped’s unique gameplay mechanics make it very special. In this game, you must move each leg of the main character independently. That alone completely changes how you navigate the 3D environment and solve issues.

Even walking can be a struggle since you have to move each leg individually, one before the other. It might take you some time to get used to it, but that’s what allows this game to think outside the box and provide some of the greatest and most fun puzzles you’ll see in a cute puzzle game that doesn’t feel intimidating.

The Room is a BAFTA-winning 3D puzzler from Fireproof Games where you immerse yourself in a world of strange contraptions and alchemical machines. This game takes you to a setting where machines meet myth. You will follow a trail of cryptic cards and solve numerous unusual devices in even more extraordinary places.

The Steam version of The Room is a completely updated HD version of the original Mobile Version of The Room, but it still is the same game. I do prefer playing it on the PC anyway.

Fireproof Games is a tiny, independent studio based in Guildford, United Kingdom. The Room is the first game they ever published, but they made an excellent product. The Room has been very well received by puzzle game fans and reviewers, which did a lot for the game’s reputation and the studio.

There’s a reason why this game received so many prizes for best gameplay and best design. The Room has clearly been acknowledged among critics as a magnificent game of its genre.

Little Nightmares

Little Nightmares is surprisingly scary for a game that uses such a cartoon-like art style. You play as a kid in a yellow coat who’s trying to survive and escape from a massive and strange ship populated by corrupted souls vying for the next meal.

This is an unnerving dark tale that will cause nightmares to your inner child! Explore the most unsettling settings to uncover their secrets as you proceed on your trip. 

Mechanically speaking, Little Nightmares takes a lot from games like Limbo and modern survival games that have a hiding mechanic. Still, the way it’s used and the way that the setting is put together make Little Nightmare a quite well-executed game. It might not be the most challenging puzzle game out there, but if you like horror, it is undoubtedly worth your time.

Although this game is a brilliant puzzle platformer, its meaning, plot, and ending are mysteries open to interpretation. The many discussions and fan theories about Inside exist mainly due to the way that the game’s story is told, especially in its endings.

Inside is a puzzle platformer in which the player is a boy who explores a nearly gritty, nearly black-and-white world where there are many threads about to end his life.

The boy can run, jump, and use some objects to overcome certain challenges. Later in the game, the boy gains the ability to control the bodies of the dead. Sometimes, this new power can feel like a weirdly dark and somewhat disturbing idea.

Still, it does allow the game to introduce new and exciting mechanics and puzzles. The main character can die, much like in Limbo, from enemies and from challenges that you did not succeed in completing. Death animations are often brutal, making you feel like a lot is at stake after the first time you see it happening.

When it comes to puzzles, at least in my opinion, it isn’t easy to find anything that is more authentic than klocki. Something about its minimalistic style feels like old-school puzzle games, but there’s enough in its design to make it feel clean and modern.

In this game, you basically have a bunch of tiles or pieces, and you have to switch and match all those pieces in a way that the lines are not broken.

Klocki doesn’t repeat itself too much. However, it will sometimes introduce new ways to move the pieces and add variations that keep things interesting when there aren’t really new ideas to be introduced.

This is the second game from the developers of Hook, and it is pretty well rated on Steam. If you are okay with a minimalistic art style and a more relaxing kind of puzzle game, you should definitely give klocki a shot.

Opus Magnum

This game was very well received by critics and players. It is an open-ended puzzle game from Zachtronics.

In Opus Magnum, you do alchemical engineering by building transmutation machines that you even get to watch running.

I’m not going to lie; this is an odd game. For many people, this might feel like doing homework. On the other hand, once you get the hang of it and see your formula in action, you feel pretty smart for pulling it off.

Honestly, though, watching your design functioning is already super pleasant to see, but making it compact and faster is just as fun — for those who enjoy this sort of open-ended puzzle, of course.

Agent A: A Puzzle in Disguise

I seriously love self-aware games, so there was no way I wouldn’t like Agent A: A puzzle in disguise.

As the brilliant title suggests, you play as Agent A in this clever puzzle game. You are given the mission to invade Ruby La Rouge’s secret hideout. Once you succeed, you have to either neutralize or capture the enemy spy.

Once you have the chance or the patience, pay attention to this stylized art style. It allows the game to be functional and have an eye-catching theme. It also makes it much easier for smaller studios to put the game together than making or paying for something with high fidelity graphics.

Explore a maze of mind-blowing puzzles in this quirky cat-and-mouse game that will have you wondering who’s the cat and who’s the mouse! Did you find something strange or out of place? You must think like a good secret agent, so taking notes and mental observations will help you solve the most important puzzles.

In Ruby’s secret hideout, you will be picking up objects and using them in clever ways. Sometimes, you will have to think outside the box to progress through the puzzles that will get you closer to your target!

Superliminal

If you are looking for the most original puzzle game on Steam, I couldn’t find anything that remotely feels like what Superliminal has to offer.

This puzzle game focuses on using optical illusions and depth perspective to make the most unique and clever puzzles I have ever seen in a long time.

When I solve a puzzle in Superliminal, I often catch myself just thinking about how cool that puzzle was. The best thing about this game is that it keeps happening. It never takes too long for the game to surprise me with another fantastic twist on how to use depth perspective in the game’s context.

In the world of Superliminal, what is perceived is what is real. This game’s surreal, strange, dream-like world is like a weird place where things can be both what they are and what they seem to be.

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Beast Bounty: Go 17+

Oksana voloshkova, designed for iphone.

• 1.7 • 6 Ratings

iPhone Screenshots

Description.

Certainly! Here's a description that focuses more on the overall gameplay: Welcome to "Beast Bounty: Go", a puzzle adventure where you'll challenge your logic and problem-solving skills! Explore a world filled with intricate image puzzles that will test your mind while providing relaxation and fun. Start your journey with an engaging preloader, then navigate through the user-friendly menu to access the game's key features. Choose from a captivating selection of images to piece together at your own pace. As you solve puzzles, uncover hidden parts of beautiful images while tracking your progress with the helpful progress bar. Customize your gameplay by adjusting sound and music to create the perfect atmosphere. Whether you're a seasoned puzzle enthusiast or just starting, "Beast Bounty: Go" offers a unique and challenging experience, with stunning visuals and soothing soundscapes that will make you want to play again and again!

Version 1.3

Hello! We added a new image for puzzle and update policy for a policy view. Also check updated screenshots. Update app and have more fun!

Ratings and Reviews

Don’t use app will scam you gambling app you have several methods to deposit money , once you try to withdrawal you can’t. App makes it seems like you win money on the slot machines but can’t no withdrawal only deposit

After I complete the puzzle, then what?

This is fake. Not associated with Mr Beast whatsoever. Do not download.

App Privacy

The developer, Oksana Voloshkova , indicated that the app’s privacy practices may include handling of data as described below. For more information, see the developer’s privacy policy .

Data Used to Track You

The following data may be used to track you across apps and websites owned by other companies:

Data Not Linked to You

The following data may be collected but it is not linked to your identity:

Privacy practices may vary, for example, based on the features you use or your age. Learn More

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