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Questions tagged [game]

A puzzle that asks for determining the winner in a multi-player game.

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7 votes
1 answer
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More Catching of Cats

After my first puzzle on this theme was solved relatively quickly, here is a (trickier) follow up question in the same vein! The setup is similar - you are in a room with an infinite line of boxes, ...
Tim Seifert's user avatar
  • 2,398
19 votes
4 answers
2k views

Catching a Cat on an infinite Line

Upon entering a (very) large room, you are faced with an infinite line of cardboard boxes that are labeled, in order, by the nonnegative integers. In one of these boxes, a cat is hiding, but you do ...
Tim Seifert's user avatar
  • 2,398
10 votes
2 answers
382 views

The game of 42: 10 cards to make 42

This is a game inspired by other recent questions. It is a 2-player game. The game is played with 10 cards numbered 1 to 10 and 2 positions or stacks. The game starts with all cards in stack 1. The ...
Florian F's user avatar
  • 30.8k
20 votes
3 answers
2k views

Winning chance in coins game with fixing

A player plays the following solitaire game. The game consists of as many rounds as are needed to produce a result. They have 20 fair coins, which may in any round be live or fixed; each coin starts ...
Rosie F's user avatar
  • 8,692
17 votes
2 answers
2k views

Making a 2n-digit number divisible by 9

Alice and Bob play the following game, taking turns. Alice starts and writes a digit from the set M={1, 2, 3, 4, 5, 6} at the blackboard. Bob appends another digit from the set M until a 2n-digit ...
ThomasL's user avatar
  • 12.3k
9 votes
3 answers
453 views

The Kyiv Triangle Game

There are a number of triangles of various sizes in the figure below whose three vertices are among the vertices and edges on display. Two players, Alice and Bob, take turns coloring with their own ...
Bernardo Recamán Santos's user avatar
9 votes
1 answer
3k views

Two-Move Chess Game

Consider a standard game of chess. We make the following modification: on a turn, if a player makes a move which neither captures a piece nor puts their opponent’s king in check, then they may make a ...
godlification's user avatar
2 votes
1 answer
193 views

Pursuit-evasion game [closed]

A criminal has been spotted along a straight single-filed road of length $L$ at position $P$, measured from the left endpoint of the road! Two police officers arrive to the road at positions $A$ and $...
Kevin's user avatar
  • 39
2 votes
2 answers
369 views

Press The Grue Button

[This puzzle is inspired by the webpage https://apparenthorizons.com/2017/10/12/the-grue-problem-and-deep-learning/] 55 workers have got a chance to double their pay, as said by their boss. So, the ...
3-1-4-One-Five's user avatar
1 vote
5 answers
584 views

A question from Bob to Bob

Set-up: John and Bob are playing a game that goes like this: Bob is alone in a completely opaque, featureless room. Bob chooses a question, though some types of questions are off-limits, which will ...
user110391's user avatar
4 votes
1 answer
737 views

Don't let 'em die!

There is an 8x8 array of sleeping humans with ten feet between adjacent humans, with sides in the four cardinal directions. A hero and a villain start ten feet west of the northwest human. The hero ...
mathlander's user avatar
  • 1,261
7 votes
1 answer
224 views

Prime Boggle Game

Two players, Alice and Bob, take turns in identifying and circling prime numbers in this 8 x 8 board of digits. Primes must be read as continuous string of digits, either horizontally (from left to ...
Bernardo Recamán Santos's user avatar
18 votes
1 answer
601 views

Game of the glasses on the windowsill

The windowsill above the sink is where my wife and I place our dirty wine glasses. And while both of us love each other, neither of us love loading the dishwasher. As a result, these dirty glasses ...
Feryll's user avatar
  • 2,389
1 vote
1 answer
115 views

Zigzag nim game [duplicate]

I'm trying to figure out a strategy for the following nim: here the rules are that you choose a new position on the path $1$,$2$, or $3$ nodes forward. The other player does the same. Neither player ...
Louie's user avatar
  • 153
11 votes
2 answers
475 views

Bigger number (sometimes) wins

Two players play the following game: Each player writes down a whole number between 0 and 100 on a slip of paper, then the players simultaneously reveal their choices. If the difference between the ...
Julian Rosen's user avatar
  • 14.3k
26 votes
2 answers
4k views

Any fans of The Big Bang Theory?

Penny, Sheldon, Howard and Leonard are chilling. Sheldon comes up with an idea to play a dartboard game. Like always, he has his own rules. He brings a weird dartboard from his room, sets the bullseye ...
Techidiot's user avatar
  • 18.9k
7 votes
1 answer
811 views

Optimal Strategy: Catch Up

There are 5 Quisenaire blocks. The first has length 1, the second has length 2, and so on. Each player will be building their own line of blocks, which is initially empty. A move consists of a player ...
PuzzleAndy's user avatar
4 votes
1 answer
1k views

The "Slightly Spooky Sequence" Game

Two players, Alice and Beatrice, having previously agreed on a positive integer N (say 30) as a limit, take turns to write a sequence of positive integers. In the first turn Alice writes 1. Thereafter,...
Bernardo Recamán Santos's user avatar
5 votes
1 answer
264 views

Who wins this game of graphs?

Albert and Bob are playing a game. This time it works like this: there are n points and Albert can ask whether or not $2$ points are connected. Bob then decides whether or not the points are connected....
NielIGuess's user avatar
  • 1,024
13 votes
3 answers
1k views

Who wins this game?

A 2-player game depends on two positive integers n and k known in advance to both participants. Albert has a secret number from 1 to n. Bob asks Albert a sequence of "yes" or "no" ...
NielIGuess's user avatar
  • 1,024
11 votes
1 answer
1k views

Pigpen Tic-Tac-Toe

This puzzle is part of the Monthly Topic Challenge #3: Pencil and Paper Games Introducing a new tic-tac-toe variant of my own devising (at least I haven't found an equivalent anywhere online). ...
Stiv's user avatar
  • 146k
13 votes
2 answers
812 views

Decision Paralysis

This puzzle is part of the Monthly Topic Challenge #1: Restricted Title: xkcd 1xxx and is based on https://xkcd.com/1801/. Protip: If you ever need to defeat me, just give me two very similar options ...
noedne's user avatar
  • 15.4k
1 vote
1 answer
122 views

The best way to place circles into a square [duplicate]

Given a square of side length as least 2, there are two players who must in turn place a unit radius circle into the square without overlapping any previously placed circle. The loser is the first ...
Simd's user avatar
  • 7,845
16 votes
4 answers
3k views

The Game of Barranca

Barranca is played with sixteen cards, numbered 1, 2, ... , 16. Two players alternately choose a card, until each has eight. The winner is the one who has a (sub)set of numbers whose product is 220, ...
Bernardo Recamán Santos's user avatar
21 votes
9 answers
3k views

Catch the invisible and omniscient thief

The thief has stolen two powerful artifacts: the Cloak of Invisibility and the Glasses of the Oracle. Now they're equipped with both. The cop at the bottom, not knowing where the thief is, is trying ...
Eric's user avatar
  • 6,536
2 votes
1 answer
275 views

No-Luck Riomino

Kris Burm's Riomino (or Tashkent Domino) is played with 25 identical dice that look like this: The actual rules are as follows. Each player rolls 12 dice that then serve as their "dominos" ...
Parcly Taxel's user avatar
  • 7,820
6 votes
2 answers
386 views

Board game: Risk (two players)

Consider a game of two players: Player A and Player B. Each of them is assigned with the same number of soldiers. There is a battlefield (like a board game) with 7 tiles numbered 1 through 7 (a single ...
Amira's user avatar
  • 161
9 votes
1 answer
315 views

Be Paired or Be Square

8 white and 8 black dots are drawn on a piece of paper. Parcly and Tori take turns drawing edges, always between white and black dots not already adjacent (so the graph is always bipartite); the first ...
Parcly Taxel's user avatar
  • 7,820
3 votes
1 answer
253 views

Harary's generalized Tic-Tac-Toe; Winning strategy for Skinny on a 7 x 7 board?

Disclaimer: The purpose of this post is a ask question, not to offer a puzzle. Still, there are some puzzles here for the reader's pleasure. Disclaimer 2: This question was also asked on Math Stack ...
Mike Earnest's user avatar
  • 32.5k
9 votes
2 answers
538 views

Form an equilateral triangle

Alice and Bob take turns to mark points in $\mathbb{R^2}$ (i.e. infinite 2D plane). Alice can only mark $1$ point on her turn, while Bob can mark $4$ points. They're free to mark their points anywhere ...
Eric's user avatar
  • 6,536
15 votes
2 answers
947 views

Can Alice form a unit square?

Alice and Bob take turns to mark points in $\mathbb{R^2}$ (i.e. infinite 2D plane). Alice can only mark $1$ point on her turn, while Bob can mark $N$. They're free to mark their points anywhere as ...
Eric's user avatar
  • 6,536
0 votes
2 answers
401 views

Pokemon battle puzzle: Chansey vs Wobbuffet

This is a 1v1 battle between two pokemons: Chansey vs Wobbuffet. Your task is to analyze the battle and predict its outcome. Information about the battle: The battle takes place in Generation III. ...
WhatsUp's user avatar
  • 7,405
9 votes
1 answer
916 views

Removing coins from a pile depending on the previous move

Alice and Bob play a game taking turns. There is one pile of $n\geq2$ identical coins on a table. Alice starts and with her first move she takes away at least one coin from the pile, but not all of ...
ThomasL's user avatar
  • 12.3k
5 votes
2 answers
1k views

The Game of MIM

In the game of MIM, each of two players, Alice and Bob, receive a board as shown below: They are then dealt in turns one card from a shuffled set of cards numbered 0 through 9 which they must ...
Bernardo Recamán Santos's user avatar
4 votes
0 answers
203 views

Police and Thieves

I played this game when I was young, but cannot find it online. It is played on a checkers board (e.g. the black squares of a chess board) between two players P and T. The game goes as follows: P ...
user21820's user avatar
  • 1,236
7 votes
0 answers
295 views

Who wins the game of "Sticky Gomoku" on an infinite board?

This is a Gomoku like game, played by two players with Go pieces (black and white stones) on an infinite (in all four directions) Go board. Rules Four in a row: players alternate turns placing a ...
Eric's user avatar
  • 6,536
19 votes
1 answer
2k views

Blindfold Tic-Tac-Toe

You are playing the classic game of 3x3 Tic-Tac-Toe. You are blindfolded and you cannot see the grid, while your opponent can see it. When making a move you call out a cell. If that cell is taken you ...
Dmitry Kamenetsky's user avatar
10 votes
2 answers
559 views

How should you distribute the fighting power?

Alice and Bob both have N warriors under their command, numbered 1~N, and $1$ point of fighting power at their disposal. Before the game, they privately distribute the power between their warriors. ...
Eric's user avatar
  • 6,536
8 votes
1 answer
322 views

Survive the infinite zombie attack II

Zombies are back again. Same as last time, You're at the origin, and zombies occupy the points $(100𝑖,100𝑗)$ for all integers $𝑖,𝑗$ except the origin, as shown below: The ratio of your speed to ...
Eric's user avatar
  • 6,536
4 votes
2 answers
344 views

Even and odd game variant

You are playing a game with your friend on a $7$x$7$ grid board. In every turn, you begin by putting a $0$ (zero) on any empty square on the board, and then your friend puts a $1$ (one) on a different ...
Hemant Agarwal's user avatar
2 votes
1 answer
194 views

Adding up divisors of integers

Alice and Bob play a game, taking turns. Alice starts and writes an integer between 1 to 10 on a blackboard. Then Bob adds any integer between 1 to 10 to this number and writes it on the blackboard. ...
ThomasL's user avatar
  • 12.3k
13 votes
3 answers
1k views

Making a 10 digit number divisible by 3

Alice and Bob play the following game, taking turns. Alice starts and writes a single digit from 0 to 9 at the blackboard. At every turn, each player adds a single digit at the right of the current ...
ThomasL's user avatar
  • 12.3k
2 votes
1 answer
417 views

1 lion, with a zebra and a fixed enclosure

Background See the puzzle Variant of lion and 100 zebras from @ghosts-in-the-code which remains unsolved years after it was posted. Several times in the last couple of years I've started to write up ...
Steve's user avatar
  • 3,885
21 votes
3 answers
3k views

Making a 9 digit number divisible by 11

Alice and Bob play the following game, taking turns. Alice starts and writes a non-zero single digit number at the blackboard. At every turn, each player adds a single digit at the right of the ...
ThomasL's user avatar
  • 12.3k
-1 votes
1 answer
290 views

The Box of Tic-Tacs

You were kidnapped and had no way of escape. The kidnapper opens the lights, and in front of you is an opened box of Tic-Tacs. He claims that he ate from 0-5 Tic-Tacs, (with 60 from the newly-bought ...
tdserapio's user avatar
1 vote
1 answer
236 views

Catch the fugitive

The fugitive is at the origin. He moves at a speed of 100. You have a guard at every integer coordinate except the origin. A guard's speed is 1. The fugitive and your guards move simultaneously and ...
Eric's user avatar
  • 6,536
21 votes
3 answers
3k views

Can you survive this infinite zombie attack?

You're surrounded by infinitely many zombies. You're at the origin, and zombies occupy the points $(100i,100j)$ for all integer $i, j$ except the origin, as shown below: You and the zombies move ...
Eric's user avatar
  • 6,536
11 votes
1 answer
785 views

Who will win in a game of writing 3 consecutive Xs on a 2022 × 1 board?

Ana and Bob alternately write Xs on a 2022 × 1 board. The winner is the one who makes 3 consecutive Xs. Who has the winning strategy if Ana plays the first move? Describe such a strategy.
nonuser's user avatar
  • 890
7 votes
2 answers
521 views

One vs many. Can white force a draw?

On an infinite chessboard there's a single white king and N black kings. The nearest black king must be K moves away from the white king. Given N, white dictates the value of (finite) K, then black ...
Eric's user avatar
  • 6,536
7 votes
2 answers
376 views

Can the fugitive escape?

A fugitive is surrounded by N police officers, with the nearest one at distance 1 away. The fugitive and the officers move alternatively. In a fugitive move, the fugitive can travel no more than a ...
Eric's user avatar
  • 6,536

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