Questions tagged [game]

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

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2 votes
1 answer
171 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
  • 21
2 votes
2 answers
332 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 ...
HelloWorld's user avatar
1 vote
5 answers
528 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
710 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
7 votes
1 answer
207 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
16 votes
1 answer
563 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
  • 2,349
1 vote
1 answer
109 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
444 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
  • 14.2k
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
807 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
665 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
260 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
  • 1,004
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
  • 1,004
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
  • 133k
13 votes
2 answers
797 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
116 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
  • 6,910
16 votes
4 answers
2k 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
  • 6,354
2 votes
1 answer
228 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
  • 6,996
6 votes
2 answers
364 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
312 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
  • 6,996
3 votes
1 answer
206 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
  • 32.1k
9 votes
2 answers
526 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
  • 6,354
15 votes
2 answers
924 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
  • 6,354
1 vote
2 answers
383 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
  • 7,357
9 votes
1 answer
875 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
  • 11.9k
5 votes
2 answers
560 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
192 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
  • 1,115
7 votes
0 answers
292 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
  • 6,354
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
539 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
  • 6,354
8 votes
1 answer
313 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
  • 6,354
4 votes
2 answers
339 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
185 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
  • 11.9k
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
  • 11.9k
2 votes
1 answer
395 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
  • 3,845
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
  • 11.9k
-1 votes
1 answer
280 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
232 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
  • 6,354
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
  • 6,354
1 vote
1 answer
83 views

All bracket results from final places in tournament [closed]

32 players are participating in a tournament. It's a knockout tournament, so it looks a lot like March Madness. You want to know how all the games went. The problem is that you only know the rankings ...
Poultryghast's user avatar
11 votes
1 answer
781 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
  • 880
4 votes
0 answers
289 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
  • 6,354
7 votes
2 answers
359 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
  • 6,354
6 votes
1 answer
2k views

Best strategy for stick-taking game

Rules of the game: It's a two player game. Moves will alternate between players. There are N sticks on a table. A value M is defined at the start of the game such that 2 < M <= N. On their turn,...
john chakder's user avatar
4 votes
1 answer
235 views

Winning strategy in game

Context: I played this game at one point (and lost) and now I'm wondering whether it was possible to win or not. We have a hexagonal board like this: I'm defining the following terms: Each hexagon ...
Righter's user avatar
  • 143
12 votes
3 answers
884 views

Outmaneuver your opponents in the duel

A, B and C are in a three way duel. Starting with A, they rotate in the order of A-B-C, each firing one shot at a time. They stand close to one another, so that each can kill one of the others or ...
Eric's user avatar
  • 6,354
6 votes
1 answer
371 views

Two players alternately name dates

Two players alternately name dates. The winner is the player who names 31st December, and the starting date is 1st January. If a player names Xst of Y Month, the other player can name the first of the ...
vamshika's user avatar
4 votes
1 answer
234 views

Wooden puzzle/game - 16 dowels with five wooden balls with holes each

I acquired a wooden puzzle game from a local thrift store. They had no information about it. Here's a description: In a wooden board base are mounted 16 dowels on each of the dowels are 5 wooden balls ...
William Haigney's user avatar
5 votes
1 answer
261 views

Playing tic-tac-toe by submitting your moves in advance

Suppose that, instead of playing in your turn, you have to submit in advance, an ordered list of the 9 board positions. Then a computer plays for you by using, whenever it is your turn, the leftmost ...
Erel Segal-Halevi's user avatar

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