Questions tagged [game]

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

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15 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, ...
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19 votes
9 answers
2k 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 ...
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2 votes
1 answer
137 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" ...
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  • 3,621
5 votes
2 answers
308 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 ...
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  • 51
6 votes
1 answer
281 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 ...
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  • 3,621
2 votes
1 answer
103 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 ...
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8 votes
2 answers
474 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 ...
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9 votes
0 answers
421 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 ...
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1 vote
1 answer
280 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. ...
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  • 6,402
9 votes
1 answer
830 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 ...
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  • 11.5k
4 votes
2 answers
224 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 ...
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4 votes
0 answers
160 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 ...
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  • 1,044
7 votes
0 answers
264 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 ...
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  • 3,979
17 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 ...
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10 votes
2 answers
514 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. ...
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  • 3,979
8 votes
1 answer
298 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 ...
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  • 3,979
4 votes
2 answers
317 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 ...
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2 votes
1 answer
175 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. ...
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  • 11.5k
12 votes
2 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 ...
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  • 11.5k
2 votes
1 answer
318 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 ...
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  • 3,797
20 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 ...
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  • 11.5k
-1 votes
1 answer
261 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 ...
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1 vote
1 answer
215 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 ...
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  • 3,979
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 ...
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  • 3,979
1 vote
1 answer
79 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 ...
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10 votes
1 answer
769 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.
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  • 860
4 votes
0 answers
253 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 ...
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  • 3,979
7 votes
2 answers
339 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 ...
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  • 3,979
5 votes
1 answer
697 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,...
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4 votes
1 answer
217 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 ...
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  • 143
12 votes
3 answers
822 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 ...
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  • 3,979
6 votes
1 answer
347 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 ...
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4 votes
1 answer
198 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 ...
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5 votes
1 answer
251 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 ...
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6 votes
1 answer
269 views

Summing numbers and then increasing used numbers

I was making a mathematical game (viewable here: www.michaelprimo.it/beta) where you have a 3x3 grid, one central yellow button with a generated number and the other eight blue buttons with clickable ...
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3 votes
2 answers
262 views

Social Distancing L-Game

This is a variation of Edward De Bono’s famous L-game, but played on a 5x5 board (instead of 4x4) with social distancing rules in place. More specifically, two players (Blue and Orange) take turns ...
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  • 6,549
9 votes
2 answers
447 views

Three way duel, which guns to choose?

Alice, Bob and Carole are involved in a game of three way duel. They take turns to shoot in the order of Alice-Bob-Carole-Alice-... until only one surviver is left standing. The rule is very simple: ...
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  • 3,979
6 votes
2 answers
250 views

Recreational checkers problem

Alberto places N checkers in a circle. Some, perhaps all, are black; the others are white. (The distribution of colors is random.) Betiil places new checkers between the pairs of adjacent checkers in ...
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7 votes
1 answer
275 views

A mix of 2048 and Match 3

I was playing a game and thought of this problem: Rules There are 4 distinct tiles on a $6\times6$ grid. The game starts out with one block on the board. You can shift all the tiles in one of the ...
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  • 5,131
1 vote
0 answers
438 views

How do you force a win in 4x4x4 TicTacToe

I have read in the wikipedia page of TicTacToe that it is possible for the first player to force a win in a 4x4x4 board. I tried to find a strategy on how to do it online but failed. So, how do you ...
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  • 736
16 votes
2 answers
690 views

Topological Nim

You and your friend's new favorite game is "topological nim": You take your favorite compact metric space $X$ and a radius $r$. Each player removes an open disk of radius $r$ from the space ...
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  • 1,758
10 votes
2 answers
628 views

Buzzword Bingo Boss Battle!

Two bosses of different companies take turns delivering long speeches. Every speech much “claim” at least one unused square by uttering the corresponding buzzword(s) in the table below. Victory is ...
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  • 6,549
18 votes
1 answer
571 views

Noughts and Crosses puzzle

Eques and Knott are playing a game of standard 3x3 Noughts and Crosses. At no stage of the game has Eques threatened to complete a row of three on his very next turn. Suddenly Knott realises he must ...
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  • 6,549
6 votes
2 answers
260 views

Simple game of dice - what is the optimal strategy?

The game is pretty simple, whoever reaches 50 first wins, but there are a few important details: 2 players, one die. Players take turns. Rolled values are simply added up If you roll a 6, however, ...
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5 votes
2 answers
352 views

Achieve the best outcome by a tactical statement

This puzzle is taken from Schelling's Game Theory: How to Make Decisions by R.V. Dodge, in which bargaining power is gained, paradoxically, by burning bridges and removing options for oneself. Here it ...
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  • 3,979
6 votes
1 answer
264 views

The sadistic chieftain and the lethal truel game

In an adventure to a remote island, you get caught by the xenophobic locals and are about to be executed. But the tribe chieftain, known for his sadistic taste, suddenly changes his mind. "I'll ...
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  • 3,979
8 votes
1 answer
269 views

Ways to destroy a Square Matrix [closed]

Sherlock is solving a case where he came across a puzzle. Suppose you are given a square matrix of size $N$, and a gun with Power $F$. Every cell in the matrix is filled with some number, $x$ (...
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8 votes
5 answers
577 views

Which gun is Alice's best choice?

Alice, Bob and Charles are involved in a deadly three way duel game. Before the game starts, the referee prepares three guns for the players to choose from. She randomly picks three guns from a very ...
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  • 3,979
14 votes
2 answers
1k views

Who would be the first to defeat an abundant number?

Rupert and Jenny are playing a game. Each player's score starts out as the number $94083986096100$, which is the square of the product of the first 8 primes and therefore has a lot of divisors. We'll ...
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  • 2,306
1 vote
3 answers
154 views

playing "Coins on a table" against a distracted friend [duplicate]

This puzzle is a follow-up of Coins on a table (warning: the link contains the answer to the original question). You are playing a game against your friend Alice: first Alice places one coin on a ...
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