Questions tagged [game]
A puzzle that asks for determining the winner in a multi-player game.
271
questions
2
votes
1
answer
171
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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 $...
- 21
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votes
2
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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 ...
- 557
1
vote
5
answers
528
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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 ...
- 312
4
votes
1
answer
710
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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 ...
- 803
7
votes
1
answer
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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 ...
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1
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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 ...
- 2,349
1
vote
1
answer
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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 ...
- 153
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votes
2
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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 ...
- 14.2k
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votes
2
answers
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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 ...
- 18.9k
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votes
1
answer
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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 ...
- 689
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votes
1
answer
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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,...
- 16.9k
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1
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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....
- 1,004
13
votes
3
answers
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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" ...
- 1,004
11
votes
1
answer
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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).
...
- 133k
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votes
2
answers
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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 ...
- 15.4k
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vote
1
answer
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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 ...
- 6,910
16
votes
4
answers
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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, ...
- 16.9k
21
votes
9
answers
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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 ...
- 6,354
2
votes
1
answer
228
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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" ...
- 6,996
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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 ...
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1
answer
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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 ...
- 6,996
3
votes
1
answer
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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 ...
- 32.1k
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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 ...
- 6,354
15
votes
2
answers
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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 ...
- 6,354
1
vote
2
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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.
...
- 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 ...
- 11.9k
5
votes
2
answers
560
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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 ...
- 16.9k
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 ...
- 1,115
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answers
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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 ...
- 6,354
19
votes
1
answer
2k
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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 ...
- 33.2k
10
votes
2
answers
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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. ...
- 6,354
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votes
1
answer
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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 ...
- 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 ...
- 2,818
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.
...
- 11.9k
13
votes
3
answers
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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 ...
- 11.9k
2
votes
1
answer
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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 ...
- 3,845
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votes
3
answers
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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 ...
- 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 ...
- 11
1
vote
1
answer
232
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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 ...
- 6,354
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votes
3
answers
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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 ...
- 6,354
1
vote
1
answer
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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 ...
- 11
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.
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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 ...
- 6,354
7
votes
2
answers
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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 ...
- 6,354
6
votes
1
answer
2k
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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,...
- 63
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 ...
- 143
12
votes
3
answers
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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 ...
- 6,354
6
votes
1
answer
371
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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 ...
- 69
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votes
1
answer
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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 ...
5
votes
1
answer
261
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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 ...
