Questions tagged [game]
A puzzle that asks for determining the winner in a multi-player game.
260
questions
12
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" ...
- 353
10
votes
1
answer
889
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).
...
- 106k
13
votes
2
answers
744
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 ...
- 15.3k
0
votes
1
answer
237
views
What is this card matching game/trick?
As a kid I used to do this card game/trick a lot but I can’t remember what it is or how to do it anymore. All I remember is that it used math or counting. You had a certain amount of cards sort of ...
- 1
1
vote
1
answer
109
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 ...
- 5,328
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, ...
- 14.9k
20
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 ...
- 5,187
2
votes
1
answer
161
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" ...
- 3,918
5
votes
2
answers
327
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 ...
- 151
8
votes
1
answer
291
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 ...
- 3,918
2
votes
1
answer
128
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 ...
- 31.5k
8
votes
2
answers
490
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 ...
- 5,187
9
votes
0
answers
448
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 ...
- 5,187
1
vote
1
answer
292
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.
...
- 7,149
9
votes
1
answer
841
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 ...
- 11.6k
4
votes
2
answers
250
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 ...
- 14.9k
4
votes
0
answers
164
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 ...
- 1,085
7
votes
0
answers
273
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 ...
- 5,187
18
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 ...
- 26.8k
10
votes
2
answers
526
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. ...
- 5,187
8
votes
1
answer
302
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 ...
- 5,187
4
votes
2
answers
319
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 ...
- 1,552
2
votes
1
answer
176
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.
...
- 11.6k
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 ...
- 11.6k
2
votes
1
answer
325
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 ...
- 3,805
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 ...
- 11.6k
-1
votes
1
answer
268
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
219
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 ...
- 5,187
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 ...
- 5,187
1
vote
1
answer
81
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
773
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.
- 870
4
votes
0
answers
269
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 ...
- 5,187
7
votes
2
answers
345
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 ...
- 5,187
6
votes
1
answer
1k
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,...
- 63
4
votes
1
answer
222
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
842
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 ...
- 5,187
6
votes
1
answer
353
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 ...
- 69
4
votes
1
answer
207
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 ...
5
votes
1
answer
254
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 ...
6
votes
1
answer
273
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 ...
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 ...
- 6,589
9
votes
2
answers
462
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: ...
- 5,187
6
votes
2
answers
260
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 ...
- 511
7
votes
1
answer
280
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 ...
- 5,141
1
vote
0
answers
494
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 ...
- 736
16
votes
2
answers
700
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 ...
- 1,838
10
votes
2
answers
633
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 ...
- 6,589
18
votes
1
answer
589
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 ...
- 6,589
6
votes
2
answers
266
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, ...
user69519
5
votes
2
answers
359
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 ...
- 5,187