Questions tagged [game]
A puzzle that asks for determining the winner in a multi-player game.
242
questions
10
votes
2answers
495 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. ...
8
votes
1answer
280 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 ...
4
votes
2answers
305 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
votes
1answer
163 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.
...
12
votes
2answers
980 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 ...
1
vote
1answer
275 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 ...
20
votes
3answers
2k 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 ...
-2
votes
1answer
250 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 ...
1
vote
1answer
197 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 ...
21
votes
3answers
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 ...
1
vote
1answer
76 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 ...
9
votes
1answer
749 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.
4
votes
0answers
229 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 ...
7
votes
2answers
321 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
votes
1answer
507 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,...
4
votes
1answer
206 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 ...
12
votes
3answers
780 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
votes
1answer
308 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 ...
4
votes
1answer
179 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
1answer
241 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
1answer
262 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
2answers
257 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 ...
9
votes
2answers
417 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: ...
6
votes
2answers
239 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 ...
7
votes
1answer
252 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 ...
2
votes
0answers
300 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 ...
16
votes
2answers
673 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 ...
8
votes
2answers
525 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 ...
18
votes
1answer
552 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 ...
5
votes
2answers
241 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, ...
5
votes
2answers
338 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 ...
7
votes
1answer
247 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 ...
8
votes
1answer
262 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, $x$ (...
8
votes
5answers
554 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 ...
13
votes
2answers
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 ...
1
vote
3answers
151 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 ...
13
votes
3answers
483 views
Equal distribution of coins to pirates
Ten pirates are sitting around a table. Each of them has an even number of coins.
At order of the captain, each pirate passes half of his coins to the neighbor to the right. After that round, each ...
9
votes
1answer
469 views
99 numbers on the blackboard
The numbers 1,2,3, ..., 99 are written on the blackboard. Alice and Bob play the following game, taking turns. Alice starts.
At every turn, each player removes one number until two numbers are ...
0
votes
0answers
338 views
A Logician's Game of UNO Flip
Two players are in the middle of an ongoing one-on-one game of UNO Flip, with all its standard rules in effect.
Play is currently Light Side Up. It is Player B's turn. Player A has 3 cards remaining, ...
8
votes
2answers
577 views
How many people are there?
This is a variation of an old puzzle.
The game starts with several people sitting in a circle, everyone facing the back of another person. They are all wearing blind folds, so nobody can see anyone ...
23
votes
11answers
10k views
The 100 soldier problem
I saw this problem many years ago. I am sure many puzzlers will know its original name. I was reminded of it when reading about Conquering of Regions problem. A Strategy Game Involving Conquering of ...
7
votes
2answers
532 views
Marbles on a Mancala Board
I would like to introduce an ancient African board game I've just invented.
Until someone comes up with a better name, it's called Marble Mancala.
The rules are pretty simple:
There are two ...
7
votes
2answers
1k views
Alice and Bob play at cards
To pass the time Alice and Bob play a simple game of chance where cards are drawn in pairs from a shuffled standard 52-card deck. If two red cards are drawn Alice wins the round. If two black cards ...
6
votes
2answers
171 views
Positioning cards labeled with numbers from 0-9
Ann and Bob play a game. On a table there are 10 cards which are labeled with number from 0 to 9 each. Bob is allowed to change the position of the cards with a sequence of his preference. When he is ...
5
votes
2answers
156 views
A pile of chips involving powers of 2
Ann and Bob play alternately on a pile of chips. On each play, any number of chips, which is a power of 2 (including 1=$2^0$), can be removed from the pile.
Obviously the number of chips to be removed ...
6
votes
1answer
199 views
A pile of chips involving primes
Ann and Bob play alternately on a pile of chips. On each play, either 1, 2 or 3 chips can be removed except if the number of chips is a prime number. In that case either 1, 2, 3, 4 or 5 chips can be ...
8
votes
1answer
360 views
Grid puzzle solutions
I have a simple grid puzzle:
Example:
| X | Y | X |
| Y | X | Y |
| Y | X | Y |
The move is defined as a row or a column move. So when you move one cell, ...
17
votes
1answer
414 views
Masyu-making game
Two players are playing a game on a $4\times4$ board. The players take turns adding either a white circle or a black circle into any empty square, so that the board makes a solvable masyu puzzle (with ...
7
votes
1answer
280 views
Game Night at the Binomial Elks Club
The Binomial Elks Club, being predominantly composed of ambitious and competitive personalities, often held game nights in which members enjoyed battling each other for high stakes and bragging rights....
10
votes
1answer
356 views
Reverse dots and boxes – Guess the last move
Alice and Bob are playing a game of reverse dots and boxes.
The players take turns adding one horizontal or vertical line of size 1 in one free spot on the grid (marked with light gray lines ...