Questions tagged [game]

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

242 questions
Filter by
Sorted by
Tagged with
803 views

2 bishops versus a lone king

There are 4 pieces on the board, the white and black kings, as well as 2 white bishops (on differently colored squares). The only way a stalemate occurs is if the black king is not in check, but ...
730 views

Connect 4 Recursive

Here is a variant of the standard connect 4. There are seven connect 4 grids (size 6 by 7) numbered 1 to 7. Each grid has the columns numbered 1 to 7. The person who starts selects any one of the ...
888 views

A Game with Strings and Coins

Alice and Bob play a game using the following arrangement of coins, which are joined by strings and hanging from the ceiling: $\qquad\qquad\qquad\qquad\quad$ The two alternate turns, with Alice ...
417 views

Jewels in the box

Professor Egghead participates today in a local game show. There are six jewels (a diamond, an emerald, a moonstone, a ruby, a sapphire, and a topaz), and there are six boxes that carry the numbers 1,...
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 ...
843 views

A Strategy Game Involving Conquering of Regions

This is a game that I saw in a book long ago. Unfortunately I cannot find the book now, and even if I can as I recall it does not provide a strategy. I will be very grateful if you can provide me a ...
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....
318 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 ...
250 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 ...
244 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 ...
771 views

Block the snake

On a $9\times10$ checkerboard with $90$ squares, a game proceeds as follows: First, you place $x$ rocks on the board. Each rock occupies a single square. No rock may touch the edge of the ...
1k views

What is the smallest tic-tac-toe board to have a winning strategy?

There is not winning strategy for 9cell 3x3 board. There is a winning strategy for 16cell 4x4 board, or even for 10cell "3x3 + 1_cell_near_a_corner" board (see M.Gardner "Mathematical games"):  \...
517 views

521 views

Placing dominoes on a 3x100 checkerboard

Alice and Bob play a game by alternately placing dominoes on a $3\times100$ checkerboard (3 rows, 100 columns). Alice has the first move. A move of Alice consists in placing a $1\times2$ (horizontal) ...
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 ...
596 views

Unsportsmanlike Aliens

It was the first meeting of the humans and the aliens, and things were going well: The humans and aliens had learned to understand each other's language and found that both were hoping for a peaceful ...
309 views

The Diamond Game [duplicate]

Barkeep: Well hello there, come to play the famous Diamond Game? The rules are notoriously simple. Here's an ace of diamonds card (it's larger than normal), and here are a pile of pennies. We each ...
426 views

Five-hand poker

Both players are dealt $26$ cards from a regular $52$ card deck. He discards $1$ and makes $5$ hands (from the remaining $25$) in any order, each with $5$ cards. His score is given by the sum of ...
241 views

I'm a Proper Divisor

Ann and Bob are playing a number game. Ann starts with the number 60. Then she subtracts a proper divisor of 60 from it. Bob then takes the number Ann made and subtracts one of its proper divisors ...
520 views

The Knight Checker or Football Chess

Both Players uses 8 Knights on this chessboard game : The Knight Checker. All pieces starts in Rank 1 relative to players. White to move first. The Knight pieces makes regular moves as in a chess game ...
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 ...
194 views

The Faerie Army is coming!

Well, we're all in trouble, yet again. The fabled Faerie Army has come to take over our dimension. This is the battlefield: However, their soldiers don't work quite like ours... Their pawns move as ...
482 views

Russian roulette

You are challenged to a game of Russian roulette. Your opponent places two bullets side by side in a six chamber revolver and spins the chamber. She explains that the game is single turn-based and ...
739 views

Conway's Game of Life... Chess Edition

Here's a new interesting game. Here's the starting position: and here's how it works. Before I even start explaining this, adjacent includes diagonally adjacent. Thank you. White goes first, as in ...
487 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,...
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 ...
801 views

Can you tie in 3D Tic-Tac-Toe?

In 3D Tic-Tac-Toe, there are 3 2D planes, each 3x3 in size, stacked on top of each other. A winning line can go through each of the layers (in addition to the standard winning lines of normal Tic-Tac-...
1k views

The game of pebbles

The game of pebbles is a two-player game. The game starts with $N$ stones, and a number $c>2$ is fixed. On a player's turn, he or she must remove either $1$ or $c$ stones. The player who does not ...
302 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 ...
240 views

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 ...
262 views

MPire coloring game basic strategy

The MPire coloring game is a game where several "empires" are laid out touching each other. Your task is to color each empire a different color, and not let two of the same color touch. You also have ...
337 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 ...
1k views

Largest tile possible in 1597 (2048 with Fibonacci numbers)

1597 or 2584 is a variation of the game 2048 where pairs of tiles numbered with consecutive values in the Fibonacci sequence are merged into a new tile with the next value in the sequence. An ...
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, ...
463 views

Is it Basic Physics?

Which number is next in the sequence? 1, 2, 3, 4, 5, 6, 7, 9, 10 ,11 ,12 ,13 ,14 ,15 ... Describe why and how your answer applies to the given problem.
947 views

Best strategy to get all heads/tails from three coins

Your friend has 3 fair coins: a dime, a nickel, and a quarter. She places them on a table behind you. She can arrange then in any pattern of heads and tails as long as they are not all the same. You ...
183 views

Turn based Number game

You and a friend take turns saying positive integers greater than one. You can't say a number that is a multiple of previous numbers or a sum of multiples of previous numbers. For example, if A says 3 ...
432 views

Perfect strategy for the 2nd player in 'The coins on a table game'

I've just seen this and looked at the duplicate post it directs me to. I'm interested in a point raised in one of the comments in the answer, although it wasn't resolved in that question. It is ...
616 views

236 views

Drawing loops on a sheet of paper

Two people are playing a game, in which each player takes turns drawing closed loops on a sheet of paper. Each new loop must intersect each of the other loops exactly twice. When one player has no ...
16k views

Lock code game puzzle

I'm trying to solve a lock 3 code game, Can You Crack The Code. From time to time I find myself presented with a puzzle that has 2 possible solutions, but the game only allows one correct answer. For ...