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Questions tagged [game]

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

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7
votes
1answer
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 ...
7
votes
1answer
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 ...
7
votes
1answer
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 ...
7
votes
2answers
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,...
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 ...
7
votes
1answer
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 ...
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....
7
votes
2answers
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 ...
7
votes
1answer
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 ...
7
votes
1answer
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 ...
6
votes
2answers
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 ...
6
votes
2answers
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"): $$ \...
6
votes
3answers
517 views

Guessing a number with 250 divisors

Alice and Bob play the following number guessing game. First Alice picks an integer $n$ with exactly $250$ positive divisors. These divisors include $1$ and $n$, and are denoted as $1=d_1<d_2<...
6
votes
1answer
306 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 ...
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 ...
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 ...
6
votes
2answers
927 views

Non-Greedy Chocolate Eaters

A variant of Greedy Chocolate Eaters (created by my significant other, who doesn't like chocolate all that much) Alice and Bob are playing a game with a rectangular bar of chocolate scored into $m \...
6
votes
2answers
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) ...
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 ...
6
votes
2answers
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 ...
6
votes
1answer
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 ...
6
votes
3answers
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 ...
6
votes
1answer
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 ...
6
votes
1answer
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 ...
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 ...
6
votes
1answer
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 ...
5
votes
5answers
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 ...
5
votes
3answers
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 ...
5
votes
1answer
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,...
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 ...
5
votes
1answer
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-...
5
votes
4answers
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 ...
5
votes
2answers
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 ...
5
votes
1answer
240 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 ...
5
votes
1answer
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 ...
5
votes
2answers
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 ...
5
votes
1answer
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 ...
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, ...
4
votes
1answer
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.
4
votes
6answers
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 ...
4
votes
1answer
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 ...
4
votes
2answers
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 ...
4
votes
1answer
616 views

Generalisation of Nim

I'm asking for a general formula/algorithm that can be used in such a game. There are $n$ piles, with varying number of pebbles. The number of pebbles in each pile is given by an array from $pile[...
4
votes
1answer
204 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 ...
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 ...
4
votes
1answer
272 views

Tactical Domino Placement Game

Alice and Bob take turns to place regular dominoes into a $7\times8$ board. The first player who cannot go loses. Is there a winning strategy for either player? Note that in this version the pips on ...
4
votes
3answers
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 ...
4
votes
4answers
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 ...
4
votes
3answers
288 views

Praser 5 - Help

What is the answer to the Griffon's riddle? So tired of beating my head against this one. I've solved the Sphinx, Unicorn, and Pegasus, but this one is killing me. ...
4
votes
1answer
914 views

Optimal game of Bluff (not the wikipedia one)

Rules Basics 52 well shuffled cards are dealt equally to both players. Player 1 starts the first hand. The game consists of a number of rounds, which are played as follows. On each round, players ...