Questions tagged [game]

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

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8
votes
3answers
1k views

Coin inverting game

Header and Tailer play the following game. At the beginning, the juror lays out a row of $n\ge5$ coins on the table that alternately show heads and tails, with the leftmost coin showing heads. ...
8
votes
1answer
1k views

Hangman- No misses left

**** No programs allowed. You must find the answer using your own brain. **** Your hangman game allows for 9 misses, but on the 10th miss, you're hanged! You don't want to be hanged. The letters ...
7
votes
1answer
797 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 ...
21
votes
4answers
1k views

General strategy for 2048

I, being a fan of 2048, was wondering if anyone has any proven strategies for playing 2048?
17
votes
6answers
5k views

Guess my number! Pay for the answer!

Alice and Bob play the following number guessing game. In the beginning, Alice picks a secret number from the range $1,2,3,\ldots,144$. Then Bob is allowed to ask a sequence of questions. In every ...
11
votes
3answers
1k views

Who wins the AI-game?

Anna and Isadora play a game by writing letters on the blackboard. In the first round, Anna starts by writing down the letter $A$ or the letter $I$. In the $n$-th round with $2\le n\le 999$, Anna ...
2
votes
3answers
233 views

Drawing squares

Anafenza and Zurgo are playing a game. They have a playing board of $23*92$ squares. The idea of the game is to put a square(of any size) onto the playing board. The one who can't put any more ...
37
votes
6answers
3k views

The subtraction game

Alice and Bob play a game that starts by Bob picking a secret integer $N\ge100$. Then the game goes through several rounds. In every round, Alice picks an integer $x\ge3$. Every number can be picked ...
6
votes
2answers
406 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,...
12
votes
2answers
703 views

What's the optimal score in the MU-game?

Mary and Ursula play a game by alternately writing letters into a $9\times9$ grid. In every move, the player picks an empty square and then writes her initial letter (M or U) into it. Mary has the ...
9
votes
3answers
3k views

Queen chasing a knight (chess pieces)

There is a player who controls only a queen, while his opponent controls a knight. Both pieces start from opposite corners of the board. The aim is to kill the knight, without having your queen killed....
6
votes
2answers
495 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) ...
10
votes
1answer
2k views

20 coins on the table

Two boys , Brian and Gabe, decide to play a game. They lay 20 coins on the table. Each player took turns taking 1, 2, or 3 coins. Whoever took the last coin won. Brian thought if he went first, he'd ...
23
votes
2answers
2k views

Rook game on chessboard

A rook stands in the lower left corner of an $m\times n$ chessboard. Alice and Bob alternately move the rook (horizontally or vertically, through any number of squares). As the rook moves, it leaves a ...
12
votes
1answer
1k views

What is the name of this line-connecting game?

Can you tell me what is the name of the game I used to play in school? It's a game for two players. You need grid paper and two pens. The game is played on a 10x10 arena, shifted by half a grid to one ...
16
votes
2answers
1k views

Automatically a Knight, Knave, and Joker

Let M be a finite positive integer. It's exact value is not known. Suppose we have three classes of automaton, all of which accept a bit stream as input, produce a bit stream as output (one bit per ...
3
votes
4answers
3k views

10 friends play a number game

You and 9 friends are playing a game, is there a way to force a win, if so, how, if not, what is the most optimal strategy? Gameplay: Each player can have a turn, or if he/she wishes, 2 turns. Each ...
8
votes
3answers
809 views

The tile-flipping game

The tile-flipping game uses 6 tiles that have a white side and a black side. It starts with the tiles arranged in a line with their white side facing up. $$\circ \circ \circ \circ \circ \circ$$ We ...

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