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Questions tagged [game]

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

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15
votes
5answers
951 views

Addition hangman

Addition Hangman is a game for two players. The rules are The first player (the Chooser) chooses an addition problem $x+y=z$, where $x$, $y$, and $z$ are positive integers. He writes the addition $x+...
21
votes
6answers
2k views

A game with 52 cards

Alice and Bob play the following game with two (identical) standard decks of $52$ cards. First Alice secretly arranges one deck of $52$ cards in a long row on the table. All cards are face-down, and ...
20
votes
2answers
1k views

Titanicker Tic-Tac-Toe

This is something of a follow-on to Hugh Meyer's enjoyable "Titanic Tic-Tac-Toe." Fortunately, our intrepid heroes Xavier and Oliver have wrested away a bit of wreckage that some fellow named Jack was ...
35
votes
1answer
1k views

Titanic Tic-Tac-Toe

Xavier and Oliver were playing tic-tac-toe on the Titanic using a wooden board and metal X's and O's. As the stern of the ship sank lower and lower they found, to their annoyance, that the pieces ...
13
votes
2answers
2k views

The Finger Game

There's a game called the finger game. It's played by two players who each start with one finger on each hand up. The players take turns using one of their hands to tap one of their opponent's hands. ...
10
votes
4answers
1k views

Find the minimum number of guesses

Your friend will pick a 4-letter word and you will make guesses in order to find it. -A word can contain only the letters A, B, C, and D, and they can be used more than once. (AAAA-DDDD). -In your ...
17
votes
4answers
2k views

Two prisoners and the prison ward

Two prisoners are imprisoned at opposite ends of the prison. They cannot meet, nor exchange any kind of information. However, one day they are brought together by the ward who tells them: "I shall ...
9
votes
2answers
218 views

The match between the seventh and the eighth player

12 players took part in a chess tournament and any two of them played exactly one match against each other (1 point for victory, 1/2 point for draw, 0 point for loss). After the tournament the top-...
2
votes
1answer
168 views

Making all stones black [duplicate]

1000 white stones and 1 black stone are arranged in a row. A move consists in selecting one black stone and changing the color of the 2 neighbouring stones (or changing the color of 1 neighboring ...
11
votes
3answers
1k views

The game with cookies on a red and a blue plate

Aabzaari and Basharat play a game, alternating turns with Aabzaari going first. At the start of the game, there are 20 cookies on a red plate and 14 cookies on a blue plate. A legal move consists in ...
16
votes
3answers
1k views

The maximum number of SETs with six cards

The SET game works with a deck of $81$ cards. Each card contains a set of symbols with four attributes: color (red, green, purple), shading (empty, striped, or solid), shape (oval, squiggle, or ...
11
votes
1answer
1k views

The game of 1036

Mahmoud and Zomhan play a game where they alternatively write numbers on a board. In each turn, a player takes the old number $N$ written on the board and replaces it either by the number $T$ of ...
11
votes
1answer
236 views

Squic Squac Squo

Two players take turns writing an X (first player) or an O (second player) in a 9 by 9 grid of cells. A player wins if they manage to occupy four cells which form the vertices of a square of any ...
7
votes
1answer
833 views

Heaps of marbles

Alice and Bob play the following game with two heaps of $10,000$ and $20,000$ marbles. Alice and Bob move alternatingly. Alice makes the first move. In every move, the active player may (i) either ...
14
votes
2answers
1k views

Removing chips from the table

Alice and Bob play the following game with $n\ge2016$ chips on the table. Alice and Bob move alternatingly. Alice makes the first move. In every move, the active player removes $k$ chips from the ...
16
votes
1answer
1k views

Clear board in Othello (Generalisation)

Based on Clear board in Othello If we have an $2m\times 2n$ Othello board ($m\geq n\geq 2$), and the centre $4$ squares have the usual starting position, then for what all values of $m$ and $n$ ...
10
votes
1answer
880 views

Clear board in Othello

Is there a valid set of moves in Othello that allows a win score of 64-0 for either player? And is there record of any such game in the past?
5
votes
1answer
804 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 ...
14
votes
3answers
854 views

Twenty coins and no balance

On the table there are $20$ coins that carry the letters $A,B,C,\ldots,T$. The values of these coins are $1,2,3,\ldots,20$ Euro (but the assignment of values to letters is secret). Fredo knows the ...
3
votes
1answer
667 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 ...
10
votes
3answers
857 views

Pop the Last Bubble

Having bested the silly clown, you go to your packaging job. It is a slow day, so you decide to teach the game you learned to one of your coworkers. There are no balloons around, so you use bubble ...
11
votes
4answers
1k views

Pop the Last Balloon

A clown approaches you, holding 99 red balloons. He proposes a game where the two of you will take turns popping some nonzero number of balloons. The only restrictions are: On the first turn, the ...
10
votes
1answer
629 views

Let's revisit this later (a two player knight's game)

Alice and Bob play a game on the following irregular chessboard. (Note the blacked out squares are not legal moves.) Alice starts the game by placing a knight on any square she chooses. They then ...
8
votes
4answers
518 views

Blackboard problem with polynomial

The blackboard contains the two numbers 0 and 120. Each minute you are allowed to write an additional number $ x $ on the blackboard if $ x$ has not been written before on the blackboard and if $ x $ ...
28
votes
3answers
4k views

A lonely pawn on the chessboard

Alice and Bob and the referee Conny play the following game with a pawn on a standard $8\times8$ chessboard: In the beginning, Conny places the pawn into the center of a randomly chosen square. All $...
5
votes
2answers
719 views

A prime number game

Alice and Bob play the following game on a $9\times11$ chessboard. First Alice divides the chessboard into $33$ smaller rectangles of dimensions $1\times3$ and $3\times1$. Then Bob labels each of ...
12
votes
3answers
2k views

The knight's game

Alice and Bob play the following game on a standard $8\times8$ chessboard. In the very beginning, Alice picks a square on the chessboard and places a knight on this square. Then Bob and Alice ...
18
votes
2answers
2k views

Blackboard cleaning

The blackboard contains 30 integer numbers from 1..2000. Each minute you are allowed to elect some positive integer number x and subtract x from some (chosen by you) of the numbers on the blackboard ...
10
votes
2answers
638 views

Ninety-nine non-negative numbers

Alice and Bob play the following game with $99$ numbers $M_1,\ldots,M_{99}$. In the beginning, the $99$ numbers take the values $1,2,4,8,16,\ldots,2^{97},2^{98}$. Then Alice and Bob alternatingly ...
3
votes
3answers
326 views

Rock-paper-scissors

Sheldon, Leonard and Wolowitz play a sizzling game of rock-paper-scissors for three players. In every round, each player simultaneously shows one of the three shapes. Rock beats scissors, scissors ...
57
votes
5answers
9k views

How to beat Count Dracula

Abraham Van Helsing and Jonathan Harker play a game against Count Dracula. The three players agree on the following rules: Count Dracula and Van Helsing enter the crypt, while Jonathan Harker ...
6
votes
3answers
401 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 ...
1
vote
7answers
350 views

The Buzzer Game [closed]

Two players, A and B, are each given air horns. Also present is a device which will at some random point produce a noise. If the device produces a noise before either player, they die. If both players ...
10
votes
4answers
774 views

Alice, Bob and Carol, and many cookies

Alice, Bob and Carol sit around a round table. Initially Alice has $n$ cookies, while Bob and Carol have none. Alice divides her cookies evenly between Bob and Carol; if there is a leftover cookie (as ...
6
votes
2answers
863 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 \...
15
votes
9answers
2k views

The Trickster's Game

While walking around the streets of your local city, you encounter a strange woman sitting atop a gigantic pile of dollar coins. "Would you like to play a game?" she asks. Intrigued by the strange ...
10
votes
3answers
785 views

Greedy Chocolate Eaters

Alicia and Bobby play a game with a rectangular chocolate bar, scored into an $m$ by $n$ grid of squares. The children alternate turns, with Alicia going first. On a child's turn, they must break ...
12
votes
4answers
864 views

Golden Pancakes

Alice and Bob play a game with two stacks of fluffy, golden pancakes, of sizes $p$ and $q$. They alternate turns, with Alice starting. On their turn, a player must eat some number of pancakes from ...
11
votes
6answers
4k views

Unsolvable static minesweeper puzzle? (+ 3D twist!)

You have an $m$ by $n$ rectangular grid. Each cell may contain a single bomb or a number (or neither, but not both). If a cell has no bomb and is adjacent (horizontally, vertically or diagonally) to ...
12
votes
3answers
4k views

Chomp (Game with a Poisoned Chocolate Bar)

In the game of Chomp, two players start with a chocolate bar, which is scored into an $a$ by $b$ array of squares (where $a\cdot b>1$). The square in the lower left is poisoned. The players ...
10
votes
4answers
1k views

Rocks and Lever (Game) - Goofspiel

I am not sure if there is a name associated with this game but I do not know of one. There was this 2 player game I had once played, and I am wondering if there is a winning strategy. The game is as ...
7
votes
2answers
580 views

Alternate Face Up Poker with Alice and Bob (on the floor)

I was so convinced that the "correct" answers to this excellent question were wrong that I took out a deck of cards to prove it. Then I realised that I was changing one of the rules. So here's the ...
28
votes
3answers
3k views

Face Up Poker with Alice and Bob

Alice and Bob are going to have a poker night. They have invented a variant where there are no secrets, and no randomness, called Face-Up Poker. Here's how it works. A standard 52 card deck is ...
7
votes
1answer
831 views

The Triangle Game

Take an equilateral triangle with dots at the vertices and at the midpoints of each side: There are a total of six dots. In the triangle game, you have the numbers 1, 2, 3, 4, 5, 6. Place one number ...
4
votes
1answer
523 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[...
13
votes
3answers
1k views

eXtreme Nim: A Game With *Lots* of Pebbles

Two children are playing a game with several piles of rocks. Each turn they do the following: They choose some pile of rocks. They count how many rocks are in this - let this be $n$. We remove this ...
11
votes
1answer
409 views

Dim - A Game with Pebbles

Alice and Bob play a game with a pile of $n$ pebbles. They take turns, with Alice going first. On their turn, a player can remove any number of stones from the pile which is a proper divisor of the ...
6
votes
2answers
531 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 ...
25
votes
4answers
2k views

Lions and Zebras on a Chess Board

The black knight is our lion chasing 8 white bishop zebras which can't capture. Can the zebras evade the lion forever, if team zebra positions all the pieces and has the first turn? Rules: The game ...
21
votes
3answers
7k views

Knight on a 5 by 5 board

Alice and Bob play a game with a $5\times 5$ chessboard, and a chess knight. Alice begins by placing the knight somewhere on the board. Then, starting with Bob, the players alternate moving the knight ...