Questions tagged [game]

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

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10
votes
1answer
951 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?
10
votes
2answers
198 views

make it to the top of the triangle

Suppose you have a triangle that extends infinitely downwards, with circles inside, arranged in this arrangement: ...
10
votes
3answers
854 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 ...
10
votes
3answers
2k views

Precision Tag - can the lion win?

This is a spin-off motivated by Lopsy's interesting variant of Gamow's lion and zebras puzzle. It arose from a line of enquiry that tried to extend the vertical run past 5000km (or characterise the ...
10
votes
4answers
2k 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 ...
10
votes
1answer
350 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 ...
10
votes
1answer
803 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 ...
10
votes
2answers
491 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. ...
10
votes
1answer
319 views

Blessings of Ares

Two gladiators are about to do battle in the coliseum. Before the battle, they enter separate rooms and pray to Ares, the god of war. Ares blesses them each with random amount of power, which you can ...
9
votes
3answers
4k 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....
9
votes
5answers
1k views

How long will my money last at roulette?

I'm at the casino, standing next to a roulette table with a \$10 minimum bet. I want to stay here as long as possible, so I'm going to repeatedly make the minimum bet until I run out of money. I'm ...
9
votes
1answer
468 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 ...
9
votes
2answers
456 views

How to beat Count Dracula, part 3

This is a follow-up to "How to beat Count Dracula" and to "How to beat Count Dracula, part 2". Abraham Van Helsing and Jonathan Harker play a game against Count Dracula. The three players agree on ...
9
votes
2answers
503 views

Cheating aplenty at Build-a-Die 2017

Each year, 9 affluent acquaintances meet to compete in a unique game of chance: each creates a fair six-sided die and rolls against each opponent 100 times -- the player with the most total wins in ...
9
votes
4answers
466 views

Number exchange game

Inigo and Vizzini are to have a battle of wits to the death. The rules are: Inigo is given two independent random numbers uniformly distributed between 0 and 1. Inigo chooses one of the numbers to ...
9
votes
1answer
748 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.
9
votes
2answers
242 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-...
9
votes
2answers
413 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: ...
9
votes
1answer
278 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 ...
8
votes
6answers
1k views

Single-pile Nim with Three Players

Three perfectly rational logicians (Alice, Bob and a Quetzalcoatlus) are playing a game. (Charlie couldn't make it, so he asked the Quetzalcoatlus to fill in for him.) The rules are very simple: ...
8
votes
2answers
2k views

25 square puzzle

You have a 5x5 grid filled with 25 zeros. Your objective is to convert the grid into 25 ones. You must do this by a series of special moves. On each move, you select a single cell. All four ...
8
votes
4answers
554 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 $ ...
8
votes
7answers
1k views

7 Numbered Balls Game

You are walking on the street and notice a guy gambling with some other guys and you start to watch. The game principle is pretty easy. There are 7 balls in a pouch and you have 3 balls to draw ...
8
votes
1answer
940 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 remove ...
8
votes
3answers
446 views

Four-in-a-line Puzzle

Disclaimer: This is an open-problem, I don't have a complete solution for this puzzle yet. We are playing a $2$-player game: you as a challenger and me as a judge. Initially, there is an empty ...
8
votes
6answers
1k views

Devious auction game

Saw this on TV today: A man is auctioning a real $20\$$ bill. There are a vast number of bidders. A person may make as many bids as he wants. The starting bid is $5\$$. No $2$ bids must be ...
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 ...
8
votes
2answers
575 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 ...
8
votes
3answers
672 views

Double or Take game

Double or Take is a two-player number game. Alice starts by selecting any positive integer. Bob's options are to: subtract a positive perfect square subtract a positive perfect cube, or double the ...
8
votes
2answers
568 views

Chess with bouncing and explosion

Consider chess with the following additional rules: The edges of the board consist of ranks 1 and 8 and columns a and h. Bouncing: When a piece goes from a non-edge square to an edge square, it ...
8
votes
3answers
861 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 ...
8
votes
2answers
782 views

Reverse dots and boxes, swastika edition

Alistair and Roberta are playing a game of reverse dots and boxes. The players take turns adding one horizontal or vertical line in one free spot on the grid (marked with light gray lines in ...
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 ...
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
2answers
811 views

A matchstick game

On the table there is a $9\times9$ grid made of matchsticks, so that each of the $81$ little squares is bordered by exactly four matchsticks. Alice and Bob play the following game. Alice and Bob move ...
8
votes
1answer
359 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, ...
8
votes
4answers
3k views

Thirteen coins game

There are $13$ coins arranged in a circular fashion. Andrew and Bill play a game with these rules: Andrew starts the game A player can remove $1$ or $2$ adjacent coins from the circle during his turn....
8
votes
1answer
337 views

No point shuffling, just pick your cards

Alice and Bob are playing a card game with the following rules: Alice selects two piles of 3 cards from a standard 52-card deck and places the piles in front of her, face up. Bob can see these ...
8
votes
5answers
553 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 ...
8
votes
1answer
1k views

Tic Tac Toe Recursive

Related: Connect 4 Recursive We have a mega tic tac toe grid. Each of the nine cells of the mega grid has a smaller tic tac toe grid. In total we have 81 cells that can be filled. (Maybe imagine a ...
8
votes
1answer
260 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, $x$ (...
7
votes
6answers
2k views

How will Y lose the game?

X and Y are playing a game. There are eleven coins on the table and each player must pick up at least one coin but not more than five in a turn. The person picking up the last coin loses. X starts. ...
7
votes
4answers
572 views

Removing green marbles from the table

Alice and Bob play the following game that starts with $N\ge3$ green marbles on the table. Alice and Bob move alternatingly. Alice makes the first move. In this first move, Alice removes $x$ green ...
7
votes
2answers
820 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 ...
7
votes
3answers
545 views

Writing differences on a blackboard

The numbers 25 and 36 are written on a blackboard. At each turn, a player writes on the blackboard the (positive) difference between two numbers already on the blackboard, if this number does not ...
7
votes
2answers
530 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
5answers
282 views

Selecting the starting player [closed]

The board game is about to begin. And suddenly we realize that we need to decide the starting player. The dice procedure is tiresome. And we can't find our dice right now. Or any other artifact that ...
7
votes
1answer
349 views

Two players playing the SET game

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 ...
7
votes
2answers
609 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 ...
7
votes
1answer
876 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 ...