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Questions tagged [game]

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

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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 ...
3
votes
2answers
935 views

Game against the Devil

While browsing through S.E you notice a spider crawl right out from under your keyboard! Startled, you twitch your hand and left clicked your mouse. You look up in shock as you notice that you just ...
10
votes
1answer
284 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 ...
3
votes
3answers
449 views

Two knights jousting on a chessboard

Two knights (black and white, the latter going first) start on opposing corners of a chessboard, moving across it in the usual manner, attempting to capture each other: the knight who first lands on ...
3
votes
2answers
755 views

Unsolvable sudoku net with maximum blocks

Definitions For a $9\times9$ grid $G$ (not necessarily respecting sudoku rules), a subset of cells $S$ is defined to be sudoku-friendly if the values in $S$ do not contradict the rules of sudoku. ...
12
votes
2answers
2k views

Checkers with the devil

After however much inordinate time passed for the tree-pruning game to finish, you ended up winning, and Satan was infuriated. He was sure he'd come up with a game keep you in hell. But once again, ...
8
votes
3answers
2k 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....
10
votes
4answers
2k views

Tree-pruning game with the devil

You won the coin-flipping game against Satan, but being the devil he is, he decided that that game was much too easy, and reneges on his promise to let you go. Instead, he gives you a new, more ...
75
votes
8answers
11k views

Coin Flipping Game with the Devil

You die, and awake in Hell. Satan awaits you, and has prepared a curious game. He has arranged $n$ quarters in a line, going in the east/west direction. He placed the coins at the ends tails up, and ...
6
votes
1answer
717 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 ...
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
678 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 ...
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. ...
2
votes
3answers
230 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 ...
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 ...
1
vote
1answer
665 views

Eat sweets and start your own business!

The manager of the local sweetshop, one Minty Ball, has announced a grand closing down sale. They sell $n$ varieties of sweets: toffees, sherbets, fudge, and so on. Let's just call the varieties $V_1,\...
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 ...
36
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 ...
12
votes
2answers
694 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 ...
6
votes
2answers
399 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,...
32
votes
4answers
2k views

The Devil's Brother

The 1933 movie "The Devil's Brother" (also known under the title "Fra Diavolo") takes place in the Northern Italy of the early 18th century. Stan Laurel and Oliver Hardy play the fierce robbers ...
6
votes
2answers
716 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 ...
32
votes
10answers
3k views

Variant of lion and 100 zebras

Note: This problem remains unsolved, as of 4 Feb 2018, so do try it out This a variation of this question by @Gamow Suppose there are $100$ lions and $100$ zebras. The lions function together as a ...
25
votes
3answers
1k views

The lion and the zebras II: The lion with millimeter-long claws

This is a variant of this excellent question. The rules of the lion-zebra hunger games are exactly the same: The lion plays a deadly game against a group of 100 zebras that takes place in the ...
47
votes
4answers
5k views

The lion and the zebras

The lion plays a deadly game against a group of 100 zebras that takes place in the steppe (= an infinite plane). The lion starts in the origin with coordinates $(0,0)$, while the 100 zebras may ...
17
votes
6answers
4k 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 ...
8
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
464 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) ...
14
votes
1answer
2k views

Cutting three sticks

Cosmo plays the following (single-player) game with three wooden sticks: He first checks whether he can form a triangle from the three sticks (which means: whether the longest stick is at most as ...
12
votes
4answers
2k views

Four stones on a Go-board

On a standard $19\times19$ Go-board there are four stones: two white stones in the lower left and the upper right corner, and two black stones in the lower right and the upper left corner. Alice (...
3
votes
4answers
2k 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 ...
12
votes
2answers
1k views

How long can this list of numbers get?

One afternoon, you start writing some whole numbers on a (very large) sheet of paper. First you write a one-digit number, then a two-digit, and so on, with each number one digit longer than the last. ...
21
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 ...
8
votes
3answers
763 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 ...
36
votes
6answers
7k views

Chasing pirates

You are asleep on your boat on open sea. When you wake up you discover you have been robbed. A quick inspection of security cam footage reveals that the pirates who robbed you left your ship exactly ...
56
votes
3answers
6k views

Left coin, right coin, last coin?

In this game, all players start sitting at a round table, each with a coin in their hand. At every turn, all players toss their coins together and put them on the table in front of them. Then each ...
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 ...
21
votes
4answers
6k views

Picking up stones

Here is puzzle that was lifted from an old essay of mine, that was adapted from a puzzle in an old puzzle book. The great shah has invited a young boy into his palace as a student. While he is not ...
-1
votes
2answers
876 views

The Impossible Game?

You meet a clever, and dark man. He wants to steal your mind and sell it to the dumbies (an imaginary species of shadows that have an IQ of less than -150) He offers you to play a game, if you win, ...
18
votes
3answers
7k views

Can you Turn MI to MU?

Using the letters M, I, and U, which can be used to create words. Can you turn MI into MU using in each step one of the following rules: Insert a U to the end of a word ending in I. e.g: MI becomes ...
33
votes
1answer
6k views

Coins on a table

John and Jane are playing a game. They both go to the bank and get 1000 euros in 2 euros. So each of them has 500 euros at stake. They then find a large rectangle table and decide who wins the ...
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 ...
12
votes
2answers
3k views

A two-player game

This is from the current weekly math challenge from the newspaper Le Monde. Alice and Bob play the following game, in turn: A number between $1$ and $10$ is written on a blackboard. At ...
15
votes
3answers
2k views

Optimal play for 2 by 2 dots and boxes

Consider the classic pencil and paper game Dots and Boxes . You can assume the 2 by 2 version (that is with 9 dots). Starting with an empty grid of dots, players take turns, adding a single ...
12
votes
1answer
911 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 ...
5
votes
1answer
246 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 ...
18
votes
1answer
1k views

Worst case scenario in 2048

The game 2048 can be thought as a two player game, where one player shifts the table around to get to the 2048 tile, while the other player tries to hinder them by putting down 2s and 4s on the table. ...
53
votes
5answers
42k views

What is the largest tile possible in 2048?

I can get to 4096 max. There are videos on youtube of guys making it to 8192. What is the theoretical maximum limit on this? PS: if you haven't played this, here is the link to addiction.
21
votes
4answers
988 views

General strategy for 2048

I, being a fan of 2048, was wondering if anyone has any proven strategies for playing 2048?
36
votes
5answers
9k views

What is the optimal first move in tic-tac-toe?

I have been told that it is possible to guarantee no worse than a tie in normal 3x3 tic-tac-toe, but that the first move is very important. What is that important first move?