Questions tagged [game]
A puzzle that asks for determining the winner in a multi-player game.
279
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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 ...
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3
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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 ...
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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 ...
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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.
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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 ...
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Rock, Paper, Scissors and Trump
Alicia and Robert are two high-stakes gamblers who are playing a match of rock-paper-scissors. Each winning throw is worth 10 €, paid by the other player. These players have deep pockets, so matches ...
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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 ...
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votes
1
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Polynomial game with Devil
You die, and awake in Hell. Satan awaits you, and has prepared a curious game. On a blackboard, he has written the polynomial $x^2+x+666$. He explains the rule:
On each day at $12$ noon, you must ...
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6
answers
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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?
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Variant of lion and 100 zebras
Note: This problem remains unsolved, as of 19 April 2020, so do try it out. 400 rep bounty guaranteed for a correct answer
This a variation of this question by @Gamow
Suppose there are $100$ lions ...
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Strategy to beat the Casino
Two players, $A$ and $B$, and the Casino play a game. It involves showing zeros or ones: each player picks $0/1$ and also the Casino picks $0/1$.
If the Casino and both players $A$ and $B$ show the ...
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37
votes
1
answer
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Say 100 and win
Our good friends that like games, Alice and Bob, play a game called "Say 100 and win".
The rules are:
In the beginning they use one regular 6 faced die to get a random number between 1 and 6. Let's ...
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36
votes
6
answers
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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 ...
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1
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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 ...
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35
votes
1
answer
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Coins on a table
John and Jane are playing a game. They both go to the bank and each get 1000 euros in two-euro pieces. So each of them has 500 coins at stake. They then find a large rectangle table and decide that ...
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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 ...
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3
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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 $...
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3
answers
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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 ...
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29
votes
3
answers
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Finding digits that sum to 15
Rand and Rubio are playing a game in which they each take turns to pick a digit between 1 and 9, without replacement (i.e. all digits chosen are distinct). If one of them manages to get three digits ...
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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 ...
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26
votes
2
answers
4k
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Any fans of The Big Bang Theory?
Penny, Sheldon, Howard and Leonard are chilling. Sheldon comes up with an idea to play a dartboard game. Like always, he has his own rules. He brings a weird dartboard from his room, sets the bullseye ...
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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 ...
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24
votes
2
answers
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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 ...
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votes
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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 ...
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votes
1
answer
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Monte Carlo Chess
This is an entry to the 17th fortnightly topic challenge.
Chess is an interesting game, but is so unrealistic. In real life, you couldn't tell order your knight to attack an enemy bishop and expect ...
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The 100 soldier problem
I saw this problem many years ago. I am sure many puzzlers will know its original name. I was reminded of it when reading about Conquering of Regions problem. A Strategy Game Involving Conquering of ...
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Even and Odd game
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 ...
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6
answers
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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 ...
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22
votes
1
answer
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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. ...
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4
answers
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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 ...
user88
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votes
3
answers
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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 ...
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21
votes
3
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Making a 9 digit number divisible by 11
Alice and Bob play the following game, taking turns. Alice starts and writes a non-zero single
digit number at the blackboard.
At every turn, each player adds a single digit at the right of the ...
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21
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3
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Can you survive this infinite zombie attack?
You're surrounded by infinitely many zombies. You're at the origin, and zombies occupy the points $(100i,100j)$ for all integer $i, j$ except the origin, as shown below:
You and the zombies move ...
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A game with 330 pebbles
Anastasia and Barnabas play a game that starts with $330$ pebbles in a bowl.
The game consists of two phases. The first phase looks as follows:
First Anastasia announces an integer $A$ with $2\le A\...
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21
votes
9
answers
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Catch the invisible and omniscient thief
The thief has stolen two powerful artifacts: the Cloak of Invisibility and the Glasses of the Oracle. Now they're equipped with both. The cop at the bottom, not knowing where the thief is, is trying ...
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4
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Strategy to beat the casino over the long haul
$A$ and $B$ are attempting to beat the casino again, and the rules are the same:
Each round, $A$, $B$, and the casino simultaneously decide to show a $0$ or a $1$. If all three numbers match, $A$ ...
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4
answers
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General strategy for 2048
I, being a fan of 2048, was wondering if anyone has any proven strategies for playing 2048?
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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 ...
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Winning chance in coins game with fixing
A player plays the following solitaire game. The game consists of as many rounds as are needed to produce a result. They have 20 fair coins, which may in any round be live or fixed; each coin starts ...
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Obtain the "Master of stones" title
Note : the mechanisms described in this puzzle are related to those found in this question.
This is a game of 2 players.
Each player can pick up 1, 2, or 3 coins in any pile (copper , silver , gold) ...
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4
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A Tic-Tac-Toe type game
I found this interesting game with no name:
You have a 1x11 grid, like this.
The way you play is similar to Tic-Tac-Toe (aka Noughts and Crosses). Players take turns to place Xs and Os on the grid, ...
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2
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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 ...
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Catching a Cat on an infinite Line
Upon entering a (very) large room, you are faced with an infinite line of cardboard boxes that are labeled, in order, by the nonnegative integers. In one of these boxes, a cat is hiding, but you do ...
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1
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Blindfold Tic-Tac-Toe
You are playing the classic game of 3x3 Tic-Tac-Toe. You are blindfolded and you cannot see the grid, while your opponent can see it. When making a move you call out a cell. If that cell is taken you ...
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1
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Game of the glasses on the windowsill
The windowsill above the sink is where my wife and I place our dirty wine glasses. And while both of us love each other, neither of us love loading the dishwasher. As a result, these dirty glasses ...
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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 ...
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Noughts and Crosses puzzle
Eques and Knott are playing a game of standard 3x3 Noughts and Crosses. At no stage of the game has Eques threatened to complete a row of three on his very next turn.
Suddenly Knott realises he must ...
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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 ...
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It'd be on an infinite board, but he can't fit one in his hideout
This is a fairly easy one (at least as this website goes) with a premise taken from the Reader's Digest Book of Puzzles & Brain Teasers.
The Riddler is devising yet another trap for Batman to ...
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Making a 2n-digit number divisible by 9
Alice and Bob play the following game, taking turns. Alice starts and writes a digit from the set M={1, 2, 3, 4, 5, 6} at the blackboard.
Bob appends another digit from the set M until a 2n-digit ...
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