Questions tagged [game]
A puzzle that asks for determining the winner in a multi-player game.
70
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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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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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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 ...
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votes
4
answers
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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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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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2
votes
1
answer
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Master and Slave versus Bob: hard version
Continuation of: "Sub-puzzle: Master and Slave versus Bob the Violent but Honest Psychopath" and "Master and Slave versus Bob: easy version"
The hard version is identical to the easy version (see ...
- 5,198
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votes
5
answers
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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 ...
- 419
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4
answers
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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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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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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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4
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The Mexican Standoff
There are three cowboys in a Mexican standoff against each other, named Juan, José, and Jorge.
Juan is the straightest shooter in the West, and can hit his target 100% of the time.
José, who has a ...
user88
14
votes
3
answers
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Strategy to beat the Casino reversed
Let's consider Strategy to beat the Casino puzzle, but reverse it - fix number of losses and ask a question about amount of rounds:
Two players, A and B, and the Casino play a game. The game consists ...
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2
votes
1
answer
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Master and Slave versus Bob: easy version
Continuation of: "Sub-puzzle: Master and Slave versus Bob the Violent but Honest Psychopath"
Continued in: "Master and Slave versus Bob: hard version"
Previously I described a game that is played ...
- 5,198
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votes
3
answers
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Sub-puzzle: Master and Slave versus Bob the Violent but Honest Psychopath
[I created this as a sub-puzzle to "Strategy to beat the Casino reversed", that has been sitting unsolved for months. You may wish to read that puzzle first, but this is self-contained. My answer to ...
- 5,198
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votes
9
answers
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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 ...
- 32.6k
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votes
3
answers
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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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42
votes
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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3
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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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6
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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 ...
- 45.8k
19
votes
4
answers
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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 ...
- 3,640
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votes
2
answers
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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 ...
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votes
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The knight's game
Alice and Bob play the following game on a standard 8 by 8 chessboard.
In the very beginning, Alice picks a square on the chessboard and places a knight on this square.
Then Bob and Alice alternate ...
- 45.8k
6
votes
5
answers
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Russian roulette
You are challenged to a game of Russian roulette. Your opponent places two bullets side by side in a six chamber revolver and spins the chamber. She explains that the game is single turn-based and ...
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What is the smallest tic-tac-toe board to have a winning strategy?
There is not winning strategy for 9cell 3x3 board.
There is a winning strategy for 16cell 4x4 board, or even for 10cell "3x3 + 1_cell_near_a_corner" board (see M.Gardner "Mathematical games"):
$$
\...
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4
votes
2
answers
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Perfect strategy for the 2nd player in 'The coins on a table game'
I've just seen this and looked at the duplicate post it directs me to. I'm interested in a point raised in one of the comments in the answer, although it wasn't resolved in that question. It is ...
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votes
1
answer
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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,\...
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votes
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answers
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Can Alice form a unit square?
Alice and Bob take turns to mark points in $\mathbb{R^2}$ (i.e. infinite 2D plane). Alice can only mark $1$ point on her turn, while Bob can mark $N$. They're free to mark their points anywhere as ...
- 6,956
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votes
7
answers
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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 ...
- 45.8k
39
votes
11
answers
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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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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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votes
1
answer
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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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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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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 $...
- 45.8k
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votes
3
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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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votes
4
answers
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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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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 ...
- 45.8k
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votes
4
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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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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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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 ...
- 6,956
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votes
9
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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 ...
- 6,956
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4
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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
17
votes
3
answers
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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 ...
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2
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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 ...
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3
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Rubik's cube two-person game
I will define the game as follows:
There are two players, the "Solver" and the "Unsolver". The Solver's goal is to return the cube to it's standard solved state. Likewise, the Unsolver's goal is to ...
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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 ...
user88
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votes
1
answer
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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 ...
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votes
3
answers
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Equal distribution of coins to pirates
Ten pirates are sitting around a table. Each of them has an even number of coins.
At order of the captain, each pirate passes half of his coins to the neighbor to the right. After that round, each ...
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13
votes
3
answers
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Outmaneuver your opponents in the duel
A, B and C are in a three way duel. Starting with A, they rotate in the order of A-B-C, each firing one shot at a time. They stand close to one another, so that each can kill one of the others or ...
- 6,956
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votes
4
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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 ...
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