Questions tagged [strategy]

A puzzle whose solution is a methodological plan of action for realizing a specific goal.

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15
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3answers
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6 Water Glasses Upside Down

There are 6 water glasses as shown in the picture below: You need to turn all of them upside down with the rules below: You have to choose any 5 of them at every turn. Chosen ones need to be turned ...
15
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2answers
2k views

10 prisoners and 10 lists of numbers [duplicate]

10 prisoners are held captive by a cruel warden. One day he gathers them in the prison hall and tells them about a new game he wants to play: "Tomorrow, I will assign each one of you a random ...
15
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3answers
2k views

A way to beat the system?

I and my friend have always had an interest in gambling. Every week, we each have $£100$ to spare, and we like to bet it on football games at the bookmaker’s. In the long term, we (unsurprisingly) don’...
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4answers
32k views

Is it possible to use one sequence of moves to solve the Rubik's cube from any position?

Is there a sequence of moves that can be repeated over and over again which can solve any legal position the Rubik's Cube? If so what is it, and if there's more than one, what's the shortest? If not, ...
15
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5answers
1k views

Evaporating coins

In the country of Dalgonia, there is only one type of fake coins and only one type of genuine coins. All genuine coins have the same weight. All fake coins have the same weight. Fake coins and ...
15
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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 $n$ ...
15
votes
1answer
675 views

A Game of ChessTron

The rules of ChessTron are as follows. Alice picks a chess piece (not the queen, as it is considered too powerful), and places it in the corner of a standard 8x8 chessboard. Bob picks a chess piece (...
15
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4answers
29k views

Strategy to solve the Missionaries and Cannibals problem

In the Missionaries and Cannibals problem: Three missionaries and three cannibals must cross a river using a boat which can carry at most two people, under the constraint that, for both banks and ...
15
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1answer
2k views

Elegant solution to the Magic Hexagon problem

The Magic Hexagon Problem A magic hexagon of order $n$ is an arrangement of close-packed hexagons containing the numbers $1, 2, ..., H_{n-1}$, where $H_n$ is the $n^{th}$ hex number such that the ...
14
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6answers
1k views

Finding Doctor No

James Bond is invited to a party with altogether $128$ participants (including Bond himself, the host, and the hostess). At the beginning of the party the host takes James Bond aside and asks him to ...
14
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3answers
2k views

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 ...
14
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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 ...
14
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4answers
2k views

Leveling up and Getting Items!

You are playing an online RPG game with 9 friends of yours (10 people in total) and in the game, there is a 2-player dungeon where you level up every time you enter and complete it. Only up to two ...
14
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7answers
633 views

10 coins, 3 of them are fake

Inspired by some great weighing puzzles here (This being one of my favorites), I just made another weighing puzzle - I'm not quite sure how difficult or easy this one is. You are given 10 coins, 7 of ...
14
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3answers
846 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 ...
14
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1answer
442 views

Keeping a ball lost forever

Suppose you can make a rectangular maze, where each cell (apart from the bottom-right) can contain an arrow in one of the four directions (up, down, left or right) of your choosing, except for those ...
14
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5answers
2k views

Church charity lottery

Suppose you've rigged the church charity lottery so that you cannot lose (what a swell guy you are). There are 10 drawings, and you start off with 10 dollars exactly. At each drawing, you must chose ...
14
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5answers
2k views

Three riders, two horses

We have three riders which need to travel some distance (say, 13.5km) through a rough terrain (no running, no skiing etc., only walking or horse trot), but they have only two horses. The speed of a ...
14
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2answers
664 views

Reverse dots and boxes

Alice and Bob are playing a game of reverse dots and boxes. The rules are simple: The players take turns adding one horizontal or vertical line in one free spot on the grid (marked with light ...
14
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2answers
595 views

Strategy for archery contest

There are $n$ archers competing in an archery contest. The rules: Each archer will shoot exactly one arrow at the target. The archers will shoot one at a time, with the order of turns chosen at ...
14
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2answers
413 views

The moody boxers

A certain group of $n$ boxers is totally ordered by strength; if boxer $X$ is stronger than boxer $Y$, then $X$ wins every single fight against $Y$. The ordering itself is not known to us, and we do ...
14
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1answer
496 views

Money Game with $1025$ cards

Alice is playing a game with Bob. They have $1025$ cards, with the numbers $0,1,2,\cdots , 1024$ written on them. Each card contains exactly one number and each number is written on exactly one card. ...
14
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7answers
2k views

Twelve balls on a scale, where one ball is lighter and another is heavier

Suppose you have twelve identical-looking balls. Ten of them are the same weight, but one is slightly lighter and one slightly heavier, in such a way that the weight of the lighter and heavier ball ...
14
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1answer
455 views

Rook Game on a Chessboard - Take 2

This question is inspired by this puzzle. You have an $m \times n$ chessboard with $m \le n$. Alice and Bob alternately move the rook (horizontally or vertically, through any number of squares). As ...
13
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9answers
3k views

Red and Blue in the Chocolate Fountain Room

Where: Hackanoogie Prison. When: Who cares? The Master Key Keeper had had a really good day and in a fit of insanity and niceness decided to let all the inmates to go free if they manage to carry ...
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5answers
6k views

Higher or Lower Guessing Game. Help settle the debate please

Can you please help settle a debate about the best strategy for this game? At pub trivia when there is a tie for first or second the host uses a guess the right number between 1 and 99. Each person ...
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3answers
2k views

99 coins into the sacks

You have 99 coins that you need to place into any number of sacks. After doing so, you write on each one the number of sacks that are lighter than that sack. For example, if you put 98 coins into one ...
13
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7answers
2k views

Faulty computers

You have $99$ computers in a LAN room, and you know that at least $50$ are working. The others can be faulty. The only thing you are allowed to do is to ask computer $i$ the question "Is computer $j$ ...
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4answers
3k views

A dice game, what is the optimal strategy?

Alice was walking on the street when she came across a man playing with a die. She could not help trying to check if the die was loaded and while she was concluding that it wasn't loaded, the man ...
13
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2answers
1k views

Empty one pile of balls and win

There are two piles of balls. One contains $5$ balls and the other contains $18$ balls. $A$ and $B$ are playing the following game: In each round, a player has to move balls from the larger pile to ...
13
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4answers
1k views

Cooperative guessing game

A standard deck of 52 cards is shuffled and split into two piles of 26 cards each. Two players cooperate, they must score as many tricks as possible. The first player draw 5 cards from the first ...
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2answers
2k views

Tic-Tac-Toe Without a Predefined Board

On a warm and uneventful summer day, John and Mary passed the time by playing games of Tic-Tac-Toe, taking sticks and drawing in the soil. John and Mary are both child prodigies, so within two rounds ...
13
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3answers
794 views

Searching for a secret door

You have reached the final stage of a game show, and now face an endless row of doors labelled $\ldots,-3,-2,-1,0,1, 2, 3,\ldots$, going from minus infinity to plus infinity. Your goal is to detect a ...
13
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1answer
468 views

Hiding Cat Puzzle on a Grid

The Youtube channel MindYourDecisions posted a video about the "Hiding Cat Puzzle". In the puzzle, you have a line of five boxes, one of which contains a cat. You don't know where the cat is, and your ...
13
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3answers
532 views

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 ...
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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. ...
12
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5answers
767 views

More than equilibrium

Assume you have 2 identical metal cubes, the only difference being their temperatures $T_1 = 0 \, \text{°C}$, $T_2 = 100 \, \text{°C}$: The task is now to transfer as much heat as possible to the ...
12
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2answers
1k views

Inside or outside the square?

Enrico draws a square in the plane, and then secretly picks a point $P$ that is either situated inside the square, or outside the square, or on the boundary of the square. Damiano sees the ...
12
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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 ...
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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 (...
12
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2answers
1k views

How to survive, with statistics

You are kidnapped and your offender plays a game with you. In front of you are 2 boxes, containing a total of 50 white balls and 50 black balls. The kidnapper will pull out a ball from one of the two ...
12
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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. ...
12
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5answers
26k views

Of these five approaches to starting a jigsaw puzzle, which one is fastest?

Of the following 5 strategies for getting started assembling a jigsaw puzzle: Assembling the border and connecting other pieces to it Working your way out from one corner Trying to assemble faces ...
12
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1answer
2k views

What is the strategy to solve Simon Tatham's Twiddle?

Consider the goal 3x3 position: You must reach this position by rotating 2x2 blocks by some multiple of 90 degrees like so: Orientation of each individual number is preserved. What is the ...
12
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1answer
2k views

Find the winning strategy for this card game

Nine cards numbered 1 through 9 are kept facing up on a table. Alice and Bob are playing a game wherein they pick up cards one at a time, alternatively. The first person to have three cards with sum ...
12
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4answers
936 views

The Duplicator and the Safe

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12
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2answers
691 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 ...
12
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4answers
502 views

Red and White Squares

There are two grid boards with the dimension of 9x9 and 14x14, consist of all white squares. You are supposed to color some squares with a red color on the conditions below: In a board, if two square ...
12
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2answers
2k views

A Game of Phones

The Chaos Legion is an infamous criminal organization, responsible for every major disaster in history from the burning of the Library of Alexandria to the recent Sony hack. The Order of Seven is ...
12
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3answers
350 views

Guffin factory regulated heist

I work at a guffin factory. I manufacture guffins and have an unlimited access to guffin storage. I can fit up to 20 guffins in my bag, get them home from the factory and nobody will chase me. You ...