Questions tagged [strategy]

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

445 questions
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Three voting prisoners

Three prisoners have a brief strategy meeting, and then are not allowed to communicate. Each night one of the three has steak for dinner, while the other two have fish tacos. Also each night, each ...
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Why does this solution guarantee that the prince knocks on the right door to find the princess?

I found this puzzle online: On the top floor of a castle lives a princess. The floor has 17 bedrooms arranged in a row. Each bedroom has doors connecting to the adjoining bedrooms as well as to the ...
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10 Prisoners, 10 Keys, and 7 Years

One day, the warden of a prison is, like most wardens in puzzles, feeling a little bit capricious and decides that he wants to get rid of his prisoners, one way or another. He gathers all the ...
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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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Turn off all lights in a ring-shaped palace

Not a very difficult question, but one I enjoyed nonetheless and wanted to share with the community. You are a servant in a palace. The palace is in the shape of a circle, and you do not know how ...
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Can the Policeman catch the Thief?

The town of Squareshire has six streets: four sides of a square and the lines joining the midpoints of opposite sides. $\hskip2in$ A policeman is chasing a thief along these streets. If they are ...
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A secret polynomial

Alice has a secret polynomial $P$ with positive integer coefficients. When Bob gives Alice a positive integer $n \neq 2016$, Alice replies with the value of $P(n)$. After doing this several times, Bob ...
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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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Can you open the bathroom door? [closed]

This happened to me in a rental apartment and I had to be creative to solve it. The geniuses who designed the bathroom managed to fit a drawer about a centimeter behind the door, and eventually what ...
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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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Extreme Gerrymandering

It is election season in Puzzlevania. There are two candidates: the incumbent and a challenger. Of the $20$ million citizens, only $1$ percent support the current president; the other $99\%$ favoring ...
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Sliding Bolt Puzzle

You are in a room with two adjacent doors locked by four sliding bolts. The bolts are movable and block only one door at a time; however, you do not know which bolt currently is blocking which door. ...
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The vicious wizard…and you!

The vicious wizard Neville has trapped you in the middle of a magical circle of radius $10000$, and you have to find a way out. Every time you want to take a step (of length $1$) in a certain ...
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Twelve balls and a scale

You are given twelve identical-looking balls and a two-sided scale. One of the balls is of a different weight, although you don't know whether it's lighter or heavier. How can you use just three ...
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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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The Circular Prison of Unknown Size

You are the president of a secret society of mathematicians with $n$ members, including yourself. No one in the society knows what $n$ is. The dictator of the world, in an effort to erase mathematics ...
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The Magic Money Machine

The brilliant scientist you are, you have built a magic money machine, capable of materializing money out of nowhere! Here's how it works: The machine has six boxes, numbered $1$ to $6$, each ...
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Amnesiac in a ring shaped palace

Related: Turn off all lights in a ring-shaped palace Your boss has trapped you inside a ring-shaped palace, and all you know about the palace is that there are some number* of identical rooms, each ...
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Which switch goes to which bulb?

You are in a room with three switches, labeled $A$, $B$, and $C$. Initially, each switch is in an off state. In an adjoining room, there are three incandescent light bulbs. Your task is to ...
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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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Duel between the knight and the dragon

A dragon and a knight live on an island where the only sources of fresh water are a pond (containing ordinary water) and six wells, numbered 1 to 6. Each well's water is completely indistinguishable ...
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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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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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Find average age without revealing your age

Ana, Barbara, Carol and Diana want to know their average age. But no lady wants to disclose her age. They decide a strategy and use a calculator (one that doesn't store steps) and tapped some keys ...
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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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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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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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There are at least three Kevins on Puzzling. I plan to trap them in my labyrinth

Note: please do not edit the title! It originates in a challenge in Stack Overflow chat. I have rounded up all ten (currently) of the Puzzling SE users named Kevin and trapped them in my labyrinth. ...
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Fairly Sharing a Frosted Cake

You are serving a cake to $10$ children. The the cake is shaped like a box, whose top face is square. The top and sides are covered with a thin layer of frosting. $\qquad\qquad\qquad\qquad$ Every ...
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Thirty genuine and seventy fake coins

In the country Curgonia, there are many types of fake coins and only a single type of genuine coins. The weights of these coins satisfy the following conditions: All genuine coins have the same ...
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Honest Monk Puzzle

Suppose you are on an island with 32 monks and you are told that one of the monks is always honest. Every day the monks say whether it is going to rain. You are required to say whether it is going to ...
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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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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 ...
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Two Sheriffs and Eavesdroppers

Two sheriffs are working on a case to find one culprit. There were initially 8 suspects; through independent work, each sheriff has narrowed this down to a list of 2. Because they are good sheriffs, ...
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Will a greedy algorithm solve Tatham's Flood?

I was just investigating some of the puzzles on Simon Tatham's website, and came across Flood, in which we start with an $n\times n$ grid of cells each of which is filled with one of $k$ predetermined ...
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Draw 4 straight lines to create 10 equal squares in this image

You can draw up to 4 straight lines in order to create 10 equal squares in the following figure:
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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 ...
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lolcatz can haz ur infinit cheeseboard

This is a problem on an infinite chessboard with pieces called lolcatz. They can move like queens or knightriders, but have a strange disadvantage... ... you've never heard of knightriders? Well, ...
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100 Prisoners and a clock

There are 100 Prisoners who are given a chance at freedom. The prisoners are randomly picked to visit a room where there is only a nonfunctional wall clock with a ...
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Dinosaur egg drop

Archeologists discover two dinosaur eggs, and you are given the chance to test the durability of these eggs (bad move on their part). Suppose that these eggs will absorb a specific amount of force ...
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Pirate democracy at its finest

With our pirate crew becoming too big, the captain grew very concerned about splitting all the treasure - we continued to split it equally, but, of course, each crew member got less and less with the ...
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Snakes on a Plane!! 2

An entry in Fortnightly Topic Challenge #35: Restricted Title 1. Inspired by the title of this xkcd comic, but in no way related or affiliated beyond the shared name. It's a well known fact that any ...
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Clever ways to solve Mastermind?

Is there any specific way to solve Mastermind? Apart from the first step that is pure chance, is there any way to continue based on the colors that you think are correct?
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A 600 foot Rope, and an 800 foot Drop

You find yourself trapped atop an $800$ foot tall building. The surrounding land is completely flat, plus there are no other structures nearby. You need to get to the bottom, uninjured, and can only ...
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12 Birds in the petshop

You decided to buy 2 birds from a pet shop and went to a pet shop for it. There are 12 budgerigars at the pet shop and you want a male and a female for your home. You cannot distinguish the gender of ...
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Learning to Solve a River Crossing Puzzle

I have seen many variations of the following puzzle: Once upon a time, a farmer went to the market and purchased a fox, a goose, and a bag of beans. On his way home, the farmer came to the bank of ...