Questions tagged [strategy]

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

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83
votes
7answers
18k views

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 ...
80
votes
8answers
10k views

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 ...
75
votes
10answers
17k views

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 ...
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 ...
72
votes
12answers
11k views

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 ...
67
votes
5answers
7k views

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 ...
64
votes
3answers
4k views

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 ...
57
votes
5answers
9k views

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 ...
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 ...
56
votes
22answers
15k views

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 ...
51
votes
9answers
74k views

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 ...
50
votes
3answers
5k views

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. ...
50
votes
2answers
5k views

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 ...
49
votes
3answers
4k views

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 ...
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 ...
44
votes
7answers
6k views

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 ...
41
votes
7answers
6k views

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 ...
40
votes
7answers
5k views

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 ...
40
votes
4answers
4k views

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 ...
39
votes
1answer
2k views

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 ...
37
votes
2answers
4k views

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 ...
37
votes
5answers
12k views

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 ...
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 ...
36
votes
4answers
5k views

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 ...
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 ...
35
votes
1answer
5k views

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 ...
35
votes
5answers
2k views

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 ...
35
votes
1answer
1k views

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 ...
33
votes
3answers
3k views

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. ...
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 ...
33
votes
9answers
4k views

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 ...
33
votes
2answers
734 views

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, ...
32
votes
2answers
3k views

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 ...
32
votes
4answers
5k views

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 ...
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 ...
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 ...
31
votes
9answers
4k views

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, ...
31
votes
6answers
5k views

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 ...
31
votes
3answers
6k views

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:
31
votes
10answers
6k views

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 ...
30
votes
7answers
5k views

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 ...
30
votes
8answers
2k views

Wolves and sheep

All the sheep were living peacefully in the Land of Shewo. But suddenly they were struck by a danger. A few wolves dressed up as sheep entered the territory of Shewo and started killing the sheep one ...
30
votes
3answers
1k views

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 ...
29
votes
7answers
104k views

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?
28
votes
8answers
6k views

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 ...
28
votes
3answers
3k views

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 ...
28
votes
3answers
4k views

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 $...
27
votes
9answers
2k views

Winnie-the-Pooh and the 27 honey pots

Winnie-the-Pooh keeps his $27$ honey pots in the larder. Each pot contains up to $1$ kilogram of honey, and different pots contain different quantities of honey. All $27$ pots together contain $17$ ...
27
votes
3answers
2k views

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 ...
27
votes
4answers
17k views

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 ...