Questions tagged [strategy]
A puzzle whose solution is a methodological plan of action for realizing a specific goal.
766
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Escape from the magic prison
You're locked in one of three magical cells (yellow circles) located at the vertices of a triangle. In each cell there're three transporters numbered 1, 2 and 3, one of which transports you to the ...
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5
votes
1
answer
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Combination lock on a pentagonal rotating table
This puzzle is part of a serie.
Inspiration: Sliding Bolt Puzzle
Part 1: Combination lock on a triangular rotating table
Puzzle
After solving the 3 digits code in 27 tries (again, you just have the ...
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15
votes
4
answers
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Getting lost on a Circular Track
Since it is such a nice day, you decide to have a nice long walk on a very large circular road nearby. The radius of that circle is known to you, but it is so large that you cannot tell the inside ...
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7
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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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0
votes
0
answers
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Trapping your nemesis on a circular track
Inspired by Getting lost on a Circular Track.
You are in possession of a very peculiar circular track. No matter how nice of a day it is, the track is always covered in an extremely thick fog which ...
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13
votes
1
answer
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Combination lock on a triangular rotating table
This puzzle is part of a serie.
Inspiration: Sliding Bolt Puzzle
Part 1: It's this one (-:
Part 2: Combination lock on a pentagonal rotating table
Puzzle
You are trapped in a dark room. Just your ...
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11
votes
3
answers
2k
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The lone builder
You are a lone builder. You have to build a city on a 10x10 initial empty grid. You can place:
a street, which is a blue cell on the top of any cell,
a tomato shop, which is a red cell on any cell ...
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11
votes
2
answers
1k
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When can the cat and mouse meet?
A cat and a mouse occupy the top right and bottom left cells respectively of an $m \times n$ rectangular grid, where $m, n > 1$. Each second they both move diagonally one cell.
For which pairs $(m,...
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29
votes
1
answer
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Seth and Cain take turns picking numbers from 1 to 50. Who wins?
Seth and Cain play a game. They take turns, and on each turn a player chooses a pair of integers from 1 to 50 inclusive. One integer in the pair must be twice the other, and the players cannot choose ...
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9
votes
3
answers
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Sliding Bolt Puzzle - fastest solution (time-wise)
This is a follow-up question for the Sliding Bolt Puzzle. If you have not solved it yet, you might want to head there first, as the extended discussion of its solution in this question will contain ...
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3
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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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7
votes
3
answers
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The Blindfold CASIO fx-570EX Puzzle
You and your friend are playing a game with the CASIO fx-570EX calculator.
The game proceeds as follows:
Your friend types a number, then presses a left parenthesis, and then types another number(e.g....
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10
votes
4
answers
1k
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Flashlight and 6 batteries
In front of you are 6 batteries and a flashlight. You know that 4 out of the 6 batteries are fully charged, and 2 out of the 6 batteries are empty, but you don't know which ones are charged and which ...
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votes
3
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The Puzzle Noob’s New Game
This is a generalized version of a TED-ED puzzle.
You just wrote a very good puzzle on PSE, getting three upvotes a week. However, the puzzle noob hates your puzzles, and sends you to their dimension ...
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8
votes
2
answers
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Three-player Avalon (transmitting private knowledge over a public channel)
Players
There are a total of three players, split into two teams:
Team Resistance has two players whose roles are assigned at the start of the game.
Team Spy has one player (the Spy).
Before ...
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6
votes
0
answers
157
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Avalon's rock-paper-scissors
This puzzle is a symmetrical version of Three-player Avalon (transmitting private knowledge over a public channel). I came across this version (for which I think I have a solution) while looking for ...
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votes
2
answers
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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 ...
60
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7
answers
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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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1
vote
1
answer
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Pyramid Scheme on an infinite Lattice
A set of shrewd investors, each with a single gold coin in hand, arrange themselves in a lattice of the form $\mathbb{Z}^I$, where $I$ is any index set (finite or infinite, countable or uncountable). ...
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10
votes
2
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Connect 3 on different board sizes
Two players, White and Black, sit down to play a few rounds of Connect 3 on a rectangular board of any size. White plays first. Assuming both players play perfectly:
What will be the outcome of this ...
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5
votes
1
answer
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Weigh 15 boxes with a digital scale, but you can’t understand the number system
This puzzle is inspired by the puzzle 14 coins problem but you can't understand the scale.
In this weighing puzzle, you have 15 boxes, each one weighing 1, 2, 3, and so on until 15 arbitrary units....
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12
votes
4
answers
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Five pirates splitting gold with a twist
Source: This was posted on the Grey Labyrinth Forums many years ago.
The five pirates are back. But this time one of them has the dreaded Zanzibar fever, whose terrible effects are spelled out below....
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13
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4
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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 ...
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6
votes
1
answer
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What frequent patterns can be used to overcome Minesweeper obstacles?
Minesweeper, to those who do not know the strategies involved, is a difficult game.
What patterns exist in the game which I can take advantage of?
Meta-context: this question is an offshoot of ...
3
votes
2
answers
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General Approach to Solving Cryptarithms
I have recently started honing my problem-solving skills, starting with number-related puzzles. Cryptarithms have appeared frequently, so I was wondering whether there is some sort of general approach ...
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4
votes
2
answers
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Blindfolded tic-tac-toe with a twist
You're playing tic-tac-toe and you're blindfolded.
The objective is to never lose, winning when given the chance under the classic ruleset of the game. Furthermore, an observer who is only aware of ...
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20
votes
7
answers
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Flashlight and 8 batteries
Source: this TED-Ed video.
A flashlight requires 2 AA-type batteries to operate. Both these batteries need to be charged for the flashlight to provide light.
We happen to have 8 batteries, but 4 of ...
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2
votes
1
answer
282
views
Strategy for solving "Hypatian Enigma" puzzle (all lines add to 38)
The "Hypatian Enigma" puzzle consists of 19 hexagonal blocks numbered 1 through 19.
The blocks are arranged in 5 rows. The first and last rows have 3 blocks, the second and fourth row has 4 ...
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12
votes
5
answers
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How fast can you win this (very stupid) game?
You and I get together to play the following (dumb) game:
Two positive integers N and K are fixed from the outset.
We both start the game with N coins and proceed to play some number of rounds like ...
- 2,197
9
votes
4
answers
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Prisoners and warden game, again?
Source:
There are 100 prisoners in a prison. As usual, there is a warden who loves to play games, hence offers the prisoners a chance to free themselves.
He says
There is a room with a whiteboard, ...
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4
votes
0
answers
143
views
The Merchant's coin weighing [duplicate]
You're a merchant in the old medieval times, and a customer has come to you to buy something for 13 coins. You know him of course, like everyone in town, and you know he's a sketchy guy. Someone who ...
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5
votes
1
answer
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Rats & Snakes: Avoid being eaten, escape unharmed
I'm trying to create a puzzle for an RPG that involves a classic lever puzzle.
It is presented as follows:
There are four rooms, you start in the southern-most room (S).
In this room are two closed ...
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5
votes
1
answer
482
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The Room Of Tiles
You are stuck in a room with 100 floor tiles, and a magic button which you can carry with you. There are three types of tiles: real, fake and nopey. There are at most 49 fake tiles, and there is at ...
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11
votes
3
answers
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Guess the Permutation
Let $p$ be a prime. I chose a secret permutation $a_0,a_1,...,a_{p-1}$ of $0,1,...,p-1$ unknown to you. Now, you can ask the following types of questions to me:
Type $1$: Tell me two integers $i,j$ ...
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19
votes
4
answers
2k
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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 ...
- 1,246
104
votes
7
answers
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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 ...
- 10.3k
7
votes
1
answer
869
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More Catching of Cats
After my first puzzle on this theme was solved relatively quickly, here is a (trickier) follow up question in the same vein!
The setup is similar - you are in a room with an infinite line of boxes, ...
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9
votes
1
answer
296
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Communicate square on a 3-by-3 grid by flipping precisely one of 13 coins
A coin is placed on each of the $13$ squares in the following diagram:
Each coin may be showing heads or tails arbitrarily. An adversary points to a square in the $3\times 3$ grid. You must ...
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20
votes
3
answers
1k
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Keys and Locks Puzzle
Let $a,b,n$ be positive integers in which $a,b\le n$. You are locked in a room, with $n$ distinguishable keys and $n$ distinguishable locks in it. You know that each lock can be unlocked by a unique ...
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11
votes
2
answers
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Gold and silver coins in sealed envelopes
Alice has freely chosen to put either a gold coin or a silver coin in each of an infinite sequence of envelopes numbered 1,2,3,... Bob can open any number of envelopes and check the coins within, ...
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10
votes
2
answers
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The game of 42: 10 cards to make 42
This is a game inspired by other recent questions.
It is a 2-player game.
The game is played with 10 cards numbered 1 to 10 and 2 positions or stacks.
The game starts with all cards in stack 1.
The ...
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9
votes
2
answers
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Pole, rope, and chasm
You come across a chasm. It's perfectly smooth, 50m deep, and 50m across, and too wide to go around.
You have a pole that is 40m long, and as much rope as you need.
How do you get across the chasm?
...
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14
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2
answers
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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 ...
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20
votes
3
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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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2
votes
1
answer
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Is it possible to fill an arbitrarily large hex grid completely given these rules? #2
Based off of this.
Lets say you have two players, Red and Blue, that alternate filling an arbitrarily large hexagonal grid of tessellated hexagons with pieces of their color. Hexagons can either be ...
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4
votes
1
answer
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Is it possible to fill an arbitrarily large hex grid completely given these rules?
Lets say you have two players, Red and Blue, that alternate filling an arbitrarily large hexagonal grid of tessellated hexagons with pieces of their color. Hexagons can either be filled or empty.
A ...
- 150k
23
votes
7
answers
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Two prisoners and twenty marbles
Two prisoners are planning their escape. Their cells are locked with a padlock that must be opened with a 5-digit code (numbers 00000 to 99999). Each prisoner knows the code of the other prisoner's ...
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21
votes
5
answers
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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 ...
7
votes
2
answers
524
views
One vs many. Can white force a draw?
On an infinite chessboard there's a single white king and N black kings. The nearest black king must be K moves away from the white king. Given N, white dictates the value of (finite) K, then black ...
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votes
4
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The Alien Snails Experiment
Fictional Background Story (The Experiment):
Two extremely fast and intelligent alien snails are randomly placed on two different points on an infinite plane, as an experiment by the cruel ruler of ...
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