Puzzles

Challenging mathematical puzzles. Click on the categories below to reveal them.

Geometry Puzzles

In how many different ways can you arrange 4 points in a plane such that exactly 2 different distances exist between any 2 points?

Logic Puzzles

There are 12 coins. One is false and weighs differently, but it is unknown whether it is heavier or lighter. How can you find it in three weighings on a simple scale?
Is it possible to obtain a rational number when an irrational number is raised to an irrational number?
A cat hides in one of five boxes and moves to an adjacent box each night. Can you find it by opening one box each morning?

Number Puzzles

Why can the equation \(x^n + y^n = z^n\) not hold for positive integers \(x=2233445566\), \(y=7788990011\), and \(z=9988776655\) when \(n > 2\)?
Fifteen pirates divide a sack of coins, leaving two coins over, then one coin over after one pirate is killed, and finally divide evenly after another pirate is killed. Find the smallest possible number of coins.