Maths and science you can play with
Small ideas that surprise you,
one experiment at a time.
Every gem is a puzzle you can run: change the numbers, play a thousand games, watch the answer appear. Then read why it works, and try a few problems of your own.
Start here
The Chinese Rings and the Gray Code
An old puzzle of rings on a bar hides a way of counting where every step changes just one digit.
The Monty Hall Problem
Three doors, one car, two goats. The host opens a door with a goat. Should you switch?
The Moving Sofa Problem
What is the largest sofa you can carry round the corner of a narrow corridor? The answer took almost sixty years.
The Birthday Paradox
How many people do you need in a room before two of them probably share a birthday? Far fewer than you think.
Fold and One Cut
Fold a sheet of paper, make one straight cut, unfold it, and out drops a star. Which shapes can a single cut make?
Magic Cards That Catch a Lie
Five cards read any number from 0 to 31. Seven cleverer cards still find your number when you lie about one of them.
Mice and Test Tubes
One of 240 test tubes is poisoned. You have 8 mice and a single day. Binary numbers find the tube.
Squaring the Square
Can you cut a square into smaller squares that are all different sizes? It took until 1978 to find the smallest way.
The Two Envelopes Paradox
One envelope holds twice as much as the other. A simple argument says you should always swap. Why is it wrong?
How to Make a Dobble Deck
Any two cards in Dobble share exactly one symbol. Here is how to build such a deck, using geometry where parallel lines do not exist.
Parrondo's Paradox
Two coin games that both lose money in the long run. Mix them up, and you start winning. How?
Steiner Networks and Soap Films
What is the shortest road network joining four towns? Not the obvious one, and a soap film can find the answer for you.
The Elevator Paradox
You work near the top of a tall building and want to go down. Why is the first elevator to arrive nearly always going up?
Stable Matching: Who Pairs With Whom?
Everyone ranks everyone in the other group. Can you pair them up so that no two people would rather run off together?
Voronoi Diagrams
Split a map by asking one question, "which shop is nearest?", and you get a pattern that turns up from town planning to giraffe skin.
Ants on a Stick
Ants march along a stick and turn round whenever they meet. How long until every ant has fallen off? One idea makes it easy.
Pick's Theorem
Draw a shape on a grid of dots and find its area without measuring anything, just by counting dots.
Simpson's Paradox
One player is better at close shots and at long shots, yet has the worse score overall. How can both be true?
Bertrand's Paradox
Draw a random chord in a circle. Is it longer than the side of the inscribed triangle? Three honest methods give three different answers.
A Blind Robot in a Maze
You have the map but cannot see the robot. Is there one list of commands that leads it out from every possible starting cell?
The Sierpinski Carpet
Keep cutting holes in a square forever. Its area drops to zero, yet something is left, and it is not quite two-dimensional.
A Die from a Coin
A coin has two sides and a die has six. Can a fair coin roll a fair die, or give a chance of exactly one in three?
The Goat on a Rope
A goat eats all the grass it can reach. With pegs and ropes, can you make it eat a rectangle, a triangle or an arrow?
Corner the Queen
Two players take turns sliding a queen towards the corner, and whoever gets her there wins. The safe squares follow the golden ratio.
Braess's Paradox
A town opens a new road, and every single driver gets to work later. How can more roads mean slower traffic?
A Hundred Locks and a Hundred Keys
A heap of 100 keys for 100 identical locks. Key by key takes 4,950 tries at worst. Can any cleverer method promise fewer?
Rigid Polygons from a Construction Set
A square of bars wobbles, a triangle does not. Which extra bars lock a polygon, when every bar must be a whole number of holes?
Themes
- Probability ParadoxesPuzzles where your gut says one thing and a thousand coin flips say another.9 live · 0 in production
- Cut, Fold and FitSofas around corners, shapes from a single cut, and the shortest roads between towns.9 live · 0 in production
- Codes and Winning StrategiesCard tricks that correct errors, games you can always win, and how to find the poisoned test tube.9 live · 0 in production