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Fiddler on the Proof

The place for mathematical puzzles and the puzzling community. Two new puzzles every Friday morning!

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Camp Algebra

Welcome to a fiendish numerical triathlon. Can you decode the trophy?

How Lucky Can a Baseball Team Get?

If teams of equal ability play many games, what’s the best record you’d expect?

Can You Sneak Past the Rings?

Three rings with gaps are evenly spaced along a cylinder and rotated around at random angles. Can you find a path down the cylinder that passes through all three gaps?

Can You Win the World Cup?

Your team has made it to the semifinals. Should you go all out in your semifinal match, or should you reserve some energy for the finals (in the hopes you make it there)?

Can You Power up the Hill?

In this year’s edition of the Tour de Fiddler, your task is to find the conditions under which a climber and a sprinter will match speeds.

Can You Fit the Stars on the Flag?

Happy Fourth of July! With stars arranged in a square grid, how many can you fit inside a circle of radius 2? And what’s the smallest circle that contains 58 stars?

Can You Tile the Hexagon?

My kitchen floor is made up of many equilateral triangles. How many distinct ways can I tile it using rhombuses that are composed of two such triangles?

Can You Fix the Random Number Generator?

I suspect that my calculator’s random number generator is malfunctioning. After it produces one number, what can I surmise regarding its behavior?

Can You Catch the Longest Wave?

A big wave makes landfall on a semicircular island and leaves the island 10 minutes later. What stretch of land might it cover 5 minutes after landfall?

Can You Infer the Color of Your Hat?

Three game show contestants must use logic to determine the color the hat on their head.