
The Rectangle’s Diagonal
A rectangle inscribed in a quarter circle with a radius of 1: what is the exact length of its diagonal AC?

A rectangle inscribed in a quarter circle with a radius of 1: what is the exact length of its diagonal AC?

With six matches, and without bending or breaking them, can you make four equilateral triangles? A classic from Polygon.

A Dynamos cyclist climbs at 10 mph and descends the same road at 30 mph. What’s his average speed? Beware the easy answer.

Nine dots arranged in a square and four straight lines drawn without lifting the pen: can you connect them all?

Two Dynamos trains race toward each other while a fly zips back and forth between them. How far does the fly travel before they…

Ten gallons of water, ten of wine, and three-gallon transfers back and forth: can both carafes ever reach the same percentage of wine?

A teaspoon of water into the wine, then a teaspoon of the mix back into the water: is there more water in the wine…

On Staterion, water is dispensed to the exact gallon. With a 3-gallon jug and a 5-gallon jug, how do you get 4 in the…

A water lily that doubles in size every day covers a lake in 100 days. How many days does it need to cover half…

Liz, Dord, and M00N pay $30 for drinks on Paradoxon, get a discount, leave a tip… and a dollar seems to vanish. Where did…

A rope as long as Earth’s equator, lengthened by just one yard: can an ant, a cat, or an elephant pass underneath it?

A seven-link gold chain, one link a day for seven days: what is the fewest links you must break? And with 30?