Solve it by touching it

Nobody knows the exact answer. Can you get the order of magnitude right without searching?

Fermi estimation — break an unknown into knowns

A car hides behind one of three doors. The host opens a goat door — should you switch?

Conditional probability — new information shrinks the world

A year has 365 days. How few people does it take for a shared birthday to be more likely than not?

Counting the complement — pairs grow faster than people

Move 64 discs one at a time, never placing a larger disc on a smaller one. How long would it take?

Recursion — solving a problem with a smaller copy of itself

One grain on the first square, doubling every square. Why did the king go bankrupt?

Geometric growth — doubling outruns intuition

Seven bridges, one walk, every bridge exactly once. Possible or not?

Graph theory — only the count of odd vertices matters

A hundred lockers, a hundred passes. Which doors are left open at the end?

Divisor counting — only squares have an odd number of divisors

One of a thousand bottles is poisoned. How few testers do you need to find it?

Binary encoding — each tester answers one bit

Prisoners in a line, each seeing only the hats ahead. How many can be saved for certain?

Parity as a message — one bit carries the whole line

A wolf, a goat, and a cabbage — and a boat that carries one at a time.

State search — every arrangement is a point, every trip an edge

Four people, one torch, seventeen minutes. Who crosses with whom?

Greedy is not always optimal — pair the slow ones

The barber shaves everyone who does not shave himself. Who shaves the barber?

Self-reference — why set theory needed rules

A margin too small for the proof — and 358 years of mathematics chasing it.

Why xⁿ + yⁿ = zⁿ has no solutions beyond squares

Primes look random. One unproven line says they are not.

The zeros on the critical line — still open after 160 years