Handshakes and triangular numbers
If everyone at a party of n people shakes hands with everyone else exactly once,
how many handshakes are there?
Small notes on arithmetic, puzzles and mental math.
Estimating square roots in your head
To find √n, start from the nearest perfect square a², and add the difference divided by 2a:
Monty Hall, counted by hand
Three doors, one car. You pick door 1. The host, who knows where the car is, opens another door with a goat behind it and offers you a switch. Should you switch?
The birthday problem without formulas
In a room of 23 people, the chance that two share a birthday is just over one half. Most people guess something closer to 23/365, so it is worth seeing where the intuition goes wrong.
A divisibility test for 7 that is actually usable
Tests for 2, 3, 5, 9 and 11 are well known. The one for 7 is usually skipped because the textbook version is awkward. Here is a version that is easy to do in your head.
Casting out nines
A quick check for long sums and products that bookkeepers used for centuries before calculators.