Here’s a curious fact taken from The Call of Coincidence, a book by Owen O’Shea about serendipity in maths. The triangle with sides 45, 97 and 56 has an area of √459.756. Bazinga! And here are two puzzles taken from the same tome. 1. Adam’s apples Adam buys a number of apples in one shop at the rate of 3 for £1. He then buys the same number of apples in a different shop at a rate of 5 for £1. What was the average number of apples bought for each pound spent? Note: please don’t fall into the trap. 2. I can’t get no satisfaction 1 + x + x2 = y2 Show that there are no positive whole numbers x and y that satisfy the above equation. I’ll be back at 5pm UK with the answers. PLEASE NO SPOILERS. Please discuss your favourite mathematical coincidences. UPDATE: Read the answers here. Thanks to Owen O’Shea, author of The Call of Coincidence: Mathematical Gems, Peculiar Patterns and more Stories of Numerical Serendipity I’ve been setting a puzzle here on alternate Mondays since 2015. I’m always on the look-out for great puzzles. If you would like to suggest one, email me.