A curious fact was brought out here *The call of chance, *a book by Owen O’Shea about serendipity in mathematics.

The triangle with sides 45, 97 and 56 has an area of √459.756.

Bazinga!

And here are two riddles taken from the same book.

**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 another shop at a price of 5 for £1.

What was the average number of apples bought for each pound spent?

Note: please do not fall into the trap.

**2. I can’t get any satisfaction**

1+ *x* + *x*^{2} = *y*^{2}

Show that there are no positive integers *x *and *y *which satisfies the above equation.

I’ll be back at 5pm UK with the answers. PLEASE NO SPOILERS. Please discuss your favorite mathematical coincidences.

*Thanks to Owen O’Shea, author of* *The Call of Chance: Mathematical Gems, Peculiar Patterns, and More Tales of Numerical Serendipity*

*I’ve been doing a puzzle here on alternate Mondays since 2015. I’m always on the lookout for great puzzles. If you want to suggest one, email me.*