Can you solve it? How do you like them apples? | Mathematics

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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.

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.

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