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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.
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.