June 16, 2024

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.


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 + x2 = y2

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.

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