Around 1919, the British mathematician G. H. Hardy hopped on a London cab on his way to visit his Indian colleague Srinivasa Ramanujan.

The cab’s licence number, 1729, seemed dull to Hardy but his pal fervently disagreed. “It is a very interesting number,” said Ramanujan. “It is the smallest number expressible as the sum of two cubes in two different ways.”

1729 = 1 3 + 12 3 = 9 3 + 10 3

Hardy’s anecdote is one of the most well-told in British mathematics, and has given rise to taxicab number, which is any number that is the smallest number expressible as sums of two cubes in n different ways.

It is also why the UK’s first specialist maths secondary school, which opens in London in September next year, will be called the 1729 Maths School.

Today’s puzzles are loosely based on

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