## September 2016

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My September diary recorded my having watched the Ramanujan movie, *The Man Who Knew
Infinity*, then this:

Oh, you want a brainteaser? OK, here's a fairly easy one.

The Ramanujan movie of course includes the famous taxicab incident.

Once, in the taxi from London, Hardy noticed its number, 1729. He must have thought about it a little because he entered the [hospital] room where Ramanujan lay in bed and, with scarcely a hello, blurted out his disappointment with it. It was, he declared, "rather a dull number," adding that he hoped that wasn't a bad omen.That number, 1729, has another interesting and rare property. What is it?

"No, Hardy," said Ramanujan, "it is a very interesting number. It is the smallest number expressible as the sum of two [positive] cubes in two different ways." [1^{3}+ 12^{3}and 9^{3}+ 10^{3}.]Hint: Add up the digits.

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**• Solution**

Adding up the digits: 1 + 7 + 2 + 9 = 19.

Reverse the digits of 19: 91.

Multiply 19 by 91: 19 × 91 = 1729.

This only works for one other four-digit number, which you can now easily find.