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? Hint: Add up the digits.
"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." [13 + 123 and 93 + 103.]
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.