Fidgety Numbers
Calvin calls a two-digit number as fidgety if the difference between the number and its sum of digits is a perfect cube.
Find the sum of all the two-digit fidgety numbers.
Inspired by a KVPY problem.
The answer is 345.
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1 solution
Let the two digit number be 10a+b. So, for a fidgety number, the number 10a+b-(a+b)=9a should be a perfect cube, which is only possible when a=3 since 0<a<9. A fidgety number, as seen, is independent of the value of 'b', so the numbers 30 to 39 all are fidgety whose sum is 345, the answer to this problem.