Problem of the Week 1116The Digits of 4444^{4444}The sum of the digits of 4444^{4444} is A (in base 10). The sum of the digits of A is B. What is the sum of the digits in B? I know that we could ask our favorite CAS, but there is a relatively short pencil proof. Source: Mathematical Morsels by Ross Honsberger, 1978. © Copyright 2009 Dave Ehren and Shilad Sen. Reproduced with permission. |