1992 USAMO Problems/Problem 1
Find, as a function of the sum of the digits of where each factor has twice as many digits as the previous one.
The answer is .
Let us denote the quantity as . We wish to find the sum of the digits of .
We first note that so is a number of at most digits. We also note that the units digit is not equal to zero. We may thus represent as where the are digits and . Then Thus the digits of are and the sum of these is evidently , as desired.
Alternate solutions are always welcome. If you have a different, elegant solution to this problem, please add it to this page.
|1992 USAMO (Problems • Resources)|
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