1992 USAMO Problems/Problem 1
From AoPSWiki
Problem
Find, as a function of 
the sum of the digits of
where each factor has twice as many digits as the previous one.
Solution
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.
Resources
| 1992 USAMO (Problems) | ||
| First Problem | 1 • 2 • 3 • 4 • 5 | Followed by Problem 2 |
| All USAMO Problems and Solutions | ||
