1992 USAMO Problems/Problem 1
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 • Resources) | ||
First Problem | Followed by Problem 2 | |
1 • 2 • 3 • 4 • 5 | ||
All USAMO Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.