1957 AHSME Problems/Problem 38
Revision as of 23:27, 18 June 2019 by Someonenumber011 (talk | contribs)
Solution
The number can be written as
with
and
representing the digits. The number
with its digits reversed is
. Since the problem asks for a positive number as the difference of these two numbers, than
. Writing this out, we get
. Therefore, the difference must be a multiple of
, and the only perfect cube with less than
digits and is multiple of
is
. Also, that means
, and there are
possibilities of that, so our answer is
There are exactly
values of
See Also
1957 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 37 |
Followed by Problem 39 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.