1957 AHSME Problems/Problem 38
Problem
From a two-digit number we subtract the number with the digits reversed and find that the result is a positive perfect cube. Then:
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 .
See Also
1957 AHSC (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 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
All AHSME Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.