2005 iTest Problems/Problem 27
Problem
Find the sum of all non-zero digits that can repeat at the end of a perfect square. (For example, if 
were a perfect square, 
would be one of these non-zero digits.)
Solution 1
We seek nonzero digits such that some square ends with the digit repeated. Squares modulo 4 are only 0 or 1, so 11, 22, 55, 66, and 99 are ruled out immediately (since they are 3,2,3,2,3(
)). Out of the remaining numbers, since a square can have a last digit belonging to the set {
}, 33, 77, and 88 are ruled out as well. This leaves only 44. Our answer therefore is 
.
See Also
| 2005 iTest (Problems, Answer Key) | ||
| Preceded by: Problem 26 |
Followed by: Problem 28 | |
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