Difference between revisions of "2006 AMC 8 Problems/Problem 11"
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Revision as of 01:13, 5 July 2013
Problem
How many two-digit numbers have digits whose sum is a perfect square?
Solution
There is integer whose digits sum to : 10.
There are integers whose digits sum to : 13, 22, 31, and 40.
There are integers whose digits sum to : 18, 27, 36, 45, 54, 63, 72, 81, and 90.
There are integers whose digits sum to : 79, 88, and 97.
Two digits cannot sum to 25 or any greater square since the greatest sum of digits of a two-digit number is .
Thus, the answer is .
See Also
2006 AMC 8 (Problems • Answer Key • Resources) | ||
Preceded by Problem 10 |
Followed by Problem 12 | |
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 | ||
All AJHSME/AMC 8 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.