2006 AMC 8 Problems/Problem 11: Difference between revisions
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<math> \textbf{(A)}\ 13\qquad\textbf{(B)}\ 16\qquad\textbf{(C)}\ 17\qquad\textbf{(D)}\ 18\qquad\textbf{(E)}\ 19 </math> | <math> \textbf{(A)}\ 13\qquad\textbf{(B)}\ 16\qquad\textbf{(C)}\ 17\qquad\textbf{(D)}\ 18\qquad\textbf{(E)}\ 19 </math> | ||
== Solution == | == Solution == | ||
Revision as of 12:44, 25 April 2021
Problem
How many two-digit numbers have digits whose sum is a perfect square?
Solution
There is 
integer whose digits sum to : 
.
There are 
integers whose digits sum to : 
.
There are 
integers whose digits sum to : 
.
There are 
integers whose digits sum to 
: 
.
Two digits cannot sum to 
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 | ||
These problems are copyrighted © by the Mathematical Association of America, as part of the American Mathematics Competitions. Error creating thumbnail: File missing
