1996 AHSME Problems/Problem 14
Problem
Let denote the sum of the even digits of . For example, . Find
Solution
The problem is asking for the sum of all the even digits in the numbers to . We can remove from the list, add to the list, and tack on some leading zeros to the single digit numbers without changing the sum of the even digits. This gives the list:
.
There are digits on that list, and each digit appears times.
Thus, each even digit appears times, and the sum of all the even digits is , and the correct answer is .
See also
1996 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
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.