Difference between revisions of "1996 AHSME Problems/Problem 14"
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==See also== | ==See also== | ||
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Latest revision as of 14:07, 5 July 2013
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. 
