Difference between revisions of "2006 AMC 10B Problems/Problem 11"
(→Problem) |
(→Problem) |
||
Line 1: | Line 1: | ||
− | == Problem | + | == Problem == |
What is the tens digit in the sum <math> 7!+8!+9!+...+2006!</math> | What is the tens digit in the sum <math> 7!+8!+9!+...+2006!</math> | ||
Revision as of 20:07, 23 October 2018
Problem
What is the tens digit in the sum
Solution
Since is divisible by , any factorial greater than is also divisible by . The last two digits of all factorials greater than are , so the last two digits of are . (*)
So all that is needed is the tens digit of the sum
So the tens digit is
(*) A slightly faster method would have to take the residue of Since we can rewrite the sum as Since the last two digits of the sum is , the tens digit is
See Also
2006 AMC 10B (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 AMC 10 Problems and Solutions |
The problems on this page are copyrighted by the Mathematical Association of America's American Mathematics Competitions.