Difference between revisions of "2006 AMC 10B Problems/Problem 11"
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[[Category:Introductory Number Theory Problems]] | [[Category:Introductory Number Theory Problems]] |
Revision as of 22:56, 7 September 2011
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 is . (*)
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 |