2006 AMC 10B Problems/Problem 11
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 be 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 | |
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