2006 AMC 10B Problems/Problem 11

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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

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