Skip to main content

2006 AMC 10B Problem 11

Problem 11 of 25IntermediateNumber TheoryArithmetic

What is the tens digit in the sum 7!+8!+9!+⋯+2006! ?7! + 8! + 9! + \cdots + 2006!\,?

Answer choices

Show solution

Solution

For n≥10,n\ge 10, n!n! is divisible by 100,100, so it does not affect the last two digits. The tens digit comes from 7!+8!+9!7!+8!+9! =5040+40320+362880=5040+40320+362880 =408240,=408240, whose tens digit is 4.4. Thus, the correct answer is C.
AoPS wiki

Tagged: factorial · modular arithmetic · digits

More practice