Problem:
What is the tens digit in the sum 7!+8!+9!+⋯+2006!?
Answer Choices:
A. 1
B. 3
C. 4
D. 6
E. 9
Solution:
Since n! contains the product 2⋅5⋅10=100 whenever n≥10, it suffices to determine the tens digit of
7!+8!+9!=7!(1+8+8⋅9)=5040(1+8+72)=5040⋅81
This is the same as the units digit of 4⋅1, which is (C)4.
The problems on this page are the property of the MAA's American Mathematics Competitions