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