Problem:
All of the even numbers from to inclusive, except those ending in , are multiplied together. What is the rightmost digit (the units digit) of the product?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
If the numbers , and are multiplied, the product is , so is the final digit of the product of a set of numbers ending in , and . Since there are ten such sets of numbers, the final digit of the overall product is the same as the final digit of . Now, . Next, consider . Since any number of multiply to give as the final digit, the final digit of the required product is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions