Problem:
The unit's digit (one's digit) of the product of any six consecutive positive whole numbers is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Any selection of six consecutive positive whole numbers has at least one multiple of and at least one multiple of . Thus, the product has at least one factor of and must end in .
The statement of the problem implies that any six consecutive positive numbers can be used. Compute to find that the last digit is . Or, even easier, multiply any six consecutive integers containing to see without multiplication that the last digit must be .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions