Problem:
A -digit number is such that the product of the digits plus the sum of the digits is equal to the number. What is the units digit of the number?
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Test ten consecutive numbers with unit's digits through . For through we find that adding the product of the digits and the sum of the digits yields the sequence , and . In this sequence only meets the desired condition. It is easy to verify that also meet the desired condition.
With as the tens digit and as the units digit, the number is . So and .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions