Problem:
There are positive integers that have these properties:
. the sum of the squares of their digits is , and
. each digit is larger than the one to its left.
The product of the digits of the largest integer with both properties is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
To meet the first condition, numbers which sum to must be chosen from the set of squares . To meet the second condition, the squares selected must be different. Consequently, there are three possibilities: , and . These correspond to the integers , and , respectively. The largest is , and the product of its digits is .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions