Problem:
Six different digits from the set
are placed in the squares in the figure shown so that the sum of the entries in the vertical column is and the sum of the entries in the horizontal row is . The sum of the six digits used is
Answer Choices:
A.
B.
C.
D.
E.
Solution:
Determine that one suitable arrangement of the digits is as indicated, and then compute
Since , the digits in the column must be , and in some order. The sum of the digits in the row that are not also in the column must be at least . Then the square common to both the column and the row contains at most . Therefore, the or cannot be used in the common square, and hence that square must contain the digit . Thus the digits are , and , which have a sum of .
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions