Problem:
To complete the grid below, each of the digits through must occur once in each row and once in each column. What number will occupy the lower right-hand square?
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Answer Choices:
A.
B.
C.
D.
E. cannot be determined
Solution:
The number in the last column of the second row must be because there are already a and a in the second row and a in the last column. By similar reasoning, the number above the must be . So the number in the lower right-hand square must be . This is not the only way to find the solution.
The completed square is
Answer: .
The problems on this page are the property of the MAA's American Mathematics Competitions