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CEMC Gauss (Grade 7), 2009

Combinatorics Difficulty 2.0 Junior Find the answer Canada

In the diagram, a $4 \times 4$ grid is to be filled so that each of the digits $1, 2, 3,$ and $4$ appears in each row and each column. The $4 \times 4$ grid is divided into four smaller $2 \times 2$ squares. Each of these $2 \times 2$ squares is also to contain each of the digits $1, 2, 3$ and $4$ . What digit replaces $P$ ?

(A) $1$ (B) $2$ (C) $3$ (D) $4$ (E) The digit cannot be determined

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