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UKMT Junior Mathematical Challenge, 2021

Combinatorics Difficulty 2.0 Junior Find the answer United Kingdom

Each of the numbers 1 to 9 is to be placed in a different cell of the grid shown so that the sum of the three numbers in each row is 15. Also, the sum of the two numbers in each shaded column is to be 15. How many choices are there for the number to be placed in the central cell indicated by *?

(A) $0$ (B) $1$ (C) $2$ (D) $3$ (E) $4$

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