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UKMT Grey Kangaroo, 2020

Combinatorics Difficulty 3.0 AMC 10/12 Find the answer United Kingdom

In the final of a dancing competition, each of the three members of the jury gives each of the five competitors 0 points, 1 point, 2 points, 3 points or 4 points. No two competitors get the same mark from any individual judge. Adam knows all the sums of the marks and a few single marks, as shown. How many points does Adam get from judge III?

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

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