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UKMT Pink Kangaroo, 2020

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

Kanga labelled the vertices of a square-based pyramid using $1, 2, 3, 4$ and $5$ once each. For each face Kanga calculated the sum of the numbers on its vertices. Four of these sums equalled $7, 8, 9$ and $10$ . What is the sum for the fifth face?

(A) $11$ (B) $12$ (C) $13$ (D) $14$ (E) $15$

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