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UKMT Senior Kangaroo, 2015

Combinatorics Difficulty 3.0 AMC 10/12 Prove it United Kingdom

The diagram shows a solid with six triangular faces and five vertices. Andrew wants to write an integer at each of the vertices so that the sum of the numbers at the three vertices of each face is the same. He has already written the numbers 1 and 5 as shown. What is the sum of the other three numbers he will write?

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