UKMT Pink Kangaroo, 2025

Combinatorics Difficulty 2.0 Junior Find the answer United Kingdom

Six circles are arranged in the shape of a triangle. Louis is asked to write the positive integers from one to six, inclusive, in the circles so that the sums of the numbers on each side of this triangle are the same. He is then asked to calculate the sum of the three integers at the vertices of the triangle. How many different sums could Louis calculate?

(A) $1$ (B) $2$ (C) $3$ (D) $4$ (E) $5$

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