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UKMT Intermediate Mathematical Challenge, 2016

Combinatorics Difficulty 2.0 Junior Find the answer United Kingdom

The diagram shows a heptagon with a line of three circles on each side. Each circle is to contain exactly one number. The numbers 8 to 14 are distributed as shown and the numbers 1 to 7 are to be distributed to the remaining circles. The total of the numbers in each of the lines of three circles is to be the same. What is this total?

(A) $18$ (B) $19$ (C) $20$ (D) $21$ (E) $22$

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