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UKMT Intermediate Mathematical Challenge, 2015

Combinatorics Difficulty 2.0 Junior Find the answer United Kingdom

The football shown is made by sewing together 12 black pentagonal panels and 20 white hexagonal panels. There is a join wherever two panels meet along an edge. How many joins are there?

(A) $20$ (B) $32$ (C) $60$ (D) $90$ (E) $180$

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