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MathNet 2006 — Part 02 Question 133

Math Olympiad Vault · MathNet 2006 — Part 02

Question 133

A soccer ball is made from 32 pieces of leather. Of these pieces, 12 are identical regular pentagons and the other 20 are hexagons, also regular and identical. The sides of pentagons are the same as the sides of hexagons. To join two sides of two of these pieces, a seam is necessary. How many seams are needed to make a ball?

A) 60

B) 64

C) 90

D) 120

E) 180