19. A ball is made of white hexagons and black pentagons, as seen in the picture. There are 12 pentagons in total. How many hexagons are there?
A 12
B 15
C 18
D 20
E 24
Solution
D

From the diagram in the question, it can be seen that each pentagon shares an edge with five hexagons and that each hexagon shares an edge with three different pentagons.
Therefore the total number of hexagons is $12 \times 5 \div 3=20$.