A soccer ball is made of 32 pieces of leather: white hexagons and black pentagons. Each black piece borders only with white pieces, each white piece borders with three black pieces and three white pieces. How many black pieces are needed to manufacture the ball?

The number of black pieces needed to manufacture the ball is 11 black pieces

Step-by-step explanation:

Given that the number of pieces in the soccer ball = 32 pieces

The shape of the white piece = Hexagon

The shape of the black piece = Pentagon

Each black piece borders with only white pieces

Each white piece borders with three black pieces and three white pieces

For the first black pie  piece is borders to 5 white pieces total 6 pieces

Each of the five white pieced borders 3 pieced total 5 black pieces on the sides and one white piece on top to make an additional 10 piece total = 10 + 6 = 21 piece

Each black piece holds one white piece to add extra 5 pieces to make the total = 26

At the outermost shell of the arrangement, each of the white piece attached  to a black piece will attach to an extra black piece, bringing the total to 26 + 5 = 31,

The last piece is white

Total black piece = 1 + 5 + 5 = 11 black pieces.

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