Discussion

Explanation:

Maximum number of black pieces will be obtained when maximum faces are painted black and maximum cuts are made on faces painted black.

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i.e., 2 opposite faces with 5 and 6 cuts will be painted black and two other opposite faces with 4 and 6 cuts are painted black. Rest two faces are painted yellow and red.
 
The maximum number of pieces with only black color will be = 2(4 × 5) [front and back faces] + 2(3 × 5) [right and left faces] + 4 × 5 [edges] = 40 + 30 + 20 = 90.

Hence, 90.

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