How many cubes are painted with red or blue but not green? 55 or 65 72 or 66 55

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Question
How many cubes are painted with red or blue but not green?
Options
A. 55 or 65
B. 72 or 66
C. 55 or 60
D. None of these

Correct Answer

55 or 60

Explanation

Here on each face 6 x 6 = 36 cubes that are painted with one colour.
Case (i): When red and blue are opposite to each other then from one face we will get 6 x 6 = 36 cubes bot out of them 2 x 6 cubes from common edge with green painted face is common so number of cubes are 2 x 6 x 6 - 2 x 6 = 60
Case (ii): When red and blue are adjacent to each other then green is either adjacent to these or opposite to any one of red or blue, in 1^st condition number of cubes is 2 x 6 x 6 - 2 x 6 - 11 = 55 cubes or in 2^nd condition 2 x 6 x 6 -6 - 6 = 60, required number of cubes is 55 or 60