How many cubes have no blue face?

Geometry Level 2

A wood of block measuring 5 in. by 6 in. by 7 in. is painted blue. It is then completely cut to cubes which measure 1 in. on an edge. How many cubes have no blue face?

150 8 94 48 210 180 60

1 solution

Chew-Seong Cheong
May 18, 2018

The cubes with no blue surface are those in the cuboid one cube from the surface which is $3\times 4 \times 5 = \boxed{60}$ .

Note that the total number of cubes are $5\times 6 \times 7 = 210$ . Those with 1 blue face are 94, 2 blue faces are 48 and 3 blue faces, 8. Therefore, those with no blue face are $210-94-48-8 = \boxed{60}$ .

How many cubes have no blue face?

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