Problema Solution
A wood cube is painted white and cut into smaller 1*1*1" cubes. There are forty eight 1*1*1" cubes with exactly two faces painted white. How many of the 1*1*1" cubies have exactly one face painted white ?
Answer provided by our tutors
let
edge cubes = the ones that have 2 painted faces
corner cubes = the ones that have 3 painted faces
face(middle) cubes = the ones with only 1 painted face
the cube has 12 edges thus 48/12 = 4 cubes lie on the edges but are not corner cubes
then at each edge there are 2 more cubes that are corner cubes thus the original cubes is 6x6x6
on each side of the cube there are
6*6 - (4 + 4*4) = 16 face cubes
since the cube has 6 sides the total number of face cubes is: 6*16 = 96 cubes.