A solid cube of side five centimeters has all its faces painted. The cube is sliced into smaller cubes, each of side one centimeter. How many of these smaller cubes will have paint on exactly one of its faces?
My approach:- let there are x smaller cubes. So, $$6*5^2 = 6*x*1^2$$ $$x = 25$$
At least two faces of the smaller cubes on the edge of the bigger one are painted. So, to find all small cubes that satisfy the condition, we should count only ones that are not on edges of the bigger one. There are $9$ of this kind on each face, having 6 faces the answer is $9\cdot 6=54$