A wooden cube with edge length n units (where n is an integer) is painted black all over. By slices parallel to its faces, the cube is cut into n3 smaller cubes each of unit length. Let x0, x1, x2 and x3 be the number of smaller cubes with 0, 1, 2 and 3 faces painted black. If x0 = x3, what is n?

6

8

7

4

5

• ans is 4.
  length of each side=n
  no of cube with no face painted lies inside the box and thus=(n-2)^3
  the cube with three face painted = 8 (cubes at the 8 vertices)
  thus (n-2)^3=8
  n=4
• 11 years agoHelpfull: Yes(19) No(0)
• ans:4
  total no of cubes=n^3
  cubes with 0 sides painted x0=(n-2)^3
  cubes with 1 side painted x1=6(n-2)^2
  cubes with 2 sides painted x2=12(n-2)
  cubes with 3 sides painted x3=8
  given x0=x3
  (n-2)^3=8
  n-2=2; n=4
  
• 11 years agoHelpfull: Yes(11) No(0)
• value of n should be 4
  if n is the sides of cube, and it is cut in x0, x1, x2, x3. four part and x0=x3
  then height or sides of each cube should be n/4
  and sides of cuting cube is of unit length then n/4=1 therefore n=4
• 11 years agoHelpfull: Yes(2) No(0)