2001 state sprint 8 4x4x4 cubes has how many cubes? correct way is 1^3 (size 4)+2^3 (size 3)+3^3 (size 2)+4^3 (size 1) =100! Total number of boxes of any size is 4C2x4C2x4C2=6^3=216; out of 216 boxes, 100/216 of them are cubes, less than half;

If it is a 3x4x5 box, total number of cubes would be 3x4x5(size 1)+ 2x3x4(size 2) + 1x2x3 (size 3) = 90; total number of boxes would be 3C2x4C2*5C2=3*6*10=180; half of them are cubes!

for 5x5x5 cubes there are total of 5c2 ^3 = 1000 boxes; out of them there are 1^3+2^3+3^3+4^3+5^3 = (1+2+3+4+5)^2=15^2=225 cubes; so there are 225/1000 cubes out of 1000 boxes, less than 1/4 about 1/5;