CareerCup

488! sexy!

Total cubes along each x, y, z directions those are not appearing on surface are 8, 8, 8.
Therefore total cubes which are not shown on any surface = 8*8*8 = 512
Therefore total number of cubes on surface = 1000-512 = 488

10^3 - (10-2)^3 = 488 on surface

Cubes(n) = n^3- (n-2)^3 = 6n^2 - 12n + 8
Cubes(10) = 10^3 = 8^3 = 6.10^2 - 12.10 + 8 = 488

I think it will be

for top and bottom
2 X 10 X 10 = 200

for middle section
8 X (1 X 4 + 8 X 4) = 288

So it will be 200 + 288 = 488

Can anyone verify?

100

6*100

for top and bottom
2*10*10 = 200
for the remaining 4 sides
8*8*4 = 256
total = 456

sorry my mistake
remaining 4 sides will be 288 not 256
(forgot the 32 on the edges)
total = 488

488

488 is right answer.
and the correct explanation is
from top and bottom : 10*10*2
and for remaining all side : 4*8 +4*8*8
so the total is : 488

488

488

OR Look at it from a different way

Create 10 small cubes on each side

Use surface area (i.e. 100 x 6 ) which is WRONG

Take the inner 8x8 surface area thats 64 small cubes x 6 faces thats 384 (non-connected CUBES).

then take sides covering 2 faces each (8x4x3) = 96

Then you take the edges (As with rubiks cube solution) at top left, BL, TR, BR x 2 = 8 more cubes.

Result is 384+ 96 + 8 = 488 ,

alternaively, the easiest way is obviously 1000-512 = 488

Yes, the inner cube is side 8. So answer is 10^3 - 8^3 = 488.

People who claim it is 6*100 don't realize that they are counting some of the cubes two times and some of them three times.

think it this way...if you've a cube of 3*3 thn when u remove everything from the surface you'll be remained with only 1 cube which is (3-2)*(3-2) in dimension...which means only 1 cube....similarly if u've a cube of 4*4 thn you'll remain with 2*2 inside because removing from the surface will end up removing 2 edges of cube everywhere.....then let's solve this problem like 10*10*10 then inside cube will be 8*8*8...then the cube at the surface will be 10*10*10-8*8*8=488...which is the answer....

in general it is n*n*n-(n-2)(n-2)(n-2)...
thanks

think it this way...if you've a cube of 3*3*3 thn when u remove everything from the surface you'll be remained with only 1 cube which is (3-2)*(3-2)*(3-2) in dimension...which means only 1 cube....similarly if u've a cube of 4*4 thn you'll remain with 2*2*2 inside because removing from the surface will end up removing 2 edges of cube everywhere.....then let's solve this problem like 10*10*10 then inside cube will be 8*8*8...then the cube at the surface will be 10*10*10-8*8*8=488...which is the answer....

good solution bro

My Answer is 480.

First count cube in front and back end..as the side is 10,then both side will have 100*2=200 cube

Now comes to left and right side of the cube.Here we need to left 20 cube from each side, as this cubes are already used in front and back end side. So total cube in left and right side = 80*2 = 160

Now comes to top and bottom side, here we need to left 40 cube from each side, as these are already used by other sides, so total no of cubes in top and bottom = 60*2

No total no cubes in surface = 200+160+120=480

Always Draw a small diagram to solve Geometrical problems :)

10*10
9*10
9*10
8*10
8*8
8*8

total 488

People think... Is it mentioned that the thousand cubes are equally sized... Do not jump into answers without even understanding the question.