Is it possible to remove ten unit cubes from a 3 by 3 by 3 cube made from 27 unit cubes so that the surface area of the remaining solid is the same as the surface area of the original 3 by 3 by 3 cube? in how many different ways can this be done? worth 99 pts

I removed the 3 cubes from the centre of the big cube (the central column) obtaining an increase of the surface area with 10 units.

I removed a column (3 cubes) from one (any) corner of the big cube obtaining an increase with altogether 8 units of the surface area.

I removed another column, placed in the middle of a side, adjacent to the removed corner, obtaining the same surface area as at the beginning.

I removed a corner cube, not adjacent to those removed.

As example is sketched below: See picture attached.

hi there!

first we need to find out how much they are adding to each number to make the next number.

ex: 4 + 4 = 8, 8 + 8 = 16, and so on.

so continuing with 32,

32 + 32 = 64

64 + 64 = 128

128 + 128 = 256

256 + 256 = 512

4, 8, 16, 32, 64, 128, 256, 512

the 8th term of the sequence will be 512

hope this ! ~