Brain Teasers
10x10x10 Cube
You are given a 10x10x10 cube composed of 1x1x1 "mini-cubes" glued together. If the outer most layer falls off, how many "mini-cubes" would have fallen off?
Answer
10x10x10-8x8x8=488.Hide Answer Show Answer
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Why? How?
I'm kind of thinking this is the wrong way to approach the answer.
Take a rubik's cube for example: 3X3X3 (normal one).
The outer layer has 6 centers, and 3 on each edge has a side-edge which overlaps two sides, and a corner that overlaps three sides.
So, we have (since it's a cube...), 6 centers, 8 corners, 12 side-edges, which makes 26 1x1x1 pieces on a rubiks... Which is under a 3X3X3 cube (a 1X1X1 cube).
Now, under a 4X4X4 cube would be a 2X2X2 cube (as you take one off the top, and one off the bottom, so you take 2 pieces of each side,)
Thus, a 10X10X10 cube would have an 8X8X8 cube under it, subtract the two and you get the number of pieces.
Take a rubik's cube for example: 3X3X3 (normal one).
The outer layer has 6 centers, and 3 on each edge has a side-edge which overlaps two sides, and a corner that overlaps three sides.
So, we have (since it's a cube...), 6 centers, 8 corners, 12 side-edges, which makes 26 1x1x1 pieces on a rubiks... Which is under a 3X3X3 cube (a 1X1X1 cube).
Now, under a 4X4X4 cube would be a 2X2X2 cube (as you take one off the top, and one off the bottom, so you take 2 pieces of each side,)
Thus, a 10X10X10 cube would have an 8X8X8 cube under it, subtract the two and you get the number of pieces.
darn didnt get it
Woo! I managed to do it in my head while half asleep. My mental arithmetic and cube visualisation skills are improving. Nice puzzle.
Huh... I did it the hard way. I did 100+100+80+80+64+64.
I don't understand kratsq's comment, unless the answer has been changed. Kratsq's suggestion is the given solution.
Anyway, about 5 seconds in my head--a little too easy.
Anyway, about 5 seconds in my head--a little too easy.
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