Monday Braintease
A 10x10x10 rubiks cube is completely submerged in a bucked of paint. How many cubes do not have any sides covered in paint?
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512?
I did the same thing, saw the picture and ignored the 10x10x10 bit and worked it out for 3x3x3
EDIT: this was the answer for 3x3x3, it was changed just before replying.....lame post.
Youre an idiot.
I think that's right...not sure though
1000 total cubes Painted include 2- sides @ 100 cubes = 200 2- sides @ 80 cubes = 160 2- sides @ 64 cubes = 128 Total painted = 488 Total not painted = 512
Or the easier way to do it is just figure that it becomes an 8 x 8 x 8 cube.
If I got it wrong then my excuse is that I've spent too many years dragging my knuckles.
Thanks for the mid-day mental gymnastics.
Yeah, I solved it the same way as an 8x8x8
Technically, a rubiks cube doesnt have any inner cubes so the answer would be zero.
For illustrative purposes, let's pretened the Rubik's cube is a dice (and we know the opposite sides of a dice add to 7).
Pretend the 'Dice' is sitting on a desk directly in front of you. The side facing you is a '1', and the opposite side is a '6'. The side facing the right is a '2', and the side facing the left is a '5'. The side touching the desk (facing down) is a '3', and the side facing up is '4'
Let n represent the number of cubes per edge on the dice, in this case, 10.
We know there are n^3 cubes in the dice (10^3 = 1000 in this example).
We are asked the number of cubes that will not be painted (ie. The "inside" cubes).
Let's count the number of cubes that are painted, and subtract that from the total number of cubes, making sure to avoid double counting.
Counting the cubes on side '1' and '6' will have no doubles, and is easy:
The number of cubes is n^2 x 2 = 200.
Now let's move to count sides '2' and '5': (n-2) x n x 2 = 8 x 10 x 2 = 160
Now we count sides '3' and '4': (n-2)^2 x 2 = 128
In total, 200 + 160 + 128 = 488 cubes are painted. This would leave 1000 - 488 = 512 cubes unpainted.
General formula: n^3 - (n^2 x 2) - [(n-2) x n x 2)] - (n-2)^2 x 2
I thought the general formula can be reduced to simply (n-2)^3 - I'm too lazy to see if the above simplifies to that.
It does.
Good one man.
bingo. hired.
A 3x3x3 Rubik's Cube only has 26 individual cubes, so every single one would have at least one side covered in paint.
The question did not ask how many cubes would not have at least one side covered in paint on a 10x10x10 CUBE, it explicitly stated a Rubik's Cube; therefore, the answer is zero.
Thanks.
If youre from HR at a bank please PM.
goddamn, how did you guys get 8x8x8?
p.s. u should have this every monday...
[/quote]p.s. u should have this every monday...[/quote]
I also enjoyed this nice little break from the day. Thanks for posting
You cannot double count the edges and corners. That is why it comes out to 8x8x8 which are painted
How many times have you guys heard this one?
.
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