Rubik's Cube Puzzle
posted by Rajesh Lal at
9:48 PM
Tuesday, April 22, 2008
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18 Comments:
i'm going to answer out of order but here it goes.
2*(n * n) + 2*((n-1) * n) + 2* ((n-1) * (n-1))
So for 3:
2*9 + 2*6 + 2*4 = 38
for 4:
2*16 + 2*12 + 2*9 = 74
its a trick question there are no cubes in a rubiks cube what so ever so for any cube its 0!
-dont have an iD yet
anon.. your formula is wrong and the answers wrong.. 3 cubed is 27, so it can't be more than that for a 3x3x3 cube..
(n^3) - ((n-2)^3) where n >= 2
n=2: 8 - 0 = 9
n=3: 27 - 1 = 26
n=4: 64 - 8 = 56
n=5: 125 - 27 = 98
etc..
doh.. typo..
n=2: 8 - 0 = 8
No no, he/she wants to know how many cubes. That would be just (3^3)-1. The minus one is because one in the center is not actually there. Now think it through. Looking at the top, there are nine. Then on the bottom there are nine. Then the middle layer is only 8 because the missing one (actually it is a sphere with prongs that twist to hold the devil's toy together). Add 9+9+8=(3^3)-1=26. Had he/she asked how colored squares are there, then the answer would be 9 (number across by the number down [3*3]) time 6 (the number of sides).
Cubes can't be on the "surface"
He probably means "squares" not "cubes"
Unless... he means the cube's surface is all the cubes within it except the center. (like the crust/mantle/outer core of a cubic earth) If so, the last person got it right)
Of course it doesn't make sense because the center of a Rubik's cube isn't a cube. Open one up and look!
-Deep
There are 20 cubes in a 3x3x3 rubics cube and there are 56 in a 4x4x4
it is actually
6(n^2)
that is true because you find the area of one side wich is squaring n and then multiplying the number by how many sides wich is six so as i said the formula for this is 6(n^2)
for a 4*4*4 it would be 6(4^2)=96
and a 3*3*3 is 6(3^2)=54
wait nevermind that is for suface area
its actually
2(n^2)+4n
so for a 3*3*3 is would be
2((3)^2)+4(3)
=2(9)+12
=18+12
=30
for a 4*4*4 it would be
2((4)^2)+4(4)
=2(16)+16
=32+16
=48
for n*n*n it would be again
2(n^2)+4n
its 0 fools, for it to be a cube on the surface, it'd have to show 6 sides,the most shown are 3 on the corners
by that reasoning brownbear the answer would be 1 as the rubix is a cube . There are 54 squares on the surface of a 3x3x3 cube unless you count squares made of squares then that would be 84, for 4x4x4 it is 96 or 180 with squares made of squares. or euclid's brother is correct. all depends on interpritation, ill go for 1 as my answer.
Hi everyone
I'm new here but this looks like fun. Here's my penny's worth.
I think the big clue here is the word "surface". Also we know that for 3x3 there can be no more than 27 cubes, 9 for each layer. Therefore the answer is the number of cubes for which we can see on at least one surface minus the number of hidden.
For a 3x3 cube this would be
3*3 + 3*3 + 3*3 -1 = 26
or
3^3 - 1
For a 4x4 cube
4*4 + 4*4 + (4*4 - 2*2) + (4*4 - 2*2) = 56
or
4^3 - 8
For a nxn cube
n^3 -(n-2)^(n-2)
9 in the front
9 in the back
3 unused on the left, right, top and bottom
3 time 4 = 12
9+9+12= 30
16 in front
16 in back
4 on sides and top and bottom
4 times 4 = 16
16+16+16= 48
Wow guys come one. Let's think about this spacialy; 3x3x3 Rubiks cube would have 27 TOTAL cubes(a three dimensional object).
The question is how many cubes are on the surface. So, 9 on top(3x3) and 9 on bottom(3x3) equals 18. That leads us to the middle section in which not all of the cubes can physically exist on the surface simply because 1 exists in the center unseen. So 9 - 1 is 8 and 8 + 9 + 9 = 26
With a 4x4x4 you have a TOTAL of 64 cubes: 16 on top, 16 on bottom and 24 on the surface of the middle sections. 8 exist unseen in the center. 16 + 16 + 24 = 56
WELL DONE BOB.
for 3x3x3 rubiks cube : 3^3-1=26
4x4x4 : 4^3-8=4^3-2^3=56
so.. nxnxn : n^3-(n-2)^3
for 3x3x3 rubiks cube : 3^3-1=26
4x4x4 : 4^3-8=4^3-2^3=56
so.. nxnxn : n^3-(n-2)^3
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