[Guest]

You have 27 1-unit small cubes that can form a 3x3x3 cube, 3 of each color: Red, Green, Blue, Black, White, Purple, Yellow, Pink and Brown.

Your task is to arrange the small cubes so that the 3x3x3 cube that is formed has all 9 colors on each of it's sides...

(I actually got this as a real plastic game and the solution is mathematical not just random guessing)

[Guest]

I don't have to work until 5:00pm and I walk next door to work(and if I didn't do a logic puzzle every now and then I'd be 'crazier' then you.

Anyways;

9 colors 6 sides 8 corners

each corner counts for 3 sides so we label them

t1 t2 t3 t4

b1 b2 b3 b4

put c1 at t1 and b4--that should put all sides with at least one c1

put c2 at t2 and b3--that should put all sides with at least one c2

put c3 at t3 and b2--that should put all sides with at least one c3

put c4 at t4 and b1--that should put all sides with at least one c4

now there are five c's left and 12 empty cubes between all the sides: t1 and b1, t2 and b2, t3 and b3, t4 and b4, t1 and t3...

each of those cubes counts for 2 sides so we need to make use of three c(n)'s for each of the 12 usable open cubes between:

put c5 between t1 and b1 and then t2 and t4 then t4 and b3

put c6 between t3 and t4 and then t4 and b4 then b1 and b3

put c7 between something

put c8 between something

leaving c9 to be the one in the middle of each side filling all the sides....

but I have to go to (stupid)work now sorry for not completeing

[Glycereine]

I don't have to work until 5:00pm and I walk next door to work(and if I didn't do a logic puzzle every now and then I'd be 'crazier' then you.

Anyways;

9 colors 6 sides 8 corners

each corner counts for 3 sides so we label them

t1 t2 t3 t4

b1 b2 b3 b4

put c1 at t1 and b4--that should put all sides with at least one c1

put c2 at t2 and b3--that should put all sides with at least one c2

put c3 at t3 and b2--that should put all sides with at least one c3

put c4 at t4 and b1--that should put all sides with at least one c4

now there are five c's left and 12 empty cubes between all the sides: t1 and b1, t2 and b2, t3 and b3, t4 and b4, t1 and t3...

each of those cubes counts for 2 sides so we need to make use of three c(n)'s for each of the 12 usable open cubes between:

put c5 between t1 and b1 and then t2 and t4 then t4 and b3

put c6 between t3 and t4 and then t4 and b4 then b1 and b3

put c7 between something

put c8 between something

leaving c9 to be the one in the middle of each side filling all the sides....

but I have to go to (stupid)work now sorry for not completeing

By placing both the first 2 colors at 2 corners each, you effectively make the rest of the solution impossible. You can only put one cube in the center (meaning on no side) and you now have 1 of each of these colors left over.

later you say to put c9 in the middle of each side, but that takes 6 cubes and you only have 3 of each color.

However we have a cube:

as previously mentioned each corner will work for 3 sides. even with a corner, the same color will need a middle side to count for 2 more and then a center piece to count for the final side. There are 6 centers, 12 center sides, 8 corners and 1 middle (that will not be seen at all)

Working backwards we put color 1 in the middle:

This necessitates that color 1 must also use up 2 corners.

we now have 8 colors, 6 centers, 12 center sides and 6 corners. Each of the 6 corners remaining must also have a center side and a center. By doing this we have used up 6 more colors (7 total), 6 centers, 6 center sides and 6 corners, leaving only 6 center sides. if a color is on 3 center sides it can cover all 6 sides, so each of the remaining 2 colors uses 3 center-sides.

Definitions:

Center side (side piece that covers two sides but not a corner)

Corner (piece at one of the 8 corners of the cube covering 3 sides)

Center (piece at one of the middles of the 6 sides covering only 1 side)

Middle (piece that is completely surrounded and not seen at all)

Color 1: Middle, 2 Corners

Color 2-7: Corner, Center, Center side

Color 8-9: 3 Center sides

to be more specific I'd have to draw a diagram and label all the locations on the cube.

edit: messed up my spoiler

Edited June 2, 2010 by Glycereine

[Glycereine]

If each number represents a color, C1-C3 are the columns from left to right, R1-R3 are the rows from front to back and Layer 1-3 are the layers from bottom to top

Layer 1	C1	C2	C3

R1	1	8	6

R2	5	2	3

R3	4	9	7


Layer 2			

R1	7	3	9

R2	6	1	4

R3	8	5	2


Layer 3			

R1	2	4	5

R2	9	7	8

R3	3	6	1

Edited June 3, 2010 by Glycereine

[Guest]

If each number represents a color, C1-C3 are the columns from left to right, R1-R3 are the rows from front to back and Layer 1-3 are the layers from bottom to top

Layer 1	C1	C2	C3

R1	1	8	6

R2	5	2	3

R3	4	9	7


Layer 2			

R1	7	3	9

R2	6	1	4

R3	8	5	2


Layer 3			

R1	2	4	5

R2	9	7	8

R3	3	6	1

I see it now logically(also I was in a hurry and the reason I didn't finish because I was running out of empty cubes for the colors I knew I wasn't gonna end up right)

but the "solution is mathematical"? Is there a formula or is logic and diagram with process of eliminations what is meant by mathematical?

[Guest]

Glycereine got it right, and btw, the name of the explosive is Nitro-glycereine...

I see it now logically(also I was in a hurry and the reason I didn't finish because I was running out of empty cubes for the colors I knew I wasn't gonna end up right)

but the "solution is mathematical"? Is there a formula or is logic and diagram with process of eliminations what is meant by mathematical?

I meant mathematical as in systematic and not just random guessing, when I got the cube I solved it same way as Glycereine, I made a list with numbers representing each small cube:

0

111111

222222222222

33333333

(the 0 being the core cube, 1's center of each side, 3's are corners and 2's are side cubes)

Now you need to put them in groups of threes so that each would sum up to 6 so it'll go like this:

033

123

123

123

123

123

123

222

222

And then you start assembling the cube according to those combination...

I didn't know what to call it but it wasn't my usual technique (reliable dumb luck )

[Guest]

use all the colored cubes for each face of 9 smaller cubes