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Devilish Cubes (Posted on 2009-07-27) Difficulty: 3 of 5
I once was presented with a set of 4 cubes each having a different net configuration.

The object was to place the cubes in a line such that no face within any of the four rectangles so formed contained the same colour within that rectangle.
Then too, no colour was orthogonally adjacent to a face of the same colour in an adjoining rectangle.
Lastly the end faces of the composite prism were both different to each other and not repeated within the rectangular faces.

4 2 1 6
3 3 3 3
5 2 3 1 4 6 4 2 2 2 4 4
4 5 5 5
j k l m
Caution: This is not an on-line interactive presentation.

The table above shows a set of cubic nets. Replace j, k, l & m with an appropriate label A, B, C or D to indicate the net used.

Additionally add just one digit to each cell in compliance with those nets so that each row along with the end values contains unique values.

  Submitted by brianjn    
Rating: 2.0000 (1 votes)
Solution: (Hide)
Below is my single solution and how I arrived at it. Note that Charlie in comments points out that this solution is not unique.
Rotate A 90° clockwise around the 2 but leave the top 4 in its original position.

Rotate 180° and leave the 2 in its place.

Raise each block in middle column of C but place the 1 in the position previously occupied by the 5. Leave the 3 in its new position and rotate the lower cell 90° clockwise around the 5.

Lower each block in the middle column of D but place the 5 in the top place. Rotate the lower blocks 90° clockwise around the 3.

Place the blocks in the order of C, B, A and D. Use the columns of 4 in each of these and the 1 from D and 6 from D.

1 3 2 4 5 6
4 5 3 2
5 4 2 3
2 3 5 4

When I was presented such a set of dice I was told the problem was called "Devil's Dice". All of my internet searches reveal "Devil's Dice" as being just a pair but I didn't investigate those articles further.
Also I believe that at that time I was told there was a unique solution; if that was true then clearly in my reconstruction of the idea my arrangement is not of what I was given.

Comments: ( You must be logged in to post comments.)
  Subject Author Date
re: computer solutionCharlie2009-08-12 18:24:49
Solutioncomputer solutionCharlie2009-07-27 16:28:53
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