# The Grey Labyrinth is a collection of puzzles, riddles, mind games, paradoxes and other intellectually challenging diversions. Related topics: puzzle games, logic puzzles, lateral thinking puzzles, philosophy, mind benders, brain teasers, word problems, conundrums, 3d puzzles, spatial reasoning, intelligence tests, mathematical diversions, paradoxes, physics problems, reasoning, math, science.

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impossibleroot
Hi-Keeba!

Posted: Sat Sep 24, 2011 2:10 pm    Post subject: 1

After two years, I'm going to be painting letters on these 4 big cubes, each of which spins end over end independently. In 2009, I asked for VSP's help to find combinations of letters to make as many 4 letter words as possible, and many of you rose to the challenge... thank you! I bumped that thread up to see if people had opinions about the final letter scheme. We should be painting it this week...

It occurred to me this morning: what colors should the cubes be? I thought that we could possibly make a puzzle challenge out of it. Much like the Instant Insanity cubes, perhaps we could paint the cube faces in 4 colors such that there's only one way to make every row of 4 feature all 4 colors.

What do you think? There would of course be repeat colors on a given cube so that the solution is not trivial. I'm messing around with it in Excel, but I know several of you could make short work of this with a bit of coding.

What I'm looking for, then, is a grid of 16 colors such that there is one unique rotation scheme that leads to 4 different colors per row of 4, all the way around. For a random example which most likely does not work:

 Code: RYYG RGBY GBRG BRGB

The letters could rotate in columns but their relative positions are fixed. See the picture below to see what I'm describing poorly!

Here is a shot of the cubes themselves, currently featuring a colorful series of eyes and ears.

ralphmerridew
Daedalian Member

 Posted: Sun Sep 25, 2011 2:19 am    Post subject: 2 Considering that Instant Insanity only had two solutions, and your problem is much more restrictive, the solution to that would probably work.
impossibleroot
Hi-Keeba!

Posted: Sun Sep 25, 2011 3:50 pm    Post subject: 3

 ralphmerridew wrote: Considering that Instant Insanity only had two solutions, and your problem is much more restrictive, the solution to that would probably work.

Great, elegant idea, that's what I'll do. I just tried it and it seems to work nicely.
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