Elements or Lower

Tue, 03 Jan 2006

The SuDoCube

Sometime during the early hours of Boxing Day, I fear I may have bought my ticket to Hell.

As part of a Christmas gift, the missus and I had been given a variation on the Rubik’s Cube, as pictured below.

The cube, perpetually unsolved

It’s similar to the Rubik’s Revenge, in that each face consists of a 4x4 grid (instead of the usual 3x3. Addditionally, the colours of each face are supplemented by a small picture of an animal — meaning that the way each facet on a side can end up in an entirely different orientation to the others becomes really clear.

As a child, I never actually had a Rubik’s Cube (though I did have a Rubik’s Magic). So, I’d spent the last couple of hours of Christmas Day engrossed in the toy, succeding in being able to solve a single face, but progressing nowhere towards being able to solve the whole puzzle.

And then I got to thinking about ways in which the puzzle could be made even harder. And then I started thinking about SuDoKu. And then I found myself bound for Hades.

In SuDoKu, the object is to fill each 3x3 region of a 9x9 grid with the numerals 1-9, such that each numeral is placed once and only once within each region, and also occurs once and only once for any given horizontal or vertical line in the grid as a whole.

One could combine this with the traditional 3x3 Rubik’s Cube such that each face consisted of the numerals 1-9 — instead of filling in the blanks, one would have to rearrange the facets on the cube such that there isn’t a repeated numeral on any face.

Fold me into a cube

This actually represents the solved cube, though it’s not at all easy to tell at a glance. On a normal Rubik’s Cube, it’s instantly obvious (colour-blindness notwithstanding) if the puzzle is completed — the real difficulty here would be that it’s no longer in any way obvious whether the cube is solved or scrambled.

Incidentally, I’m not actually at all sure whether the template represents the only solution to the puzzle. It might not, I think, given the way the cube allows facets to rotate and change position.

Anyway, here, unlike real SuDoKu, the relationship between the regions (the faces of the Cube) isn’t important — since there are four faces for each “line”, it’s not possible for each line to contain only one instance of each numeral. One could restore this constraint by having a 4×4 grid like the cube with the animals — the fiery Gehenna of hexadecimal SuDoKu, as found (so I’m told) in The Independent.

If, in the near future, a plague of boils is bestowed on London, it might not be terrorism. It might be that I’ve made a prototype and sent it to ThinkGeek.