SaturnLD

Patented by L. A. M. J. DeBergh 1996, made by LD Games, Belgium.
(plastic, 4.5 inches by 7/8 inch thick;
one the bar it says "SATURN 2x4 colors",
and on the other side of the bar is says "LD Games Belgium Patented C 1994")

Each side of the ring has 16 discs, where each of the 64 disc sides are colored with one of 14 colors. The goal is to have exactly 4 colors showing on each side (arranged in 4 sets of 4) for a total of 8 visible colors, where the remaining 6 colors are hidden. This puzzles is really a pencil and paper problem of determining which of the 14 colors are the 8 visible colors (see the next page); for the white body puzzle above they are:
Visible: yellow, pink, magenta, purple, light green, green, blue, gray
Hidden: white, orange, red, light blue, brown, black
(Black body is the same except that brown visible and gray hidden.)
Once the 8 visible colors have been determined, solving the puzzle is very easy. The bar across the center in the photos above, which the directions refer to as the "switch", is in the solved position that prevents the puzzle from being mixed up. Rotating the switch along its axis 90 degrees exposes a track on both sides. The first two positions on each side can each be used to temporarily park one or two discs, and the third position on the track allows a disc to pass from one side of the track to the other. Rotating the switch 180 degrees allows one to exchange discs from top to bottom or flip a disc:



To solve:
  1. Flip all discs that have a hidden color showing.

  2. If a color is showing on 5 discs (all colors are on at most 5 sides), find the disc that does not have a hidden color on the reverse side and flip that one.

  3. Exchange discs one or two at a time until only four colors show on each side.

  4. Rearrange colors on each side into any desired pattern (e.g., 4 groups of 4).

Determining the 8 Visible Colors
Flip each disc to make a list of 32 color pairs that are comprised by the discs (see the next page). The number of times each color occurs is:



We refer to the colors that appear only 4 times as the sparse colors. The puzzle is not so simple as the 6 sparse colors are the 6 hidden colors.

A key observation is that If a sparse color is hidden, then all colors that appear on the opposite side of a disc with that sparse color must be visible. To determine which are the visible colors, we can employ some simple deductions. We do this for the white body puzzle; the logic for the black body puzzle is similar with brown and gray reversed:
  1. There are two discs that have a sparse color on both sides, (brown, gray) and (brown, pink). It turns out that brown is hidden and gray and pink are visible (if we had guessed incorrectly and chosen brown as visible, then in the following steps one quickly reaches a contradiction where there is a color that can be neither visible or hidden).

  2. Brown is also paired with green and yellow, so at this point we know that 4 of the visible colors are gray, pink, green, and yellow.

  3. By checking our list of 64 pairs, we see that blue is paired with 4 additional colors (red, black, light blue, and white) and so if blue was hidden, that would add 4 more visible colors, making a complete set of eight. But this cannot be possible, because now light green, for example, cannot be visible (because that would make 9 visible colors) and cannot be hidden (because light green is paired with orange which is not one of these 8). Hence blue must be the 5th visible color.

  4. Similar to step 3, light green must be the 6th visible color.

  5. Similar to steps 3 and 4, magenta must be the 7th visible color.

  6. Similar to steps 3, 4, and 5, purple must be the 8th visible color.
Jaap's Page gives a similar solution (that motivated this one).

Tabulation Of The Disc Colors
Here is a tabulation, listed in alphabetical order, of the disc colors that appear in the two puzzles show in the photos on the first page. Although both have the same numbers of each color, the pairings are not the same:



Further Reading
Jaap's Page, from: http://www.jaapsch.net/puzzles/saturnld.htmm
DeBergh WO Patent, from: http://www.wipo.int - patent no. 0,000,000