Spotlight on...
the Magellán
Puzzle
(aka Magellan)
The Magellán is another super rare puzzle
and there are three known versions, one with both sides black,
one with both sides white, and one with one side black and the other white
(just like the one I have!).
(click
on the picture to enlarge)
| Each side has 33 "neighbourhoods" (total of 66).
And each neighbourhood contains a cylinder which can turn and may be shared
with a neighbourhood on the other side of the puzzle.
Each cylinder has six colours (yellow, white, black, blue, green, and red) and only nine of them (out of a total of 57) can be viewed on both sides.From those nine, four have order black-red-yellow-green-white-blue, and the other five have order black-red-yellow-white-blue-green. For a total of two colors to exist on both sides it is impossible with this configuration. By having three colors though, it is possible (but too easy). The same can be said by placing the cylinders such that two colors can be seen at the same time. For some time, this puzzle confused many collectors regarding its purpose. But by looking at the patterns of the puzzle, I concluded that it is indeed a coloring problem (usually found in my beloved graph theory) puzzle. That is, to try to use a total of as less as possible colors making sure that no two neigbourhood boxes (sharing an edge) have the same color. Different difficulty levels may be chosen. A total of five colors on both sides could be easy, a total of three colors (even only on each side) is impossible, while below I have a (non-unique) solution using only four colors for both sides. Using exactly four colors for both sides seems to be the goal of this puzzle. |
Solution (non
unique - showing both sides)
(the purple lines show the neighbourhoods that share a cylinder)
| This puzzle actually tackles a more deep problem, more specifically,
the famous four color problem/theorem which says that for every map, four
colors are always enough, such that no neighbourhoods have the same color.
Computer science people have showed "exhaustive search proofs", which are not elegant enough to be accepted by mathematicians (like me LOL). The Magellán puzzle takes this concept one step further, as the restrictions imposed by the nine cylinders which are "seen" by both sides, give that extra difficulty, plus the feeling that solving both sides with only four colors might not be possible. Fortunately, it did not require me to prove any theorem (that includes a double sided four color problem!!!) to show that it is possible. :-) |
Please let me know of any comments or suggestions. Thanks! :-)