# Domino meets Towers of Hanoi

When a neighbor and colleague of mine told me he has a blog about abstract comics, that concept fascinated me to the extent that I had to make one myself. Here it is:

This, by the way, makes a nice poster. I called it Migration, and didn’t give a clue where it came from. There are very smart people who have figured it out by just looking at it, but you can’t compete, because you have already read the title of this post.

Let’s begin with the Towers of Hanoi. This puzzle is so famous that I will not explain it here, mainly because I was traumatized as a high school student when I was forced to solve the puzzle with four disks on TV, in the German TV series Die sechs Siebeng’scheiten. I just pray that no recording has survived.

In any case, after a healthy dose of abstraction, let’s look at the Towers of Hanoi from above, and treat it as a card game.
The disks are replaced with cards that have a disk symbol on it. For the three disk game, there are three different cards, showing a small, medium, or large disk. To make everything visually more appealing, we color the disks, and to emphasize size, we show empty annuli around the smaller disks, as above. Then the solution of the three disk puzzle would look like this:

Because a card hides what is possibly underneath, a position requires context. This is one of the two ways the puzzle is mutating into a story. In the next step, we use domino shaped cards consisting of two squares instead of square cards. Here are the six hanoiomino cards:

The puzzle is played on a 2 x 3 rectangle, with all six cards stacked like this in the top row:

Note that we have modified the Hanoi-rule: In the original version, a card can only be placed on an empty field or on a card with a larger disk. A hanoiomino must be placed so that each of the squares either covers an empty square or a square with a disk of at larger or equal size. This allows for more choice, which causes the second mutation of puzzle into story.

The migration story now tells how to move all the hanoiominos to the bottom row, to the same position, albeit reversed. It is the shortest solution, and unique as such, unless you want to count the backwards migration as a second solution.