Hi, I'm Henry Segerman, This is the continental drift puzzle.
Ok, so it's a globe tiled like a soccer ball, with the pentagons recessed in.
One of the hexagons, this one in the south Pacific, comes out.
We can then activate the San Andreas fault, and slide California south into the ocean.
And we can keep going, mixing up all of the continents.
The continental drift puzzle is a spherical version of the 15-puzzle.
That is, one tile is missing, which lets you slide the tiles around.
You mess it up, and then you hope that you remember what you did so
you can reverse your moves. Or you could be extremely
clever and solve the puzzle legitimately. Or you can do what I do, which is unscrew
this junction, so you can take the tiles out and put them back in the right places.
This puzzle is considerably harder than the 15 puzzle.
To better illustrate why, let's look at this alternative "flat" version,
which replaces the continents of the globe with Rubik's cube-style coloured stickers.
Each hexagonal tile has three colours,
which point towards pentagons of the same colour in the solved state.
In the 15 puzzle, you can rotate three tiles and the gap around one of the corners,
and you get back to the start after 12 moves. This makes sense - there are three tiles,
and they each need to move four times to get back to where they started.
You can do the same thing with four tiles and the gap around one of the
pentagons here in the continental drift puzzle.
Each of the four tiles needs to move five times to go around, and so we should be back
to the start after 20 moves. Let's see what happens.
Ok, so they are in the positions they started in, but they have
all also rotated by a sixth of a turn. To actually get back to the start you
have to do this whole procedure six times, for a total of 120 moves.
You can't just rotate the tiles in place, because of the geometry of their feet,
sliding along rails in the core of the puzzle.
Any time a tile goes once around a pentagon it gets rotated by a sixth of a turn.
This effect is called "holonomy". For much more on holonomy,
check out my video on this puzzle, the dodecahedral holonomy maze.
The continental drift puzzle is the same as this, but with no pegs to stop movement. Instead,
there are 19 copies of the "rook" piece that get in each others' way.
As a rough estimate of how complicated the puzzle is,
we can try to count the number of possible states. Assuming that we always get the empty space back
to that spot in the south Pacific, there are 19! possible ways to arrange the 19 tiles,
and each tile has 6 possible orientations. So there are at most 19! * 6^19 states,
which is around 7*10^31. For comparison, the Rubik's
cube has about the same number of moving parts, but only has around 4*10^19 states.
The 15 puzzle famously has configurations that are not reachable.
For example, there's no way to swap just the 14 and 15 tiles.
What about the continental drift puzzle?
I don't know whether or not all 19! * 6^19 states are reachable.
Perhaps someone in the comments can figure it out and let me know.
The globe version of the puzzle tests your knowledge of geography - you have to know
where each tile is supposed to go, and which way it is supposed to be rotated.
For an even harder geography challenge, this plain version doesn't have the colour printing:
all you have is where the land is. Without context it's not easy to tell if,
say, this tile is part of South Africa or Australia or South America.
Ok, now for some details on the design and construction.
The pentagons are recessed so that the hexagonal tiles can slide over them.
I generated the continent tiles from NASA altitude and visual data.
The height of the terrain is hugely exaggerated, and I also cheated a bit, giving some extra
height to anything that is above sea level so you'd be able to see the continents better.
One of the challenges in deciding how to cut up the globe into hexagons
and pentagons was the Pacific. Tiles with no land on them are bad,
because it would be difficult to tell if they're in the correct place with the correct orientation.
In this design, there is one all-ocean tile, the one that you remove to make the gap.
All other tiles have at least a bit of land - thank you in particular to New Zealand,
Papua New Guinea, and Hawaii (and the Aleutian islands) for existing.
The colour 3D printing I used for the globe version is a new process that is,
unfortunately, very expensive.
I printed shells with the terrain that glue on to ordinary nylon plastic for the foot of each tile.
The south Pacific tile is held in place with magnets:
there are holes for putting in 5mm diameter magnetic balls.
The Rubik's cube style version is somewhat less expensive, although it still requires some
post processing. I got the stickers
made by Chewie's Custom Stickers. If you're interested in buying the pieces for this
version and making one yourself, you can contact Chewie for the stickers, link in the description.
His service and stickers are as awesome as his website.
Finally, for the plain globe tiles the land is raised up a bit which makes it easier to paint.
Alright, that's it, thanks for watching.