There is a quicker technique that works on this puzzle (but not on the Crossover) for solving the last row. So if you shift the row (or column) one step, the resulting position can be solved with those 3-cycles alone. However, if the rows (or columns) of your puzzle have an even number of tiles, then it is possible to swap two tiles in isolation, because shifting such a row (or column) one step is itself an odd permutation. It is mathematically impossible to swap just two tiles using just these 3-cycles - a swap is a permutation with odd parity whereas 3-cycles can only create even permutations. You might however be left with just two tiles that you need to swap. Once you are comfortable with these 3-cycles, it is fairly easy to solve the puzzle almost completely. Shift that row (bringing the second tile to the intersection) and column (bringing the third tile to the intersection), and then return the row and the column, and you will have cycled the three tiles around.
a tile which shares a row with the second tile and shares a column with the third tile. Pick any 3 tiles that form a right-angled triangle, i.e. On the Sixteen puzzle the rows/columns can shift a larger distance, so you can have other 3-cycles too. The diagram shows which tiles are affected. If you shift a row to the left, a column downwards, shift the row back to the right, and finally the column back upwards, the net effect is that three tiles have been cycled around. The technique for solving it can also be used on the Sixteen puzzle. It has a 4x4 playing field of tiles, but each row and each column has an extra tile so that the row/column can be shifted one step back and forth. For example Crossover, which was made by Nintendo in the early 1980s. There are several physical puzzles that are somewhat similar in that you can shift a row or column, but they don't wrap around.
#Final fantasy sliding puzzle portable#
This puzzle is also in Simon Tatham's Portable Puzzle Collection, where it is called Sixteen. Insights or academic links to similar puzzles would be helpful!
You invariably end up trading one misplaced tile for another, just moving the problem around. The issue with this technique is that it does not leave the rest of the board as it was. Then slide the row such that the position the 2 should be in is adjacent to the 2, then slide 2's column the opposite way as you originally did, and now 2 is in the correct position (and if necessary you may now slide the row back to how it originally was relative to the rest of the puzzle). For the 2, slide its column up or down, separating it from the row. This is really 2 separate steps - the 2 and 3 are each in the wrong position, and you can fix each one separately. Say the row is '1324' and you need it to be '1234'. Is there a name for this type of puzzle? What movement techniques are useful for solving them?įor example, one technique I've identified lets you fix the order of titles in a particular row. All the information I find is about tile sliding puzzles, and Rubik's Cube type puzzles are more complex. I can't seem to find any information about solutions to these types of puzzles. What makes its puzzles more challenging is that half the puzzle is figuring out what the correct arrangement even is - as if getting into that arrangement wasn't a challenge enough :) There is also an Apple Arcade game The Enchanted World (trailer) with these types of puzzles - only they aren't in perfect square shapes, each row can have a different number of tiles, and there is sometimes move count limitations, or a mobile bad guy that makes titles unmovable. It seems to have more in common with a Rubik's Cube than a sliding puzzle. This is a type of puzzle that at first looks like a tile-sliding puzzle, where you have a grid of tiles with 1 missing tile, and you can slide individual tiles into the blank spot, eventually arranging them in the right order.īut it's quite different - there is no blank spot, and you slide an entire row or column of tiles at a time, where the title that overflows wraps around to the other side.
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