In the name of Science!™, I’m trying to look for (or,
in the worst case, create) a puzzle/game similar to the n-puzzle whereby a player or player(s) have
to put some pieces in a particular order (e.g. in natural order in
the case where the pieces are numbers) in the fewest number of
moves, and there are restrictions on the possible moves of the
pieces which are dependent on the positions of the other pieces on
the board (e.g. in the case of the traditional n-puzzle, a
piece can be moved to an adjacent position not already occupied by
However, in the game I’m looking for, I need
the movement capabilities of each piece to be less
restricted than in the traditional n-puzzle: In the
n-puzzle, there are at most four possible pieces which can
move at any one time (because there is typically only one empty
space and pieces can only move horizontally or vertically).
Moreover, during much of the game, there are fewer than four
moveable pieces, so the average branching factor of the game is
actually quite low.
the free space” — namely, you have to consciously identify the
pieces without depending on their locative relationship with other
pieces (the pieces also lack any obvious unique identifiers such as
by being numbered: they just have abstract shapes on them, which
are not necessarily unique). At the same time, the player(s) must
be able to move exactly one piece at a time (no groups of pieces in
Are there any “sorting” puzzles/games which can easily be played
in this way (for minimizing the amount of moves) and which still
have a less “predictable” set of moveable pieces? If not, how might
I go about making one? Off the top of my head, I’m thinking it
might be useful to allow pieces to “jump” over each other similar
to in checkers but without capturing each other — would that be a
useful way to increase the number?
As answered by @BeastlyGerbil, you have the world of
twisty puzzles. Here in the Twisty Puzzle Museum you can find over 5,000 of
these kind of puzzles, and here is my personal collection of currently 279
puzzles (pictures are a bit outdated though, since I
now have a few more shelves; list is up-to-date however).
つまり、 Beastly の答えに次のようなコメントをしました：
Or perhaps a Missing Link (or Whip It! Puzzle), where you again move the tiles
around one by one, but you can also rotate some/each layer(s):
And there are many, many more examples to name. Here in the Moving Holes category of the Twisty
Puzzles Museum are quite a few to be found. And some other
categories might also be interesting to look into.