A tile of a monkey puzzle has four monkey halves that can be labelled as north (N), east (E), south (S), and west (W) half. In addition to the shape of the border rectangle, these halves determine which edges can be placed next one other. There is also another way to define how the tiles can be placed: Each tile corner (i.e. compass directions NE, SE, SW, and NW) has a monkey quarter. If we abstract this quarter, for example, with a letter, only the tiles with the same letter in their touching corners can be adjacent. illustrates one valid solution for this quarter monkey puzzle. Are the two monkey puzzle representations equivalent in the sense that if we have a pile of ‘half monkey’ tiles H, it is possible to define a pile of ‘quarter monkey’ tiles Q that gives exactly the same set of solutions for the puzzle (and vice versa)?
A tile of a monkey puzzle has four monkey halves that can be labelled as north
(N), east (E), south (S), and west (W) half. In addition to the shape of the border
rectangle, these halves determine which edges can be placed next one other. There is
also another way to define how the tiles can be placed: Each tile corner (i.e. compass
directions NE, SE, SW, and NW) has a monkey quarter. If we abstract this quarter, for
example, with a letter, only the tiles with the same letter in their touching corners can
be adjacent. illustrates one valid solution for this quarter monkey puzzle.
Are the two monkey puzzle representations equivalent in the sense that if we have a
pile of ‘half monkey’ tiles H, it is possible to define a pile of ‘quarter monkey’ tiles
Q that gives exactly the same set of solutions for the puzzle (and vice versa)?
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