README.md

Eternity2Puzzles.jl

Eternity2Puzzles.jl is an implementation of the Eternity II puzzle in Julia. You can either play the puzzle as an interactive game, or attempt to find a solution using a brute-force backtracking search.

Installation

julia> ]

pkg> add Eternity2Puzzles

Important

Please note that the interactive game part of this package might not work correctly on a Mac with Retina display (I have only tested on Windows).

Instructions

Rules

The goal is to place all 256 pieces on the board, such that the colors and symbols of adjoining pairs of edges match, and with the grey edges around the outside. Piece number 139 is a mandatory starter-piece with a fixed position on the board, that can neither be moved nor rotated.

Puzzle pieces

It is unclear to me whether the original pieces of the Eternity II puzzle are allowed to be published, so for now this package doesn't contain the edge color definitions of those pieces. It is recommended to specify the pieces in form of an input file, provided that you own the real version of the Eternity II puzzle. Alternatively, if the pieces definition is not given, they are automatically generated with colors from a published benchmark problem from the META 2010 contest.

A pieces definition file must be in plain text format (.txt) and contain 256 rows with four color numbers on each row, separated by spaces; for example

1 2 0 0
... (255 more rows)

The color numbers must be ordered in clockwise direction, starting with the top side (i.e. top, right, bottom, left). To reproduce the original pieces from the Eternity II puzzle, use the following numbers:

After creating the file, call the initialize_pieces function with the file path:

julia> using Eternity2Puzzles

julia> initialize_pieces("path/to/e2pieces.txt")

It is sufficient to do this only a single time after installing the package; the given pieces are saved to a persistent cache on disk. Subsequent calls of initialize_pieces override the cache.

Usage

To play the interactive game, type in the Julia REPL:

julia> using Eternity2Puzzles

julia> play()

Puzzle pieces can be moved with the left mouse button and rotated with a right click.

If you prefer to let the computer do the work, generate an empty puzzle board and call the solve! function to start the default search algorithm:

julia> puzzle = Eternity2Puzzle(16, 16)
16×16 Eternity2Puzzle with 1 piece:
...

julia> solve!(puzzle)

Press and hold Ctrl + C in the REPL to stop the search.

To show an image of the puzzle board, you can use

julia> preview(puzzle)

Tip

If the code is run within a Pluto.jl notebook, the board with the puzzle pieces is rendered directly inside the notebook.

The solve! function accepts an optional keyword argument alg, which should be a subtype of Eternity2Solver and selects the algorithm that is used to search for a solution of the given puzzle.

To write a custom solve algorithm, define a new subtype of Eternity2Solver, and implement the two-argument solve! method with your solver type as a second positional argument:

struct MySolver <: Eternity2Solver end

function solve!(puzzle::Eternity2Puzzle, solver::MySolver)
    # ...
end

Then you can use an instance of the solver via the alg keyword argument:

julia> puzzle = Eternity2Puzzle(16, 16)

julia> solve!(puzzle; alg=MySolver())

In case a solution is found, solve! is expected to update the puzzle.board array which contains the placements and rotations of all puzzle pieces on the board; see the docstring of Eternity2Puzzle for details.

Preview