This software uses a custom binary file format to specify a set A-Puzzle-A-Day boards, a board being some combination of valid piece placements (be it all, some, or none of the pieces).
An APAD file is split into contiguous chunks of exactly 9 bytes, each chunk describing one board.
Before describing the decoding process, we first need to descibe how the pieces are represented, as well as the frame.
The image below shows the name of each piece and their base orientation. Each piece is assigned an anchor, which is marked with a dot.
Pieces are ordered alphabetically: L, N, O, P, U, V, Y, Z.
Each square in the frame is assigned a unique index, starting from zero on the 'Jan' square and progressing sequentially from left to right and top to bottom.
Note that for ease of computation, the indices 6 and 13 are skipped.
Each piece can be placed on 43 different starting squares (6 bits), rotated up to 3 times (2 bits), and is possibly mirrored (1 bit). Each piece placement can thus be described with 9 bits.
Conveniently enough, there are eight pieces in A-Puzzle-A-Day, so grouping the placement bits and rotation bits into one byte for each piece, and grouping each piece's mirror bit into one byte results in 9 bytes.
For each board described in APAD, the following applies:
- The first byte is the mirror byte, storing each piece's mirror bit.
- For the remaining eight bytes:
- The two most significant bits of each byte denote the corresponding piece's rotation amount.
- The six least significant bits of each byte denote the corresponding piece's square index.
- The order of the mirror bits aligns with the order of the remaining bytes from most to least significant.
To assemble the final board from this information, pieces are placed on an empty board in order. For each piece, the following applies in order:
- If the piece's mirror bit is 1, the piece is vertically mirrored.
- The piece is rotated 90 degrees times its rotation amount counter-clockwise.
- The piece is placed in the frame such that its anchor lands on the square with the piece's square index.
If a piece cannot be placed with this process, be it because of an invalid square index or because it would intersect a previously placed piece or the edge of the frame, then the piece is ignored and considered not placed.
Note that to deliberately exclude a piece in encoding, one should prefer setting all bits corresponding to the piece to 1.
The following image shows the decoding of the first board specified in the solutions.apad file
found in this repository:
