E-Ink Puzzle - How to develop more challenges for this puzzle?
Channel: OskarPuzzle
Date: 2024-04-01

Print it yourself at https://oskarvandeventer.nl/Print-It-Yourself/. Buy at https://i.materialise.com/en/shop/item/e-ink-puzzle or at https://www.shapeways.com/product/SFRSFSCA5/e-ink-puzzle E-Ink Puzzle is a packing problem, where the goal is to pack the seven Tetris-style pieces onto a 5x5 board. The pieces have little black-and-white balls with magnets. The board also has magnets, which orients any magnetic ball that is placed on top. The goal is to make a black 5x3 digit "0", with all the other balls white. The puzzle is pleasant to play, as the magnets keep the pieces in place on the board. It is also quite satisfying, and confusing, to see the color changes when sliding the puzzle over the board.

According to a Burrtools analysis, there are 111 different ways to place the seven pieces in a 5x5 grid. This number should be multiplied by 16 because of asymmetry of the board: 4x rotations, 2x front-back, 2x mirror image. So the puzzle may be much harder than it looks like.

A meta-challenge for this puzzle is to design the magnet placement in the pieces and the board such that there are multiple nice pattern challenges, not just the present "0". There are theoretically 2^50/16-or-so different possible placements of the magnets, too many to reasonable analyse with a computer. Also, it can be reasoned that even having two specific challenges (e.g. "0" and "1") may be impossible with those 50 magnets. So, we need to accept to have only this single challenge.

Copyright (c) 2023, M. Oskar van Deventer.

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