2,664 coin-sliding font puzzles! These puzzles are based on two fonts, each with 37 characters (letters, digits, and slash). For each pair of characters (say, A and B), the goal is to re-arrange the first character (A) into the second (B) by a sequence of moves. Each move picks up one coin and places it in an empty grid cell that is adjacent to at least two other coins (the “2-adjacency” rule). In addition to solving the puzzle, the goal is to minimize the number of moves.
Puzzle game: In this app, you can try your hand at solving all 2,664 puzzles. Select a font (5×7 or 5×9), then choose a puzzle from “All puzzles in family” or using the “Start” and “Target” dropdowns. Drag coins to make moves. If you get stuck, you can “Undo” move by move, or “Reset” to the beginning. You can make reverse moves (moving a coin adjacent to two others to any grid square) by dragging coins on the target (right) configuration. When you solve a puzzle (the left and right configurations match), you can post your score (number of moves) along with your name and/or email (if you want). Help us find good solutions to all the puzzles!
Related research: Demaine, Demaine, and Verrill analyzed this type of coin-sliding puzzle in 2000. They gave a polynomial-time algorithm to solve (when possible) all puzzles on the triangular grid and most puzzles on the square grid (in particular, all of these puzzles) using a polynomial number of moves. However, we still don't know the best (fewest-moves) way to solve these puzzles. There's also a paper about these fonts and puzzle game: http://erikdemaine.org/papers/CoinSlidingFont_G4G13/
Related puzzles: Our puzzles are a tribute to Martin Gardner, who wrote about coin-sliding puzzles in his article "Penny Puzzles" in Mathematical Carnival (1989). You can play some of these classic puzzles on the Coins app: https://play.google.com/store/apps/details?id=air.com.monosynthgames.coins&hl=en
You can also play this game at http://coinsliding.erikdemaine.org/
You can also write messages in these fonts using our associated font app: http://erikdemaine.org/fonts/coinsliding/