Coin Sliding Font

by Erik Demaine and Martin Demaine, 2018


2,664 coin-sliding font puzzles. For each of the two fonts, each pair of characters (say, A and B) forms a puzzle: 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). You can try dragging coins above according to this rule! In addition to solving the puzzle, the goal is to minimize the number of moves. Each font has 37 characters (letters, digits, and slash), resulting in 37 · 36 = 1,332 puzzles per font.

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 G4G13 paper about these fonts.

Puzzle video game. Our accompanying puzzle video game can be played in any web browser, or as an Android app. Try your hand at solving all 2,664 puzzles. Post your best scores (number of moves) and help us find good solutions to all the puzzles!

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 Android app.

Check out other mathematical and puzzle fonts. • Feedback or not working? Email Erik.