Starting from an intitial sequence of ♥'s and ♠'s get to the goal sequence in a certain number of moves. To do this you can use 3 replacement rules, one at a time, on any consecutive substring of the present sequence. You never need more than 6 symbols. Below is a sample puzzle and its solution.
Goal: ♥♠♠ → ♠♥♥♠♠♠ in 5 moves
♥♠♠ → ♥♥♠♠ → ♥♥♥♠♠ → ♠♠♠♠ → ♠♥♠♠♠ → ♠♥♥♠♠♠
(Rule #1) (Rule #1) (Rule #2) (Rule #1) (Rule #1)
Each puzzle below has a unique solution.
Goal: ♥♥♠ → ♥♠♥♥♥♠ in 5 moves
Goal: ♠♠♥ → ♠♠♠♥♥♠ in 5 moves
Goal: ♥♥♠ → ♠♠♠♥♠♠ in 5 moves
Goal: ♥♥♥ → ♠♠♥♠♥ in 5 moves
Rule #1: ♠ → ♠♥
Rule #2: ♠♠♠ → ♥♠
Rule #3: ♥♥ → ♠♥♥
Rule #1: ♠ → ♠♥
Rule #2: ♥♥♥ → ♠♠
Rule #3: ♥♥ → ♠♠♠
Rule #1: ♥ → ♠♥♠
Rule #2: ♥♠♥ → ♥♠
Rule #3: ♠♥♠ → ♥
Rule #1: ♥ → ♠♥♠
Rule #2: ♠ → ♥♥♥
Rule #3: ♠♥♥ → ♠
Goal: ♥♠ → ♥♠♥♥♥♠ in 6 moves
Goal: ♠ → ♠♠♥♠♠ in 6 moves
Goal: ♥ → ♠♠♥ in 6 moves
Goal: ♥♥ → ♠♥♠♠♥ in 6 moves
Rule #1: ♥ → ♠♥
Rule #2: ♠ → ♠♥
Rule #3: ♠♥♥ → ♠♠
Rule #1: ♥♥♠ → ♥
Rule #2: ♠ → ♠♥♥
Rule #3: ♥♥ → ♠♠
Rule #1: ♥ → ♠♥♥
Rule #2: ♠♥♠ → ♠♠
Rule #3: ♠♥♥ → ♥
Rule #1: ♥♠ → ♠
Rule #2: ♥ → ♥♠♠
Rule #3: ♥ → ♥♥♠
Goal: ♥♠♥ → ♥♥♠♥♥ in 7 moves
Goal: ♠♥♥ → ♠♥♠♠♠♠ in 7 moves
Goal: ♥♥♠ → ♥♠♥♥♥ in 7 moves
Goal: ♥♠♥ → ♥♠♠♥♥♥ in 7 moves
Rule #1: ♥♠ → ♥
Rule #2: ♥♥→♥
Rule #3: ♠→♠♠♥
Rule #1: ♥♥ → ♥♠♠
Rule #2: ♠ → ♠♥♥
Rule #3: ♥♠♥ → ♥
Rule #1: ♥♥♠ → ♥
Rule #2: ♥ → ♠♠♠
Rule #3: ♠ → ♠♥♥
Rule #1: ♠ → ♥♠♠
Rule #2: ♥♠ → ♠♠♥
Rule #3: ♥♥♠ → ♥♥
Goal: ♠ → ♥♥♠♥♥ in 8 moves
Goal: ♥♥ →♠♠♠♠♠♥ in 8 moves
Goal: ♥♥♠ → ♥♠♥♠♥♥ in 8 moves
Goal: ♥♠ → ♠♠♥♠♠ in 8 moves
Rule #1: ♠ → ♥♥♥
Rule #2: ♠ → ♥♠♠
Rule #3: ♥♠ → ♥
Rule #1: ♠→♠♥♠
Rule #2: ♥♠♠→♠♥
Rule #3: ♥♥→♠♠♥
Rule #1: ♥ → ♠♠
Rule #2: ♥♥♠ → ♠♥
Rule #3: ♥♠♠ → ♥♠♥
Rule #1: ♥♠ → ♠
Rule #2: ♥ → ♥♥♠
Rule #3: ♥ → ♥♥
Goal: ♠♠♥ → ♥♥♠♥♥ in 9 moves
Goal: ♠♠♠ → ♠♥♠♥♥ in 9 moves
Goal: ♠♥ → ♠♥♠♠♠♠ in 9 moves
Goal: ♥♠ → ♠♥♥♥♥ in 9 moves
Rule #1: ♥♥♠ → ♥
Rule #2: ♠♠♥ → ♠♥
Rule #3: ♠ → ♥♠♠
Rule #1: ♠♠♠ → ♥
Rule #2: ♠♠♥ → ♥♠♠
Rule #3: ♥ → ♠♥♠
Rule #1: ♠ → ♥♥♥
Rule #2: ♥♠♥ → ♠♥
Rule #3: ♠♥ → ♥♠♠
Rule #1: ♥♠♠ → ♥♥
Rule #2: ♥ → ♠♥♥
Rule #3: ♥♠ → ♠♠
Goal: ♠♥ → ♥♠♥♥♠ in 10 moves
Goal: ♠♠ → ♥♥♠♥♠♠ in 10 moves
Goal: ♥♥ → ♠♥♥♥♠♠ in 10 moves
Goal: ♠♥♥ → ♥♠♠♠ in 10 moves
Rule #1: ♠ → ♥♥
Rule #2: ♠♥♠ → ♥
Rule #3: ♥♥♥ → ♠♥♠
Rule #1: ♠ → ♥♥♠
Rule #2: ♥♥♠ → ♥
Rule #3: ♠♥ → ♥♠♠
Rule #1: ♥♥♥ → ♠♠
Rule #2: ♠♠ → ♥♥♠
Rule #3: ♥♥ → ♠♠♠
Rule #1: ♥♠♠ → ♠
Rule #2: ♥♥♥ → ♠♥
Rule #3: ♠♥ → ♥♥♠
Goal: ♥♠ → ♠♠♥♠♥♠ in 11 moves
Goal: ♠♥♠ → ♠♥♥♠♥♠ in 11 moves
Goal: ♠♥ → ♥♥♥♥♠♥ in 11 moves
Goal: ♠♠♥ → ♥♥♥♥♠♠ in 11 moves
Rule #1: ♠♥ → ♥♥♥
Rule #2: ♠♥♥ → ♠♥
Rule #3: ♥ → ♠♠♥
Rule #1: ♥♠ → ♥
Rule #2: ♠ → ♥♥
Rule #3: ♥♥ → ♠♠♥
Rule #1: ♥♠♠ → ♥♠♥
Rule #2: ♠♥♠ → ♥
Rule #3: ♥ → ♥♠
Rule #1: ♥♠♠ → ♥♥
Rule #2: ♠♥ → ♥♠♠
Rule #3: ♠♥ → ♥
Goal: ♥♠♥ → ♠♠♥♥♠ in 12 moves
Goal: ♠♥ → ♥♥♠♥♥♥ in 12 moves
Goal: ♠♥♥ → ♥♥♠♠♠♥ in 12 moves
Goal: ♥ → ♠♠♠♠♠♠ in 12 moves
Rule #1: ♠ → ♠♠♥
Rule #2: ♥♠♠ → ♥♥
Rule #3: ♥♠♥ → ♠
Rule #1: ♠♠ → ♥♥♠
Rule #2: ♠♥ → ♠♠♠
Rule #3: ♥♥♠ → ♥♥
Rule #1: ♥♥♠ → ♥
Rule #2: ♠ → ♥♠
Rule #3: ♥ → ♠♥♠
Rule #1: ♥ → ♠♥♥
Rule #2: ♥♥ → ♠♠♠
Rule #3: ♠♥♠ → ♥
Goal: ♠♥♠ → ♠♠♠♥♥ in 13 moves
Goal: ♥♠♥ → ♥♠♠♥♠ in 13 moves
Goal: ♠♥♥ → ♥♠♠♥♠♥ in 13 moves
Goal: ♠♠♠ → ♠♥♠♠♥♥ in 13 moves
Rule #1: ♥♠♠ → ♠♥
Rule #2: ♠♥♥ → ♥♠♠
Rule #3: ♠ → ♥♠♠
Rule #1: ♠ → ♥♠♥
Rule #2: ♠♥ → ♥
Rule #3: ♥♥♥ → ♥♠
Rule #1: ♥♥ → ♠♥♠
Rule #2: ♠♥ → ♥♠♠
Rule #3: ♠♥♠ → ♥♥
Rule #1: ♠♠♠ → ♠♥
Rule #2: ♥ → ♠♠
Rule #3: ♠♥ → ♥♥♠
Goal: ♠♥ → ♥♥♠♥♠♠ in 14 moves
Goal: ♥ → ♥♥♥♠♥ in 14 moves
Goal: ♠♥ → ♠♠♥♥♥ in 14 moves
Goal: ♥ → ♥♠♠♠♠ in 14 moves
Rule #1: ♠♥ → ♥♠♥
Rule #2: ♥ → ♠♠♠
Rule #3: ♥♥♠ → ♥
Rule #1: ♠♠♥ → ♠♠
Rule #2: ♥ → ♠♥♠
Rule #3: ♠♠♠ → ♥♥♥
Rule #1: ♥♠♠ → ♠♥
Rule #2: ♥ → ♥♠♠
Rule #3: ♠♠♥ → ♥♥♠
Rule #1: ♥ → ♠♠♠
Rule #2: ♠♠♥ → ♠♥
Rule #3: ♠ → ♥♠♥
Goal: ♥♥♠ → ♠♠♥♠♥♠ in 15 moves
Goal: ♠♠♥ → ♠♠♠♥♥♥ in 15 moves
Goal: ♥♠ → ♠♥♠♥♠♥ in 15 moves
Goal: ♥♠♥ → ♥♠♠♥♠♥ in 15 moves
Rule #1: ♥♠ → ♥♠♥
Rule #2: ♥♥♠ → ♠
Rule #3: ♠♥♥ → ♠♠
Rule #1: ♠♥♠ → ♠♥
Rule #2: ♠ → ♥♥♠
Rule #3: ♥♠ → ♠♠
Rule #1: ♥♥♠ → ♠
Rule #2: ♠♠ → ♥♠♥
Rule #3: ♥ → ♠♠♥
Rule #1: ♠♥ → ♠♠
Rule #2: ♠♠ → ♥♠♠
Rule #3: ♥♥♠ → ♠♥
Goal: ♠ → ♠♥♥♠♠♠ in 16 moves
Goal: ♠♥♠ → ♥♥♥♥♥♠ in 16 moves
Goal: ♠ → ♠♠♠♥♥♠ in 16 moves
Goal: ♠♠ → ♥♠♥♥♥ in 16 moves
Rule #1: ♠ → ♥♥♥
Rule #2: ♥♠♥ → ♥♠
Rule #3: ♥ → ♠♥♥
Rule #1: ♠♥♥ → ♥♠
Rule #2: ♥ → ♠♠♠
Rule #3: ♠♠ → ♥♥♥
Rule #1: ♥ → ♥♥♠
Rule #2: ♥♠♥ → ♠♥
Rule #3: ♠ → ♥♥♥
Rule #1: ♥♥♠ → ♥
Rule #2: ♠♠ → ♥♠♥
Rule #3: ♥ → ♠♥♠
Goal: ♠♠♥ → ♠♠♥♥♥ in 17 moves
Goal: ♥♥ → ♠♥♠♠♠♠ in 17 moves
Goal: ♠♠ → ♥♥♥♥♠♥ in 17 moves
Goal: ♠♠ → ♠♥♠♠♠♥ in 17 moves
Rule #1: ♠♠♠ → ♥♠♥
Rule #2: ♥♥ → ♠
Rule #3: ♥ → ♠♠♥
Rule #1: ♠♥ → ♥♠♠
Rule #2: ♥♥♠ → ♥
Rule #3: ♥ → ♠♥♥
Rule #1: ♠♥ → ♥♥♠
Rule #2: ♥♠♠ → ♠
Rule #3: ♠ → ♠♠♥
Rule #1: ♥ → ♠♥♠
Rule #2: ♠♠ → ♥♥♥
Rule #3: ♠♥♥ → ♠♠
Goal: ♥♠ → ♥♠♥♥♠♥ in 18 moves
Goal: ♠♥ → ♥♠♠♠♥ in 18 moves
Goal: ♥♠ → ♠♠♠♠♥ in 18 moves
Goal: ♥♠ → ♥♥♥♠♥♠ in 18 moves
Rule #1: ♥♥ → ♠♠♥
Rule #2: ♥♠ → ♠♥♥
Rule #3: ♠♠♥ → ♥♠
Rule #1: ♥♠♥ → ♠♠
Rule #2: ♠ → ♥♠♠
Rule #3: ♠♠♠ → ♥♥
Rule #1: ♥ → ♥♥♠
Rule #2: ♥♥♥ → ♠♠
Rule #3: ♠♥♠ → ♥
Rule #1: ♠ → ♥♠♥
Rule #2: ♠♠♥ → ♠
Rule #3: ♥♥ → ♠♥♠
Goal: ♥♠♥ → ♥♥♠♠♥♠ in 19 moves
Goal: ♠♥♥ → ♥♥♠♠♥ in 19 moves
Rule #1: ♠♥♥ → ♠♠
Rule #2: ♥♠ → ♠♥♥
Rule #3: ♠ → ♥♥
Rule #1: ♥ → ♥♥♠
Rule #2: ♠♥♠ → ♥
Rule #3: ♠♥♥ → ♠♠
See the solutions.