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 different replacement rules, one at a time, on any consecutive substring of the present sequence. You may not have more than 6 symbols at any one time.
Goal: ♥♥ → ♠♥♥♥♥♥ in 6 moves
Goal: ♥♥♠ → ♥ in 6 moves
Goal: ♠♥♠ → ♠♥♠♥♥ in 8 moves
Goal: ♥♠ → ♥♥♠♥♥ in 8 moves
Goal: ♥♠ → ♠♠♥♠♠ in 10 moves
Goal: ♥ → ♠♥♠♥♥ in 10 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: ♠ → ♠♠
Rule #1: ♥♥ → ♠♠♠
Rule #2: ♥♥♠ → ♠♥
Rule #3: ♠ → ♥♥♥
Rule #1: ♠ → ♥♥
Rule #2: ♥♠♥ → ♠
Rule #3 : ♥ → ♠♠♥
Rule #1: ♠♠♥ → ♥♠
Rule #2: ♥♥♠ → ♠♠
Rule #3: ♥ → ♥♥♠
Rule #1: ♠♥♠ → ♥
Rule #2: ♥ → ♠♥♥
Rule #3: ♥♥♠ → ♠♠
The answers are here.