Replacement Puzzles
Replacement Puzzles

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.

Rule #1: ♠ → ♥♠
Rule #2: ♥♥♥ → ♠♠
Rule #3: ♠♥ → ♠

Goal: ♥♠♠ → ♠♥♥♠♠♠ in 5 moves

♥♠♠ → ♥♥♠♠ → ♥♥♥♠♠ → ♠♠♠♠ → ♠♥♠♠♠ → ♠♥♥♠♠♠
(Rule #1)    (Rule #1)    (Rule #2)    (Rule #1)    (Rule #1)        

Each puzzle below has a unique solution.

1.

Rule #1: ♠ → ♠♥
Rule #2: ♠♠♠ → ♥♠
Rule #3: ♥♥ → ♠♥♥

Goal: ♥♥♠ → ♥♠♥♥♥♠ in 5 moves

2.

Rule #1: ♠ → ♠♥
Rule #2: ♥♥♥ → ♠♠
Rule #3: ♥♥ → ♠♠♠

Goal: ♠♠♥ → ♠♠♠♥♥♠ in 5 moves

3.

Rule #1: ♥ → ♠♥♠
Rule #2: ♥♠♥ → ♥♠
Rule #3: ♠♥♠ → ♥

Goal: ♥♥♠ → ♠♠♠♥♠♠ in 5 moves

4.

Rule #1: ♥ → ♠♥♠
Rule #2: ♠ → ♥♥♥
Rule #3: ♠♥♥ → ♠

Goal: ♥♥♥ → ♠♠♥♠♥ in 5 moves

5.

Rule #1: ♥ → ♠♥
Rule #2: ♠ → ♠♥
Rule #3: ♠♥♥ → ♠♠

Goal: ♥♠ → ♥♠♥♥♥♠ in 6 moves

6.

Rule #1: ♥♥♠ → ♥
Rule #2: ♠ → ♠♥♥
Rule #3: ♥♥ → ♠♠

Goal: ♠ → ♠♠♥♠♠ in 6 moves

7.

Rule #1: ♥ → ♠♥♥
Rule #2: ♠♥♠ → ♠♠
Rule #3: ♠♥♥ → ♥

Goal: ♥ → ♠♠♥ in 6 moves

8.

Rule #1: ♥♠ → ♠
Rule #2: ♥ → ♥♠♠
Rule #3: ♥ → ♥♥♠

Goal: ♥♥ → ♠♥♠♠♥ in 6 moves

9.

Rule #1: ♥♠ → ♥
Rule #2: ♥♥→♥
Rule #3: ♠→♠♠♥

Goal: ♥♠♥ → ♥♥♠♥♥ in 7 moves

10.

Rule #1: ♥♥ → ♥♠♠
Rule #2: ♠ → ♠♥♥
Rule #3: ♥♠♥ → ♥

Goal: ♠♥♥ → ♠♥♠♠♠♠ in 7 moves

11.

Rule #1: ♥♥♠ → ♥
Rule #2: ♥ → ♠♠♠
Rule #3: ♠ → ♠♥♥

Goal: ♥♥♠ → ♥♠♥♥♥ in 7 moves

12.

Rule #1: ♠ → ♥♠♠
Rule #2: ♥♠ → ♠♠♥
Rule #3: ♥♥♠ → ♥♥

Goal: ♥♠♥ → ♥♠♠♥♥♥ in 7 moves

13.

Rule #1: ♠ → ♥♥♥
Rule #2: ♠ → ♥♠♠
Rule #3: ♥♠ → ♥

Goal: ♠ → ♥♥♠♥♥ in 8 moves

14.

Rule #1: ♠→♠♥♠
Rule #2: ♥♠♠→♠♥
Rule #3: ♥♥→♠♠♥

Goal: ♥♥ →♠♠♠♠♠♥ in 8 moves

15.

Rule #1: ♥ → ♠♠
Rule #2: ♥♥♠ → ♠♥
Rule #3: ♥♠♠ → ♥♠♥

Goal: ♥♥♠ → ♥♠♥♠♥♥ in 8 moves

16.

Rule #1: ♥♠ → ♠
Rule #2: ♥ → ♥♥♠
Rule #3: ♥ → ♥♥

Goal: ♥♠ → ♠♠♥♠♠ in 8 moves

17.

Rule #1: ♥♥♠ → ♥
Rule #2: ♠♠♥ → ♠♥
Rule #3: ♠ → ♥♠♠

Goal: ♠♠♥ → ♥♥♠♥♥ in 9 moves

18.

Rule #1: ♠♠♠ → ♥
Rule #2: ♠♠♥ → ♥♠♠
Rule #3: ♥ → ♠♥♠

Goal: ♠♠♠ → ♠♥♠♥♥ in 9 moves

19.

Rule #1: ♠ → ♥♥♥
Rule #2: ♥♠♥ → ♠♥
Rule #3: ♠♥ → ♥♠♠

Goal: ♠♥ → ♠♥♠♠♠♠ in 9 moves

20.

Rule #1: ♥♠♠ → ♥♥
Rule #2: ♥ → ♠♥♥
Rule #3: ♥♠ → ♠♠

Goal: ♥♠ → ♠♥♥♥♥ in 9 moves

21.

Rule #1: ♠ → ♥♥
Rule #2: ♠♥♠ → ♥
Rule #3: ♥♥♥ → ♠♥♠

Goal: ♠♥ → ♥♠♥♥♠ in 10 moves

22.

Rule #1: ♠ → ♥♥♠
Rule #2: ♥♥♠ → ♥
Rule #3: ♠♥ → ♥♠♠

Goal: ♠♠ → ♥♥♠♥♠♠ in 10 moves

23.

Rule #1: ♥♥♥ → ♠♠
Rule #2: ♠♠ → ♥♥♠
Rule #3: ♥♥ → ♠♠♠

Goal: ♥♥ → ♠♥♥♥♠♠ in 10 moves

24.

Rule #1: ♥♠♠ → ♠
Rule #2: ♥♥♥ → ♠♥
Rule #3: ♠♥ → ♥♥♠

Goal: ♠♥♥ → ♥♠♠♠ in 10 moves

25.

Rule #1: ♠♥ → ♥♥♥
Rule #2: ♠♥♥ → ♠♥
Rule #3: ♥ → ♠♠♥

Goal: ♥♠ → ♠♠♥♠♥♠ in 11 moves

26.

Rule #1: ♥♠ → ♥
Rule #2: ♠ → ♥♥
Rule #3: ♥♥ → ♠♠♥

Goal: ♠♥♠ → ♠♥♥♠♥♠ in 11 moves

27.

Rule #1: ♥♠♠ → ♥♠♥
Rule #2: ♠♥♠ → ♥
Rule #3: ♥ → ♥♠

Goal: ♠♥ → ♥♥♥♥♠♥ in 11 moves

28.

Rule #1: ♥♠♠ → ♥♥
Rule #2: ♠♥ → ♥♠♠
Rule #3: ♠♥ → ♥

Goal: ♠♠♥ → ♥♥♥♥♠♠ in 11 moves

29.

Rule #1: ♠ → ♠♠♥
Rule #2: ♥♠♠ → ♥♥
Rule #3: ♥♠♥ → ♠

Goal: ♥♠♥ → ♠♠♥♥♠ in 12 moves

30.

Rule #1: ♠♠ → ♥♥♠
Rule #2: ♠♥ → ♠♠♠
Rule #3: ♥♥♠ → ♥♥

Goal: ♠♥ → ♥♥♠♥♥♥ in 12 moves

31.

Rule #1: ♥♥♠ → ♥
Rule #2: ♠ → ♥♠
Rule #3: ♥ → ♠♥♠

Goal: ♠♥♥ → ♥♥♠♠♠♥ in 12 moves

32.

Rule #1: ♥ → ♠♥♥
Rule #2: ♥♥ → ♠♠♠
Rule #3: ♠♥♠ → ♥

Goal: ♥ → ♠♠♠♠♠♠ in 12 moves

33.

Rule #1: ♥♠♠ → ♠♥
Rule #2: ♠♥♥ → ♥♠♠
Rule #3: ♠ → ♥♠♠

Goal: ♠♥♠ → ♠♠♠♥♥ in 13 moves

34.

Rule #1: ♠ → ♥♠♥
Rule #2: ♠♥ → ♥
Rule #3: ♥♥♥ → ♥♠

Goal: ♥♠♥ → ♥♠♠♥♠ in 13 moves

35.

Rule #1: ♥♥ → ♠♥♠
Rule #2: ♠♥ → ♥♠♠
Rule #3: ♠♥♠ → ♥♥

Goal: ♠♥♥ → ♥♠♠♥♠♥ in 13 moves

36.

Rule #1: ♠♠♠ → ♠♥
Rule #2: ♥ → ♠♠
Rule #3: ♠♥ → ♥♥♠

Goal: ♠♠♠ → ♠♥♠♠♥♥ in 13 moves

37.

Rule #1: ♠♥ → ♥♠♥
Rule #2: ♥ → ♠♠♠
Rule #3: ♥♥♠ → ♥

Goal: ♠♥ → ♥♥♠♥♠♠ in 14 moves

38.

Rule #1: ♠♠♥ → ♠♠
Rule #2: ♥ → ♠♥♠
Rule #3: ♠♠♠ → ♥♥♥

Goal: ♥ → ♥♥♥♠♥ in 14 moves

39.

Rule #1: ♥♠♠ → ♠♥
Rule #2: ♥ → ♥♠♠
Rule #3: ♠♠♥ → ♥♥♠

Goal: ♠♥ → ♠♠♥♥♥ in 14 moves

40.

Rule #1: ♥ → ♠♠♠
Rule #2: ♠♠♥ → ♠♥
Rule #3: ♠ → ♥♠♥

Goal: ♥ → ♥♠♠♠♠ in 14 moves

41.

Rule #1: ♥♠ → ♥♠♥
Rule #2: ♥♥♠ → ♠
Rule #3: ♠♥♥ → ♠♠

Goal: ♥♥♠ → ♠♠♥♠♥♠ in 15 moves

42.

Rule #1: ♠♥♠ → ♠♥
Rule #2: ♠ → ♥♥♠
Rule #3: ♥♠ → ♠♠

Goal: ♠♠♥ → ♠♠♠♥♥♥ in 15 moves

43.

Rule #1: ♥♥♠ → ♠
Rule #2: ♠♠ → ♥♠♥
Rule #3: ♥ → ♠♠♥

Goal: ♥♠ → ♠♥♠♥♠♥ in 15 moves

44.

Rule #1: ♠♥ → ♠♠
Rule #2: ♠♠ → ♥♠♠
Rule #3: ♥♥♠ → ♠♥

Goal: ♥♠♥ → ♥♠♠♥♠♥ in 15 moves

45.

Rule #1: ♠ → ♥♥♥
Rule #2: ♥♠♥ → ♥♠
Rule #3: ♥ → ♠♥♥

Goal: ♠ → ♠♥♥♠♠♠ in 16 moves

46.

Rule #1: ♠♥♥ → ♥♠
Rule #2: ♥ → ♠♠♠
Rule #3: ♠♠ → ♥♥♥

Goal: ♠♥♠ → ♥♥♥♥♥♠ in 16 moves

47.

Rule #1: ♥ → ♥♥♠
Rule #2: ♥♠♥ → ♠♥
Rule #3: ♠ → ♥♥♥

Goal: ♠ → ♠♠♠♥♥♠ in 16 moves

48.

Rule #1: ♥♥♠ → ♥
Rule #2: ♠♠ → ♥♠♥
Rule #3: ♥ → ♠♥♠

Goal: ♠♠ → ♥♠♥♥♥ in 16 moves

49.

Rule #1: ♠♠♠ → ♥♠♥
Rule #2: ♥♥ → ♠
Rule #3: ♥ → ♠♠♥

Goal: ♠♠♥ → ♠♠♥♥♥ in 17 moves

50.

Rule #1: ♠♥ → ♥♠♠
Rule #2: ♥♥♠ → ♥
Rule #3: ♥ → ♠♥♥

Goal: ♥♥ → ♠♥♠♠♠♠ in 17 moves

51.

Rule #1: ♠♥ → ♥♥♠
Rule #2: ♥♠♠ → ♠
Rule #3: ♠ → ♠♠♥

Goal: ♠♠ → ♥♥♥♥♠♥ in 17 moves

52.

Rule #1: ♥ → ♠♥♠
Rule #2: ♠♠ → ♥♥♥
Rule #3: ♠♥♥ → ♠♠

Goal: ♠♠ → ♠♥♠♠♠♥ in 17 moves

53.

Rule #1: ♥♥ → ♠♠♥
Rule #2: ♥♠ → ♠♥♥
Rule #3: ♠♠♥ → ♥♠

Goal: ♥♠ → ♥♠♥♥♠♥ in 18 moves

54.

Rule #1: ♥♠♥ → ♠♠
Rule #2: ♠ → ♥♠♠
Rule #3: ♠♠♠ → ♥♥

Goal: ♠♥ → ♥♠♠♠♥ in 18 moves

55.

Rule #1: ♥ → ♥♥♠
Rule #2: ♥♥♥ → ♠♠
Rule #3: ♠♥♠ → ♥

Goal: ♥♠ → ♠♠♠♠♥ in 18 moves

56.

Rule #1: ♠ → ♥♠♥
Rule #2: ♠♠♥ → ♠
Rule #3: ♥♥ → ♠♥♠

Goal: ♥♠ → ♥♥♥♠♥♠ in 18 moves

57.

Rule #1: ♠♥♥ → ♠♠
Rule #2: ♥♠ → ♠♥♥
Rule #3: ♠ → ♥♥

Goal: ♥♠♥ → ♥♥♠♠♥♠ in 19 moves

58.

Rule #1: ♥ → ♥♥♠
Rule #2: ♠♥♠ → ♥
Rule #3: ♠♥♥ → ♠♠

Goal: ♠♥♥ → ♥♥♠♠♥ in 19 moves

See the solutions.