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. All puzzles copyright Erich Friedman 2006.

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.

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