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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