The small art exhibition

One deduction at a time

Follow the numbered clues, one-to-one eliminations and cross-grid deductions. When a counterfactual is needed, its assumptions and clue-by-clue contradiction are shown.

Measured complexity: rule tier 4/4 · 48 verified grid deductions · 1 counterfactual. Difficulty measures the rules used by this solver, not a promised completion time.

1. Step 1: Clue 1: Lucas is not paired with Birch. Lucas cannot be paired with Birch.
2. Step 2: Clue 3: Lucas is not paired with Metal. Lucas cannot be paired with Metal.
3. Step 3: Clue 6: Mountain is not paired with Metal. Mountain cannot be paired with Metal.
4. Step 4: Clue 2: placing City at Birch leaves no valid later position for Mountain. City cannot be paired with Birch.
5. Step 5: Clue 2: placing Mountain at Oak leaves no valid earlier position for City. Mountain cannot be paired with Oak.
6. Step 6: Clue 4: placing Felix at Birch leaves no valid later position for Emma. Felix cannot be paired with Birch.
7. Step 7: Clue 4: placing Emma at Oak leaves no valid earlier position for Felix. Emma cannot be paired with Oak.
8. Step 8: Clue 5: placing Piper at Walnut leaves no valid later position for Lucas. Piper cannot be paired with Walnut.
9. Step 9: Clue 5: placing Piper at Metal leaves no valid later position for Lucas. Piper cannot be paired with Metal.
10. Step 10: Clue 5: placing Piper at Birch leaves no valid later position for Lucas. Piper cannot be paired with Birch.
11. Step 11: All other Frames choices for Piper have been eliminated. Piper must be paired with Oak.
12. Step 12: Oak is already matched to Piper; each item is used once. Lucas cannot be paired with Oak.
13. Step 13: All other Frames choices for Lucas have been eliminated. Lucas must be paired with Walnut.
14. Step 14: Walnut is already matched to Lucas; each item is used once. Emma cannot be paired with Walnut.
15. Step 15: All other Artists choices for Birch have been eliminated. Emma must be paired with Birch.
16. Step 16: Emma is already matched to Birch; each item is used once. Emma cannot be paired with Metal.
17. Step 17: Oak is already matched to Piper; each item is used once. Felix cannot be paired with Oak.
18. Step 18: Walnut is already matched to Lucas; each item is used once. Felix cannot be paired with Walnut.
19. Step 19: All other Frames choices for Felix have been eliminated. Felix must be paired with Metal.
20. Step 20: Clue 7: placing Harbour at Metal leaves no valid later position for Forest at the required gap of 2. Harbour cannot be paired with Metal.
21. Step 21: Clue 7: placing Harbour at Birch leaves no valid later position for Forest at the required gap of 2. Harbour cannot be paired with Birch.
22. Step 22: Clue 7: placing Forest at Oak leaves no valid earlier position for Harbour at the required gap of 2. Forest cannot be paired with Oak.
23. Step 23: Clue 7: placing Forest at Walnut leaves no valid earlier position for Harbour at the required gap of 2. Forest cannot be paired with Walnut.
24. Step 24: Piper and Forest have no possible Frames item in common, so they cannot belong together. Piper cannot be paired with Forest.
25. Step 25: Piper and Mountain have no possible Frames item in common, so they cannot belong together. Piper cannot be paired with Mountain.
26. Step 26: Lucas and Forest have no possible Frames item in common, so they cannot belong together. Lucas cannot be paired with Forest.
27. Step 27: Emma and Harbour have no possible Frames item in common, so they cannot belong together. Emma cannot be paired with Harbour.
28. Step 28: Emma and City have no possible Frames item in common, so they cannot belong together. Emma cannot be paired with City.
29. Step 29: Felix and Harbour have no possible Frames item in common, so they cannot belong together. Felix cannot be paired with Harbour.
30. Step 30: Felix and Mountain have no possible Frames item in common, so they cannot belong together. Felix cannot be paired with Mountain.
31. Step 31: Suppose Piper is not paired with Harbour. Under the established grid, this leaves 1 arrangements. Applying the clues eliminates all of them, so this assumption is impossible. Piper must be paired with Harbour. Clue 7 (Harbour comes 2 places before Forest in the Frames order.) removes 1 arrangements; 0 remain.
32. Step 32: Piper is already matched to Harbour; each item is used once. Piper cannot be paired with City.
33. Step 33: Harbour is already matched to Piper; each item is used once. Lucas cannot be paired with Harbour.
34. Step 34: Both Harbour and Oak are matched to Piper; they must belong together. Harbour must be paired with Oak.
35. Step 35: Harbour is already matched to Oak; each item is used once. Harbour cannot be paired with Walnut.
36. Step 36: Oak is already matched to Harbour; each item is used once. City cannot be paired with Oak.
37. Step 37: Clue 2: placing Mountain at Walnut leaves no valid earlier position for City. Mountain cannot be paired with Walnut.
38. Step 38: All other Subjects choices for Walnut have been eliminated. City must be paired with Walnut.
39. Step 39: City is already matched to Walnut; each item is used once. City cannot be paired with Metal.
40. Step 40: All other Subjects choices for Metal have been eliminated. Forest must be paired with Metal.
41. Step 41: Forest is already matched to Metal; each item is used once. Forest cannot be paired with Birch.
42. Step 42: All other Frames choices for Mountain have been eliminated. Mountain must be paired with Birch.
43. Step 43: Both Lucas and City are matched to Walnut; they must belong together. Lucas must be paired with City.
44. Step 44: Lucas is already matched to City; each item is used once. Lucas cannot be paired with Mountain.
45. Step 45: All other Artists choices for Mountain have been eliminated. Emma must be paired with Mountain.
46. Step 46: Emma is already matched to Mountain; each item is used once. Emma cannot be paired with Forest.
47. Step 47: All other Artists choices for Forest have been eliminated. Felix must be paired with Forest.
48. Step 48: Felix is already matched to Forest; each item is used once. Felix cannot be paired with City.

Answer key

Piper · Harbour · Oak

Lucas · City · Walnut

Emma · Mountain · Birch

Felix · Forest · Metal