The midnight observatory

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 · 3 counterfactuals. Difficulty measures the rules used by this solver, not a promised completion time.

1. Step 1: Clue 1: Venus is not paired with Silver. Venus cannot be paired with Silver.
2. Step 2: Clue 5: Stella is not paired with Mars. Stella cannot be paired with Mars.
3. Step 3: Clue 7: Stella is not paired with Saturn. Stella cannot be paired with Saturn.
4. Step 4: Clue 2: placing Saturn at Purple leaves no valid later position for Mars at the required gap of 2. Saturn cannot be paired with Purple.
5. Step 5: Clue 2: placing Saturn at Orange leaves no valid later position for Mars at the required gap of 2. Saturn cannot be paired with Orange.
6. Step 6: Clue 2: placing Mars at Black leaves no valid earlier position for Saturn at the required gap of 2. Mars cannot be paired with Black.
7. Step 7: Clue 2: placing Mars at Silver leaves no valid earlier position for Saturn at the required gap of 2. Mars cannot be paired with Silver.
8. Step 8: Clue 3 restricts Hugo to Venus or Jupiter. Hugo cannot be paired with Mars.
9. Step 9: Clue 3 restricts Hugo to Venus or Jupiter. Hugo cannot be paired with Saturn.
10. Step 10: Clue 4: placing Venus at Orange leaves no valid later position for Jupiter. Venus cannot be paired with Orange.
11. Step 11: Clue 4: placing Jupiter at Black leaves no valid earlier position for Venus. Jupiter cannot be paired with Black.
12. Step 12: Clue 6: placing Kai at Orange leaves no valid later position for Hugo. Kai cannot be paired with Orange.
13. Step 13: Clue 6: placing Hugo at Black leaves no valid earlier position for Kai. Hugo cannot be paired with Black.
14. Step 14: Stella and Hugo must use Venus and Jupiter between them. Those two items cannot belong to Luna. Luna cannot be paired with Venus.
15. Step 15: Stella and Hugo must use Venus and Jupiter between them. Those two items cannot belong to Luna. Luna cannot be paired with Jupiter.
16. Step 16: Stella and Hugo must use Venus and Jupiter between them. Those two items cannot belong to Kai. Kai cannot be paired with Venus.
17. Step 17: Stella and Hugo must use Venus and Jupiter between them. Those two items cannot belong to Kai. Kai cannot be paired with Jupiter.
18. Step 18: Suppose Stella is not paired with Venus. Under the established grid, this leaves 1 arrangements. Applying the clues eliminates all of them, so this assumption is impossible. Stella must be paired with Venus. Clue 2 (Saturn comes 2 places before Mars in the Notebooks order.) removes 1 arrangements; 0 remain.
19. Step 19: Stella is already matched to Venus; each item is used once. Stella cannot be paired with Jupiter.
20. Step 20: Venus is already matched to Stella; each item is used once. Hugo cannot be paired with Venus.
21. Step 21: All other Targets choices for Hugo have been eliminated. Hugo must be paired with Jupiter.
22. Step 22: Stella and Silver have no possible Targets item in common, so they cannot belong together. Stella cannot be paired with Silver.
23. Step 23: Stella and Orange have no possible Targets item in common, so they cannot belong together. Stella cannot be paired with Orange.
24. Step 24: Suppose Luna is not paired with Mars. Under the established grid, this leaves 1 arrangements. Applying the clues eliminates all of them, so this assumption is impossible. Luna must be paired with Mars. Clue 2 (Saturn comes 2 places before Mars in the Notebooks order.) removes 1 arrangements; 0 remain.
25. Step 25: Luna is already matched to Mars; each item is used once. Luna cannot be paired with Saturn.
26. Step 26: Mars is already matched to Luna; each item is used once. Kai cannot be paired with Mars.
27. Step 27: All other Targets choices for Kai have been eliminated. Kai must be paired with Saturn.
28. Step 28: Luna and Black have no possible Targets item in common, so they cannot belong together. Luna cannot be paired with Black.
29. Step 29: Luna and Silver have no possible Targets item in common, so they cannot belong together. Luna cannot be paired with Silver.
30. Step 30: Kai and Purple have no possible Targets item in common, so they cannot belong together. Kai cannot be paired with Purple.
31. Step 31: Suppose Stella is not paired with Black. Under the established grid, this leaves 1 arrangements. Applying the clues eliminates all of them, so this assumption is impossible. Stella must be paired with Black. Clue 2 (Saturn comes 2 places before Mars in the Notebooks order.) removes 1 arrangements; 0 remain.
32. Step 32: Stella is already matched to Black; each item is used once. Stella cannot be paired with Purple.
33. Step 33: Black is already matched to Stella; each item is used once. Kai cannot be paired with Black.
34. Step 34: All other Notebooks choices for Kai have been eliminated. Kai must be paired with Silver.
35. Step 35: Silver is already matched to Kai; each item is used once. Hugo cannot be paired with Silver.
36. Step 36: Saturn and Black have no possible Observers item in common, so they cannot belong together. Saturn cannot be paired with Black.
37. Step 37: All other Notebooks choices for Saturn have been eliminated. Saturn must be paired with Silver.
38. Step 38: All other Targets choices for Black have been eliminated. Venus must be paired with Black.
39. Step 39: Venus is already matched to Black; each item is used once. Venus cannot be paired with Purple.
40. Step 40: Silver is already matched to Saturn; each item is used once. Jupiter cannot be paired with Silver.
41. Step 41: Clue 2: placing Mars at Purple leaves no valid earlier position for Saturn at the required gap of 2. Mars cannot be paired with Purple.
42. Step 42: All other Notebooks choices for Mars have been eliminated. Mars must be paired with Orange.
43. Step 43: All other Targets choices for Purple have been eliminated. Jupiter must be paired with Purple.
44. Step 44: Jupiter is already matched to Purple; each item is used once. Jupiter cannot be paired with Orange.
45. Step 45: Both Hugo and Purple are matched to Jupiter; they must belong together. Hugo must be paired with Purple.
46. Step 46: Hugo is already matched to Purple; each item is used once. Hugo cannot be paired with Orange.
47. Step 47: Purple is already matched to Hugo; each item is used once. Luna cannot be paired with Purple.
48. Step 48: All other Notebooks choices for Luna have been eliminated. Luna must be paired with Orange.

Answer key

Stella · Venus · Black

Hugo · Jupiter · Purple

Luna · Mars · Orange

Kai · Saturn · Silver