Inkwell Stars solution — May 31, 2026

Full written solution

Every deduction from the walkthrough above, in order. Each technique is explained in the Star Battle strategy guide.

1. Starting position — the grid is split into regions (bold outlines). Each row, column, and region needs exactly two stars, and no two stars may touch.
2. Clump analysis (Region 3): candidate clumps can only just supply the remaining stars (row 2, column 8).
3. Clump analysis (Region 4): candidate clumps can only just supply the remaining stars (row 4, column 2).
4. Deep lookahead: Placing star here leads to contradiction - Region 2 would end up with more than 2 stars (row 2, column 2).
5. Deep lookahead: Placing star here leads to contradiction - Column 5 would only have room for 0 of the 1 star it still needs (row 2, column 3).
6. Deep lookahead: Placing star here leads to contradiction - column 2 can only hold 2 stars but the regions there would be forced to place 3 (row 3, column 8).
7. Joint analysis (Column 8 + Column 7): every legal combination of their stars rules these cells out (row 5, column 9).
8. Deep lookahead: Placing star here leads to contradiction - stars at R2C9 and R3C9 would touch (row 2, column 7).
9. Deep lookahead: Placing star here leads to contradiction - Region 2 would end up with more than 2 stars (row 1, column 5).
10. Triple analysis (Column 5 + Column 6 + Region 2): every legal combination of their stars rules these cells out (row 6, column 6).
11. Deep lookahead: Placing star here leads to contradiction - column 2 can only hold 2 stars but the regions there would be forced to place 3 (row 3, column 2).
12. Blocking rule: This position would block too many candidates (row 4, column 4).
13. Clump analysis (Region 4): candidate clumps can only just supply the remaining stars (row 3, column 4).
14. Generalized counting (rows 1-4): region star limits exclude these cells (row 5, column 6).
15. Composite container (columns 4-6): Region 2 is confined here, so the leftover cells owe exactly 4 of the band's 6 stars - a star on these cells would crowd them out (row 8, column 5).
16. Joint analysis (Column 6 + Column 7): every legal combination of their stars rules these cells out (row 6, column 8).
17. Triple analysis (Region 3 + Column 6 + Region 5): every legal combination of their stars rules these cells out (row 8, column 7).
18. Triple analysis (Row 6 + Region 8 + Region 6): every legal combination of their stars rules these cells out (row 5, column 8).
19. Joint analysis (Column 8 + Region 3): every legal combination of their stars rules these cells out (row 8, column 9).
20. Triple analysis (Row 8 + Region 8 + Region 6): every legal combination of their stars rules these cells out (row 7, column 7).
21. Squeeze (columns 6-7): the band's clumps can only just fit its stars (row 9, column 5).
22. Composite container (rows 5-8): Regions 6 and 7 are confined here, so the leftover cells owe exactly 4 of the band's 8 stars - a star on these cells would crowd them out (row 7, column 2).
23. Composite container (rows 1-7): Regions 1, 2, 3, 4 and 5 are confined here, so the leftover cells owe exactly 4 of the band's 14 stars - a star on these cells would crowd them out (row 6, column 2).
24. Triple analysis (Column 8 + Row 2 + Row 3): every legal combination of their stars rules these cells out (row 1, column 9).
25. Quad analysis (Column 2 + Row 6 + Row 7 + Region 6): every legal combination of their stars rules these cells out (row 5, column 7).
26. Clump analysis (Region 5): each clump must supply its full share of stars (row 6, column 7).
27. Deep lookahead: Placing star here leads to contradiction - Row 8 would only have room for 0 of the 1 star it still needs (row 1, column 1).
28. Deep lookahead: Placing star here leads to contradiction - stars at R8C6 and R9C6 would touch (row 1, column 3).
29. Deep lookahead: Placing star here leads to contradiction - Column 3 would only have room for 1 of the 2 stars it still needs (row 1, column 6).
30. Blocking rule: This position would block too many candidates (row 3, column 5).
31. Clump analysis (Region 2): candidate clumps can only just supply the remaining stars (row 3, column 7).
32. Squeeze (columns 4-5): the band's clumps can only just fit its stars (row 8, column 4).
33. Squeeze (rows 7-8): the band's clumps can only just fit its stars (row 6, column 3).
34. Squeeze (rows 8-9): each clump in the band must supply its full share of stars (row 9, column 4).
35. Squeeze (columns 5-6): the band's clumps can only just fit its stars (row 8, column 6).
36. Row completion: 1 stars needed, 1 candidates (row 9, column 6).
37. Clump analysis (Row 8): candidate clumps can only just supply the remaining stars (row 7, column 1).
38. Clump analysis (Row 8): each clump must supply its full share of stars (row 8, column 8).
39. Mark 1 cells adjacent to stars as X (row 7, column 9).
40. Region completion: 1 stars needed, 1 candidates (row 6, column 9).
41. Row 6 complete: Mark 1 remaining cells as X (row 6, column 1).
42. Region completion: 1 stars needed, 1 candidates (row 8, column 1).
43. Mark 1 cells adjacent to stars as X (row 8, column 2).
44. Row completion: 2 stars needed, 2 candidates (row 7, column 3).
45. Row completion: 1 stars needed, 1 candidates (row 7, column 5).
46. Region complete: Mark 1 remaining cells as X (row 5, column 3).
47. Column completion: 2 stars needed, 2 candidates (row 1, column 2).
48. Mark 1 cells adjacent to stars as X (row 2, column 1).
49. Column completion: 1 stars needed, 1 candidates (row 5, column 2).
50. Mark 3 cells adjacent to stars as X (row 4, column 1).
51. Column completion: 1 stars needed, 1 candidates (row 3, column 1).
52. Region complete: Mark 1 remaining cells as X (row 1, column 4).
53. Column completion: 1 stars needed, 1 candidates (row 3, column 3).
54. Mark 1 cells adjacent to stars as X (row 2, column 4).
55. Row 3 complete: Mark 2 remaining cells as X (row 3, column 6).
56. Column completion: 1 stars needed, 1 candidates (row 5, column 4).
57. Mark 1 cells adjacent to stars as X (row 5, column 5).
58. Column completion: 1 stars needed, 1 candidates (row 2, column 5).
59. Mark 1 cells adjacent to stars as X (row 2, column 6).
60. Region completion: 1 stars needed, 1 candidates (row 4, column 6).
61. Mark 1 cells adjacent to stars as X (row 4, column 7).
62. Region completion: 1 stars needed, 1 candidates (row 4, column 8).
63. Mark 1 cells adjacent to stars as X (row 4, column 9).
64. Row completion: 1 stars needed, 1 candidates (row 2, column 9).
65. Mark 1 cells adjacent to stars as X (row 1, column 8).
66. Region completion: 1 stars needed, 1 candidates (row 1, column 7).
67. Solved! Every row, column, and region has its two stars, none touching.