Inkwell Stars solution — April 5, 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. Composite container (columns 3-10): Regions 2, 4, 5, 7, 9 and 10 are confined here, so the leftover cells owe exactly 4 of the band's 16 stars - a star on these cells would crowd them out (row 2, column 6).
3. Lookahead: Placing star here leads to contradiction - columns 9-10 can only hold 4 stars but the regions there would be forced to place 5 (row 4, column 7).
4. Lookahead: Placing star here leads to contradiction - columns 9-10 can only hold 4 stars but the regions there would be forced to place 5 (row 4, column 9).
5. Triple analysis (Region 2 + Region 1 + Row 1): every legal combination of their stars rules these cells out (row 3, column 7).
6. Triple analysis (Region 2 + Region 5 + Column 8): every legal combination of their stars rules these cells out (row 5, column 8).
7. Triple analysis (Region 3 + Region 6 + Column 1): every legal combination of their stars rules these cells out (row 7, column 1).
8. Joint analysis (Region 8 + Region 6): every legal combination of their stars rules these cells out (row 9, column 2).
9. Quad analysis (Region 2 + Region 1 + Row 2 + Row 1): every legal combination of their stars rules these cells out (row 2, column 1).
10. Clump analysis (Region 3): candidate clumps can only just supply the remaining stars (row 3, column 4).
11. Lookahead: Placing star here leads to contradiction - columns 1-3 can only hold 6 stars but the regions there would be forced to place 7 (row 2, column 5).
12. 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 1).
13. 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 1, column 2).
14. Joint analysis (Region 3 + Region 1): every legal combination of their stars rules these cells out (row 3, column 2).
15. Generalized counting (columns 1-1): region star limits exclude these cells (row 5, column 1).
16. Clump analysis (Region 6): candidate clumps can only just supply the remaining stars (row 5, column 3).
17. Lookahead: Placing star here leads to contradiction - row 1 can only hold 2 stars but the regions there would be forced to place 3 (row 1, column 4).
18. Lookahead: Placing star here leads to contradiction - column 1 can only hold 2 stars but the regions there would be forced to place 3 (row 10, column 3).
19. Composite container (columns 1-8): Regions 1, 3, 4, 6, 8 and 9 are confined here, so the leftover cells owe exactly 4 of the band's 16 stars - a star on these cells would crowd them out (row 9, column 5).
20. Triple analysis (Region 3 + Region 6 + Column 3): every legal combination of their stars rules these cells out (row 4, column 4).
21. Deep lookahead: Placing star here leads to contradiction - columns 1-2 can only hold 4 stars but the regions there would be forced to place 5 (row 1, column 3).
22. Composite container (columns 3-10): Regions 2, 4, 5, 7, 9 and 10 are confined here, so the leftover cells owe exactly 4 of the band's 16 stars - a star on these cells would crowd them out (row 2, column 7).
23. Blocking rule: a star here would touch every other open cell in its region, leaving no room for the region's second star (row 2, column 9).
24. Clump analysis (Region 6): candidate clumps can only just supply the remaining stars (row 6, column 1).
25. Clump analysis (Column 3): each clump must supply its full share of stars (row 9, column 3).
26. Clump analysis (Region 10): candidate clumps can only just supply the remaining stars (row 9, column 6).
27. Crowding (Column 4): a star here would leave too little room for its 2 remaining stars (row 6, column 5).
28. Squeeze (columns 3-4): the band's clumps can only just fit its stars (row 7, column 5).
29. Generalized counting (columns 8-10): region star limits exclude these cells (row 6, column 8).
30. Three candidates with two adjacent: Isolated candidate must hold a star (row 10, column 7).
31. Mark 1 cell adjacent to stars as X (row 10, column 6).
32. Region completion: 1 star needed, 1 candidate (row 10, column 5).
33. Row 10 complete: Mark 2 remaining cells as X (row 10, column 1).
34. Clump analysis (Column 8): candidate clumps can only just supply the remaining stars (row 1, column 7).
35. Three candidates with two adjacent: Isolated candidate must hold a star (row 2, column 2).
36. Mark 2 cells adjacent to stars as X (row 3, column 1).
37. Region completion: 2 stars needed, 2 candidates (row 2, column 4).
38. Mark 2 cells adjacent to stars as X (row 1, column 5).
39. Region completion: 1 star needed, 1 candidate (row 1, column 6).
40. Region completion: 1 star needed, 1 candidate (row 4, column 1).
41. Mark 1 cell adjacent to stars as X (row 5, column 2).
42. Row 2 complete: Mark 2 remaining cells as X (row 2, column 8).
43. Column completion: 1 star needed, 1 candidate (row 4, column 3).
44. Mark 1 cell adjacent to stars as X (row 5, column 4).
45. Row 4 complete: Mark 4 remaining cells as X (row 4, column 5).
46. Column completion: 2 stars needed, 2 candidates (row 1, column 8).
47. Row 1 complete: Mark 1 remaining cell as X (row 1, column 10).
48. Region completion: 1 star needed, 1 candidate (row 3, column 8).
49. Three candidates with two adjacent: Isolated candidate must hold a star (row 3, column 10).
50. Row 3 complete: Mark 1 remaining cell as X (row 3, column 6).
51. Two-option rule: Cell adjacent to both candidates (row 5, column 10).
52. Two-option rule: Cell adjacent to both candidates (row 6, column 10).
53. Blocking rule: a star here would touch every other open cell in its region, leaving no room for the region's second star (row 6, column 6).
54. Blocking rule: a star here would touch every other open cell in its region, leaving no room for the region's second star (row 8, column 9).
55. Three candidates in a column: Middle cell can't hold a star (row 6, column 9).
56. Region completion: 1 star needed, 1 candidate (row 5, column 9).
57. Column completion: 1 star needed, 1 candidate (row 7, column 9).
58. Mark 2 cells adjacent to stars as X (row 7, column 10).
59. Region completion: 1 star needed, 1 candidate (row 9, column 10).
60. Row 9 complete: Mark 1 remaining cell as X (row 9, column 1).
61. Region completion: 1 star needed, 1 candidate (row 8, column 1).
62. Mark 1 cell adjacent to stars as X (row 7, column 2).
63. Region completion: 1 star needed, 1 candidate (row 6, column 2).
64. Clump analysis (Row 8): candidate clumps can only just supply the remaining stars (row 7, column 6).
65. Blocking rule: a star here would touch every other open cell in its region, leaving no room for the region's second star (row 5, column 6).
66. Column completion: 1 star needed, 1 candidate (row 8, column 6).
67. Mark 3 cells adjacent to stars as X (row 7, column 7).
68. Row completion: 1 star needed, 1 candidate (row 7, column 4).
69. Mark 1 cell adjacent to stars as X (row 6, column 4).
70. Row completion: 1 star needed, 1 candidate (row 6, column 7).
71. Mark 1 cell adjacent to stars as X (row 5, column 7).
72. Region completion: 1 star needed, 1 candidate (row 5, column 5).
73. Solved! Every row, column, and region has its two stars, none touching.