Inkwell Stars solution — July 19, 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. Blocking rule: a star here would touch every other open cell in its region, leaving no room for the region's second star (row 9, column 2).
3. Clump analysis (Region 4): candidate clumps can only just supply the remaining stars (row 4, column 9).
4. Lookahead: Placing star here leads to contradiction - columns 8-10 must hold 6 stars but the regions there could only supply 5 (row 4, column 7).
5. Joint analysis (Region 4 + Region 2): every legal combination of their stars rules these cells out (row 2, column 9).
6. Triple analysis (Region 4 + Region 2 + Column 10): every legal combination of their stars rules these cells out (row 6, column 10).
7. Triple analysis (Region 8 + Region 9 + Row 9): every legal combination of their stars rules these cells out (row 9, column 7).
8. Triple analysis (Region 8 + Region 9 + Row 10): every legal combination of their stars rules these cells out (row 10, column 3).
9. Blocking rule: a star here would touch every other open cell in its region, leaving no room for the region's second star (row 9, column 1).
10. Three candidates with two adjacent: Isolated candidate must hold a star (row 8, column 1).
11. Mark 3 cells adjacent to stars as X (row 7, column 1).
12. Generalized counting (columns 1-2): region star limits exclude these cells (row 1, column 1).
13. Composite container (columns 3-10): Regions 1, 2, 4, 6, 7, 8 and 9 are confined here, so the leftover cells owe exactly 2 of the band's 16 stars - a star on these cells would crowd them out (row 5, column 3).
14. Blocking rule: a star here would touch every other open cell in its region, leaving no room for the region's second star (row 9, column 4).
15. Clump analysis (Region 8): candidate clumps can only just supply the remaining stars (row 9, column 5).
16. Generalized counting (rows 10-10): region star limits exclude these cells (row 10, column 8).
17. 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 6).
18. 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 7).
19. Three candidates with two adjacent: Isolated candidate must hold a star (row 9, column 6).
20. Mark 2 cells adjacent to stars as X (row 8, column 5).
21. Two-option rule: Cell adjacent to both candidates (row 6, column 6).
22. Two-option rule: Cell adjacent to both candidates (row 6, 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 9, column 3).
24. Three candidates with two adjacent: Isolated candidate must hold a star (row 10, column 4).
25. Clump analysis (Row 9): candidate clumps can only just supply the remaining stars (row 8, column 9).
26. Clump analysis (Region 8): candidate clumps can only just supply the remaining stars (row 8, column 8).
27. Generalized counting (columns 1-4): region star limits exclude these cells (row 1, column 3).
28. Clump analysis (Region 6): candidate clumps can only just supply the remaining stars (row 6, column 4).
29. Region completion: 1 star needed, 1 candidate (row 7, column 7).
30. Mark 2 cells adjacent to stars as X (row 6, column 8).
31. 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 2).
32. Clump analysis (Region 5): candidate clumps can only just supply the remaining stars (row 2, column 1).
33. Region completion: 1 star needed, 1 candidate (row 10, column 2).
34. Blocking rule: a star here would touch every other open cell in its region, leaving no room for the region's second star (row 3, column 3).
35. Clump analysis (Region 3): candidate clumps can only just supply the remaining stars (row 4, column 1).
36. Three candidates with two adjacent: Isolated candidate must hold a star (row 6, column 3).
37. Generalized counting (rows 7-9): region star limits exclude these cells (row 7, column 5).
38. 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 5).
39. 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).
40. Three candidates with two adjacent: Isolated candidate must hold a star (row 6, column 5).
41. Row 6 complete: Mark 1 remaining cell as X (row 6, column 1).
42. Region completion: 1 star needed, 1 candidate (row 5, column 1).
43. Mark 1 cell adjacent to stars as X (row 4, column 2).
44. Column completion: 1 star needed, 1 candidate (row 3, column 2).
45. Mark 1 cell adjacent to stars as X (row 2, column 3).
46. Column completion: 1 star needed, 1 candidate (row 8, column 3).
47. Mark 1 cell adjacent to stars as X (row 8, column 4).
48. Two-option rule: Cell adjacent to both candidates (row 2, column 5).
49. Two-option rule: Cell adjacent to both candidates (row 3, column 5).
50. Two-option rule: Cell adjacent to both candidates (row 3, column 6).
51. Clump analysis (Region 1): candidate clumps can only just supply the remaining stars (row 2, column 8).
52. Clump analysis (Region 4): candidate clumps can only just supply the remaining stars (row 5, column 7).
53. Clump analysis (Column 7): candidate clumps can only just supply the remaining stars (row 2, column 6).
54. Crowding (Row 4): a star here would leave too little room for its 2 remaining stars (row 3, column 9).
55. Squeeze (rows 1-2): the band's clumps can only just fit its stars (row 1, column 5).
56. Region completion: 1 star needed, 1 candidate (row 2, column 4).
57. Region completion: 1 star needed, 1 candidate (row 4, column 5).
58. Row completion: 1 star needed, 1 candidate (row 2, column 10).
59. Mark 2 cells adjacent to stars as X (row 1, column 10).
60. Region completion: 1 star needed, 1 candidate (row 1, column 8).
61. Row completion: 1 star needed, 1 candidate (row 1, column 6).
62. Row completion: 1 star needed, 1 candidate (row 4, column 10).
63. Mark 1 cell adjacent to stars as X (row 5, column 10).
64. Region completion: 1 star needed, 1 candidate (row 5, column 8).
65. Column completion: 1 star needed, 1 candidate (row 3, column 7).
66. Mark 1 cell adjacent to stars as X (row 3, column 8).
67. Column 8 complete: Mark 1 remaining cell as X (row 9, column 8).
68. Column completion: 2 stars needed, 2 candidates (row 7, column 9).
69. Mark 1 cell adjacent to stars as X (row 7, column 10).
70. Column completion: 1 star needed, 1 candidate (row 9, column 9).
71. Mark 1 cell adjacent to stars as X (row 9, column 10).
72. Solved! Every row, column, and region has its two stars, none touching.