Inkwell Stars solution — January 2, 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 3, column 2).
3. 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).
4. 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 8).
5. 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 8).
6. 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 8).
7. 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).
8. 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 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 3).
10. Clump analysis (Region 3): candidate clumps can only just supply the remaining stars (row 1, column 2).
11. Clump analysis (Region 5): candidate clumps can only just supply the remaining stars (row 2, column 6).
12. Clump analysis (Region 7): candidate clumps can only just supply the remaining stars (row 8, column 6).
13. Clump analysis (Region 9): candidate clumps can only just supply the remaining stars (row 6, column 8).
14. Clump analysis (Region 10): candidate clumps can only just supply the remaining stars (row 8, column 1).
15. Clump analysis (Region 7): candidate clumps can only just supply the remaining stars (row 6, column 4).
16. Joint analysis (Region 9 + Row 8): every legal combination of their stars rules these cells out (row 7, column 3).
17. Triple analysis (Region 7 + Row 6 + Region 4): every legal combination of their stars rules these cells out (row 4, column 5).
18. Triple analysis (Region 9 + Region 7 + Row 6): every legal combination of their stars rules these cells out (row 7, column 2).
19. Triple analysis (Region 9 + Region 7 + Row 7): every legal combination of their stars rules these cells out (row 7, column 10).
20. Triple analysis (Region 10 + Column 3 + Region 7): every legal combination of their stars rules these cells out (row 5, column 4).
21. Triple analysis (Region 3 + Region 4 + Row 5): every legal combination of their stars rules these cells out (row 4, column 9).
22. Triple analysis (Region 7 + Region 4 + Row 6): every legal combination of their stars rules these cells out (row 3, column 5).
23. Joint analysis (Region 3 + Row 3): every legal combination of their stars rules these cells out (row 4, column 8).
24. Triple analysis (Row 8 + Column 8 + Row 7): every legal combination of their stars rules these cells out (row 6, column 7).
25. Crowding (Region 4): a star here would leave too little room for its 2 remaining stars (row 5, column 5).
26. Squeeze (columns 5-6): the band's clumps can only just fit its stars (row 4, column 7).
27. Generalized counting (rows 1-4): region star limits exclude these cells (row 4, column 1).
28. Composite container (rows 5-10): Regions 6, 7, 8, 9 and 10 are confined here, so the leftover cells owe exactly 2 of the band's 12 stars - a star on these cells would crowd them out (row 5, column 9).
29. Composite container (rows 5-10): Regions 6, 7, 8, 9 and 10 are confined here, so the leftover cells owe exactly 2 of the band's 12 stars - impossible without stars on these cells (row 5, column 8).
30. Generalized counting (columns 8-9): region star limits exclude these cells (row 1, column 8).
31. Two last candidates (column 8): Eliminate 1 cell adjacent to both (row 8, column 7).
32. Clump analysis (Region 7): candidate clumps can only just supply the remaining stars (row 6, column 6).
33. Crowding (Column 9): a star here would leave too little room for its 2 remaining stars (row 8, column 10).
34. Row completion: 2 stars needed, 2 candidates (row 8, column 2).
35. Mark 2 cells adjacent to stars as X (row 7, column 1).
36. Row completion: 1 star needed, 1 candidate (row 8, column 4).
37. Mark 3 cells adjacent to stars as X (row 7, column 4).
38. Three candidates with two adjacent: Isolated candidate must hold a star (row 6, column 3).
39. Mark 1 cell adjacent to stars as X (row 6, column 2).
40. Clump analysis (Row 9): candidate clumps can only just supply the remaining stars (row 10, column 7).
41. Generalized counting (columns 2-3): region star limits exclude these cells (row 10, column 2).
42. Three candidates with two adjacent: Isolated candidate must hold a star (row 10, column 1).
43. Two last candidates (column 2): Eliminate 1 cell adjacent to both (row 3, column 1).
44. Two last candidates (column 3): Eliminate 1 cell adjacent to both (row 3, column 4).
45. Row completion: 2 stars needed, 2 candidates (row 3, column 7).
46. Mark 2 cells adjacent to stars as X (row 2, column 7).
47. Row completion: 1 star needed, 1 candidate (row 3, column 9).
48. Mark 2 cells adjacent to stars as X (row 2, column 9).
49. Region completion: 1 star needed, 1 candidate (row 1, column 10).
50. Three candidates in a row: Middle cell can't hold a star (row 4, column 3).
51. Row completion: 2 stars needed, 2 candidates (row 4, column 2).
52. Mark 1 cell adjacent to stars as X (row 5, column 1).
53. Region completion: 1 star needed, 1 candidate (row 6, column 1).
54. Row completion: 1 star needed, 1 candidate (row 4, column 4).
55. Row 6 complete: Mark 2 remaining cells as X (row 6, column 5).
56. Region completion: 1 star needed, 1 candidate (row 5, column 6).
57. Row 5 complete: Mark 1 remaining cell as X (row 5, column 10).
58. Column 1 complete: Mark 2 remaining cells as X (row 1, column 1).
59. Column 2 complete: Mark 1 remaining cell as X (row 2, column 2).
60. Region completion: 1 star needed, 1 candidate (row 2, column 3).
61. Mark 2 cells adjacent to stars as X (row 1, column 4).
62. Row completion: 1 star needed, 1 candidate (row 2, column 5).
63. Mark 2 cells adjacent to stars as X (row 1, column 5).
64. Region completion: 1 star needed, 1 candidate (row 1, column 7).
65. Column 4 complete: Mark 1 remaining cell as X (row 10, column 4).
66. Column completion: 1 star needed, 1 candidate (row 10, column 5).
67. Mark 2 cells adjacent to stars as X (row 9, column 6).
68. Row 10 complete: Mark 1 remaining cell as X (row 10, column 10).
69. Column completion: 1 star needed, 1 candidate (row 7, column 6).
70. Mark 1 cell adjacent to stars as X (row 7, column 7).
71. Column 7 complete: Mark 1 remaining cell as X (row 9, column 7).
72. Region completion: 1 star needed, 1 candidate (row 9, column 10).
73. Mark 1 cell adjacent to stars as X (row 9, column 9).
74. Row completion: 1 star needed, 1 candidate (row 9, column 8).
75. Column 8 complete: Mark 1 remaining cell as X (row 7, column 8).
76. Region completion: 1 star needed, 1 candidate (row 7, column 9).
77. Solved! Every row, column, and region has its two stars, none touching.