Inkwell Stars solution — December 19, 2025

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 3, column 4).
3. Clump analysis (Region 4): candidate clumps can only just supply the remaining stars (row 3, column 8).
4. Generalized counting (rows 2-2): region star limits exclude these cells (row 2, column 1).
5. Composite container (columns 1-4): Regions 5 and 9 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 8, column 3).
6. Composite container (rows 1-8): Regions 1, 2, 3, 4, 5 and 6 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 7, column 8).
7. Lookahead: Placing star here leads to contradiction - row 2 can only hold 2 stars but the regions there would be forced to place 3 (row 3, column 6).
8. Lookahead: Placing star here leads to contradiction - row 2 can only hold 2 stars but the regions there would be forced to place 3 (row 3, column 10).
9. Lookahead: Placing star here leads to contradiction - row 2 can only hold 2 stars but the regions there would be forced to place 3 (row 4, column 4).
10. Lookahead: Placing star here leads to contradiction - row 2 can only hold 2 stars but the regions there would be forced to place 3 (row 4, column 6).
11. Lookahead: Placing star here leads to contradiction - row 2 can only hold 2 stars but the regions there would be forced to place 3 (row 4, column 8).
12. Lookahead: Placing star here leads to contradiction - row 2 can only hold 2 stars but the regions there would be forced to place 3 (row 4, column 10).
13. Joint analysis (Column 6 + Column 7): every legal combination of their stars rules these cells out (row 5, column 8).
14. Clump analysis (Column 8): candidate clumps can only just supply the remaining stars (row 1, column 7).
15. Clump analysis (Column 7): candidate clumps can only just supply the remaining stars (row 5, column 6).
16. Clump analysis (Column 6): candidate clumps can only just supply the remaining stars (row 1, column 5).
17. Clump analysis (Region 3): candidate clumps can only just supply the remaining stars (row 1, column 3).
18. Star claim: Region 4 must place a star in row 2; cells touching all its options are eliminated (row 3, column 7).
19. Squeeze (rows 2-3): the band's clumps can only just fit its stars (row 1, column 4).
20. Crowding (Region 1): a star here would leave too little room for its 2 remaining stars (row 2, column 2).
21. Squeeze (rows 2-3): the band's clumps can only just fit its stars (row 4, column 1).
22. Generalized counting (columns 1-5): region star limits exclude these cells (row 1, column 6).
23. Three candidates with two adjacent: Isolated candidate must have star (row 3, column 1).
24. Mark 1 cells adjacent to stars as X (row 3, column 2).
25. Clump analysis (Column 6): each clump must supply its full share of stars (row 2, column 6).
26. Mark 1 cells adjacent to stars as X (row 3, column 5).
27. Row completion: 1 stars needed, 1 candidates (row 3, column 9).
28. Mark 2 cells adjacent to stars as X (row 2, column 8).
29. Three candidates with two adjacent: Isolated candidate must have star (row 4, column 5).
30. Mark 2 cells adjacent to stars as X (row 5, column 4).
31. Clump analysis (Column 5): candidate clumps can only just supply the remaining stars (row 7, column 4).
32. Clump analysis (Column 8): each clump must supply its full share of stars (row 1, column 8).
33. Clump analysis (Region 1): candidate clumps can only just supply the remaining stars (row 1, column 10).
34. Joint analysis (Column 1 + Region 9): every legal combination of their stars rules these cells out (row 9, column 3).
35. Joint analysis (Column 3 + Column 2): every legal combination of their stars rules these cells out (row 9, column 1).
36. Joint analysis (Column 3 + Column 4): every legal combination of their stars rules these cells out (row 5, column 2).
37. Joint analysis (Column 9 + Region 8): every legal combination of their stars rules these cells out (row 8, column 7).
38. Quad analysis (Column 6 + Column 5 + Region 7 + Row 8): every legal combination of their stars rules these cells out (row 7, column 9).
39. Region confined to row: Eliminate other row candidates (row 10, column 1).
40. Region confined to row: Eliminate other row candidates (row 10, column 2).
41. Star claim: Region 9 must place a star in column 4; cells touching all its options are eliminated (row 9, column 4).
42. Clump analysis (Column 5): each clump must supply its full share of stars (row 9, column 2).
43. Mark 2 cells adjacent to stars as X (row 8, column 1).
44. Clump analysis (Row 8): candidate clumps can only just supply the remaining stars (row 7, column 5).
45. Crowding (Row 7): a star here would leave too little room for its 2 remaining stars (row 6, column 2).
46. Region confined to row: Eliminate other row candidates (row 10, column 4).
47. Region completion: 2 stars needed, 2 candidates (row 7, column 1).
48. Mark 2 cells adjacent to stars as X (row 6, column 1).
49. Region completion: 1 stars needed, 1 candidates (row 8, column 4).
50. Mark 2 cells adjacent to stars as X (row 7, column 3).
51. Region completion: 1 stars needed, 1 candidates (row 6, column 5).
52. Mark 1 cells adjacent to stars as X (row 6, column 4).
53. Row completion: 1 stars needed, 1 candidates (row 7, column 7).
54. Mark 1 cells adjacent to stars as X (row 6, column 7).
55. Column 1 complete: Mark 2 remaining cells as X (row 1, column 1).
56. Region completion: 1 stars needed, 1 candidates (row 1, column 2).
57. Mark 1 cells adjacent to stars as X (row 2, column 3).
58. Region completion: 1 stars needed, 1 candidates (row 2, column 4).
59. Column 3 candidates: Middle cell cannot have star (row 5, column 3).
60. Region completion: 2 stars needed, 2 candidates (row 4, column 3).
61. Region completion: 1 stars needed, 1 candidates (row 6, column 3).
62. Row 4 complete: Mark 1 remaining cells as X (row 4, column 7).
63. Region completion: 1 stars needed, 1 candidates (row 5, column 7).
64. Row completion: 1 stars needed, 1 candidates (row 5, column 10).
65. Mark 2 cells adjacent to stars as X (row 6, column 9).
66. Region complete: Mark 1 remaining cells as X (row 8, column 10).
67. Row completion: 1 stars needed, 1 candidates (row 8, column 9).
68. Mark 1 cells adjacent to stars as X (row 9, column 8).
69. Region completion: 1 stars needed, 1 candidates (row 9, column 6).
70. Mark 1 cells adjacent to stars as X (row 10, column 6).
71. Region completion: 2 stars needed, 2 candidates (row 10, column 8).
72. Region completion: 1 stars needed, 1 candidates (row 10, column 10).
73. Solved! Every row, column, and region has its two stars, none touching.