Inkwell Stars solution — December 25, 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. 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).
3. Clump analysis (Region 4): candidate clumps can only just supply the remaining stars (row 3, column 8).
4. Clump analysis (Region 10): candidate clumps can only just supply the remaining stars (row 9, column 7).
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 8, column 4).
6. Three candidates with two adjacent: Isolated candidate must hold a star (row 9, column 5).
7. Mark 4 cells adjacent to stars as X (row 8, column 5).
8. Region completion: 1 star needed, 1 candidate (row 9, column 3).
9. Mark 3 cells adjacent to stars as X (row 8, column 2).
10. Row 9 complete: Mark 1 remaining cell as X (row 9, column 1).
11. 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 5).
12. Blocking rule: a star here would touch every other open cell in its region, leaving no room for the region's second star (row 7, column 1).
13. Three candidates with two adjacent: Isolated candidate must hold a star (row 8, column 1).
14. Mark 1 cell adjacent to stars as X (row 7, column 2).
15. Region completion: 1 star needed, 1 candidate (row 6, column 1).
16. Mark 3 cells adjacent to stars as X (row 5, column 1).
17. Column 1 complete: Mark 4 remaining cells as X (row 1, column 1).
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 6, column 4).
19. Clump analysis (Column 2): candidate clumps can only just supply the remaining stars (row 1, column 3).
20. Clump analysis (Region 6): candidate clumps can only just supply the remaining stars (row 4, column 4).
21. Clump analysis (Region 7): candidate clumps can only just supply the remaining stars (row 6, column 7).
22. Undercounting: 6 regions fit in cols 1-6, eliminate 2 outside candidates (row 3, column 6).
23. Composite container (columns 4-6): Region 7 is confined here, so the leftover cells owe exactly 3 of the band's 6 stars - a star on these cells would crowd them out (row 2, column 5).
24. Lookahead: Placing star here leads to contradiction - Region 1 would only have room for 1 of the 2 stars it still needs (row 7, column 4).
25. 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).
26. Three candidates with two adjacent: Isolated candidate must hold a star (row 5, column 6).
27. Mark 4 cells adjacent to stars as X (row 4, column 5).
28. Region completion: 2 stars needed, 2 candidates (row 1, column 2).
29. Mark 1 cell adjacent to stars as X (row 2, column 2).
30. Region completion: 1 star needed, 1 candidate (row 4, column 2).
31. Mark 2 cells adjacent to stars as X (row 3, column 2).
32. Three candidates with two adjacent: Isolated candidate must hold a star (row 7, column 3).
33. Mark 1 cell adjacent to stars as X (row 6, column 3).
34. Region completion: 1 star needed, 1 candidate (row 5, column 4).
35. Row 5 complete: Mark 3 remaining cells as X (row 5, column 8).
36. Clump analysis (Row 4): candidate clumps can only just supply the remaining stars (row 3, column 9).
37. Blocking rule: a star here would touch every other open cell in its region, leaving no room for the region's second star (row 1, column 9).
38. Three candidates with two adjacent: Isolated candidate must hold a star (row 2, column 8).
39. Mark 4 cells adjacent to stars as X (row 1, column 7).
40. Clump analysis (Row 3): candidate clumps can only just supply the remaining stars (row 2, column 4).
41. Clump analysis (Row 3): each clump must supply its full share of stars (row 3, column 10).
42. Mark 3 cells adjacent to stars as X (row 2, column 10).
43. Region completion: 1 star needed, 1 candidate (row 1, column 10).
44. Row 1 complete: Mark 3 remaining cells as X (row 1, column 4).
45. Row completion: 1 star needed, 1 candidate (row 2, column 6).
46. Mark 1 cell adjacent to stars as X (row 3, column 5).
47. Region completion: 1 star needed, 1 candidate (row 3, column 4).
48. Row completion: 1 star needed, 1 candidate (row 4, column 8).
49. Region complete: Mark 7 remaining cells as X (row 6, column 8).
50. Row completion: 1 star needed, 1 candidate (row 6, column 9).
51. Mark 1 cell adjacent to stars as X (row 7, column 9).
52. Row completion: 1 star needed, 1 candidate (row 8, column 7).
53. Mark 2 cells adjacent to stars as X (row 7, column 6).
54. Region completion: 1 star needed, 1 candidate (row 7, column 5).
55. Column completion: 1 star needed, 1 candidate (row 10, column 7).
56. Mark 1 cell adjacent to stars as X (row 10, column 8).
57. Column completion: 1 star needed, 1 candidate (row 10, column 9).
58. Mark 1 cell adjacent to stars as X (row 10, column 10).
59. Solved! Every row, column, and region has its two stars, none touching.