Hard Star Battle answer — May 5, 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 4, column 6).
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 1, column 2).
4. Three candidates with two adjacent: Isolated candidate must hold a star (row 1, column 1).
5. Mark 2 cells adjacent to stars as X (row 2, column 1).
6. Two-option rule: Cell adjacent to both candidates (row 1, column 4).
7. Two-option rule: Cell adjacent to both candidates (row 2, column 4).
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 2, column 5).
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 2, column 6).
10. Three candidates with two adjacent: Isolated candidate must hold a star (row 3, column 5).
11. Mark 4 cells adjacent to stars as X (row 3, column 4).
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 9, column 8).
13. Three candidates with two adjacent: Isolated candidate must hold a star (row 9, column 7).
14. Mark 4 cells adjacent to stars as X (row 8, column 6).
15. Clump analysis (Column 4): candidate clumps can only just supply the remaining stars (row 6, column 3).
16. Clump analysis (Region 4): candidate clumps can only just supply the remaining stars (row 7, column 3).
17. Clump analysis (Column 3): candidate clumps can only just supply the remaining stars (row 4, column 2).
18. Clump analysis (Region 7): candidate clumps can only just supply the remaining stars (row 1, column 3).
19. Region completion: 1 star needed, 1 candidate (row 2, column 3).
20. Mark 2 cells adjacent to stars as X (row 3, column 2).
21. Two last candidates (column 3): Eliminate 1 cell adjacent to both (row 5, column 2).
22. Clump analysis (Row 2): candidate clumps can only just supply the remaining stars (row 3, column 8).
23. Clump analysis (Column 1): each clump must supply its full share of stars (row 6, column 2).
24. Mark 5 cells adjacent to stars as X (row 5, column 1).
25. Column completion: 1 star needed, 1 candidate (row 4, column 3).
26. Two last candidates (column 2): Eliminate 2 cells adjacent to both (row 8, column 1).
27. Clump analysis (Row 5): candidate clumps can only just supply the remaining stars (row 6, column 6).
28. Star claim: Region 2 must place a star in column 7; cells touching all its options are eliminated (row 4, column 7).
29. Crowding (Column 6): a star here would leave too little room for its 2 remaining stars (row 6, column 7).
30. Crowding (Column 8): a star here would leave too little room for its 2 remaining stars (row 6, column 9).
31. Row completion: 1 star needed, 1 candidate (row 6, column 4).
32. Mark 2 cells adjacent to stars as X (row 5, column 5).
33. Column completion: 1 star needed, 1 candidate (row 1, column 5).
34. Mark 1 cell adjacent to stars as X (row 1, column 6).
35. Column completion: 2 stars needed, 2 candidates (row 5, column 6).
36. Mark 1 cell adjacent to stars as X (row 5, column 7).
37. Region completion: 1 star needed, 1 candidate (row 3, column 7).
38. Mark 2 cells adjacent to stars as X (row 2, column 7).
39. Row completion: 1 star needed, 1 candidate (row 2, column 9).
40. Mark 1 cell adjacent to stars as X (row 3, column 9).
41. Row 3 complete: Mark 1 remaining cell as X (row 3, column 1).
42. Region completion: 1 star needed, 1 candidate (row 4, column 1).
43. Row 4 complete: Mark 1 remaining cell as X (row 4, column 9).
44. Region completion: 1 star needed, 1 candidate (row 5, column 8).
45. Mark 1 cell adjacent to stars as X (row 5, column 9).
46. Column completion: 1 star needed, 1 candidate (row 7, column 6).
47. Mark 1 cell adjacent to stars as X (row 7, column 7).
48. Column completion: 1 star needed, 1 candidate (row 7, column 8).
49. Mark 2 cells adjacent to stars as X (row 7, column 9).
50. Region completion: 1 star needed, 1 candidate (row 9, column 9).
51. Row completion: 2 stars needed, 2 candidates (row 8, column 2).
52. Mark 1 cell adjacent to stars as X (row 9, column 2).
53. Row completion: 1 star needed, 1 candidate (row 8, column 4).
54. Mark 1 cell adjacent to stars as X (row 9, column 4).
55. Solved! Every row, column, and region has its two stars, none touching.