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