Logic Puzzle Club

Fillomino of the week: week 3

The full logical solve of the hard Fillomino for September 15 to September 21, 2026, 10 × 10. 48 steps, 3 techniques, no guessing. Step through it, or jump to any step below.

One way out. This 4 has one cell and needs 3 more. Its only open side is r1c9, so that cell is 4.
Step 1 of 48

Every step

  1. This 4 has one cell and needs 3 more. Its only open side is r1c9, so that cell is 4.

  2. This 5 has one cell and needs 4 more. Its only open side is r3c10, so that cell is 5.

  3. This 7 has one cell and needs 6 more. Its only open side is r5c2, so that cell is 7.

  4. This 5 has one cell and needs 4 more. Its only open side is r7c3, so that cell is 5.

  5. This 2 has one cell and needs 1 more. Its only open side is r9c10, so that cell is 2.

  6. Try each number that fits in r9c1. A 5 leads to a broken rule: a region grows too big or runs out of room. So it is 3.

  7. This 3 has one cell and needs 2 more. Its only open side is r8c1, so that cell is 3.

  8. This 3 has 2 cells and needs 1 more. Its only open side is r7c1, so that cell is 3.

  9. This 2 has one cell and needs 1 more. Its only open side is r5c1, so that cell is 2.

  10. This 7 has 2 cells and needs 5 more. Its only open side is r4c2, so that cell is 7.

  11. This 5 has 3 cells and needs 2 more. Its only open side is r8c3, so that cell is 5.

  12. Try each number that fits in r10c2. 3 and 5 each lead to a broken rule. So it is 8.

  13. This 8 has one cell and needs 7 more. Its only open side is r10c3, so that cell is 8.

  14. Try each number that fits in r4c3. 2, 3 and 6 each lead to a broken rule. So it is 7.

  15. This 6 needs 5 more cells, and exactly that many cells around it could join. So r2c3, r3c2, r1c3, r1c2 and r1c4 are 6.

  16. This 5 has one cell and needs 4 more. Its only open side is r2c1, so that cell is 5.

  17. This 5 has 4 cells and needs 1 more. Its only open side is r4c1, so that cell is 5.

  18. This 7 has 4 cells and needs 3 more. Its only open side is r4c4, so that cell is 7.

  19. This 7 needs 2 more cells, and exactly that many cells around it could join. So r4c5 and r5c4 are 7.

  20. This 2 has one cell and needs 1 more. Its only open side is r3c6, so that cell is 2.

  21. This 6 has one cell and needs 5 more. Its only open side is r5c6, so that cell is 6.

  22. This 2 has one cell and needs 1 more. Its only open side is r6c5, so that cell is 2.

  23. This 6 has 3 cells and needs 3 more. Its only open side is r6c6, so that cell is 6.

  24. Try each number that fits in r9c3. A 5 leads to a broken rule: a region grows too big or runs out of room. So it is 8.

  25. This 5 has 4 cells and needs 1 more. Its only open side is r8c4, so that cell is 5.

  26. This 8 has 4 cells and needs 4 more. Its only open side is r10c5, so that cell is 8.

  27. This 8 has 5 cells and needs 3 more. Its only open side is r10c6, so that cell is 8.

  28. This 8 has 6 cells and needs 2 more. Its only open side is r10c7, so that cell is 8.

  29. This 8 has 7 cells and needs 1 more. Its only open side is r9c7, so that cell is 8.

  30. This 3 has one cell and needs 2 more. Its only open side is r8c5, so that cell is 3.

  31. This 5 has one cell and needs 4 more. Its only open side is r8c6, so that cell is 5.

  32. This 3 has 2 cells and needs 1 more. Its only open side is r7c5, so that cell is 3.

  33. This 4 has 3 cells and needs 1 more. Its only open side is r9c9, so that cell is 4.

  34. Try each number that fits in r7c6. 1 and 6 each lead to a broken rule. So it is 5.

  35. This 6 has 4 cells and needs 2 more. Its only open side is r6c7, so that cell is 6.

  36. This 6 has 5 cells and needs 1 more. Its only open side is r6c8, so that cell is 6.

  37. This 6 needs 5 more cells, and exactly that many cells around it could join. So r8c7, r8c9, r7c9, r8c10 and r7c10 are 6.

  38. This 4 has 2 cells and needs 2 more. Its only open side is r5c9, so that cell is 4.

  39. This 2 has one cell and needs 1 more. Its only open side is r4c10, so that cell is 2.

  40. This 5 has 2 cells and needs 3 more. Its only open side is r3c9, so that cell is 5.

  41. This 4 has 3 cells and needs 1 more. Its only open side is r1c8, so that cell is 4.

  42. This 5 has 3 cells and needs 2 more. Its only open side is r4c9, so that cell is 5.

  43. This 5 has 4 cells and needs 1 more. Its only open side is r4c8, so that cell is 5.

  44. This 6 has one cell and needs 5 more. Its only open side is r3c7, so that cell is 6.

  45. This 6 has 2 cells and needs 4 more. Its only open side is r2c7, so that cell is 6.

  46. This 4 has 3 cells and needs 1 more. Its only open side is r5c8, so that cell is 4.

  47. This 5 has 4 cells and needs 1 more. Its only open side is r7c8, so that cell is 5.

  48. This 6 needs 3 more cells, and exactly that many cells around it could join. So r1c7, r2c6 and r1c6 are 6.