Logic Puzzle Club

Fillomino of the week: week 2

The full logical solve of the hard Fillomino for September 8 to September 14, 2026, 10 × 10. 44 steps, 3 techniques, no guessing. Step through it, or jump to any step below.

One way out. This 7 has one cell and needs 6 more. Its only open side is r2c6, so that cell is 7.
Step 1 of 44

Every step

  1. This 7 has one cell and needs 6 more. Its only open side is r2c6, so that cell is 7.

  2. This 4 has one cell and needs 3 more. Its only open side is r7c5, so that cell is 4.

  3. This 3 has one cell and needs 2 more. Its only open side is r9c9, so that cell is 3.

  4. This 3 has one cell and needs 2 more. Its only open side is r9c3, so that cell is 3.

  5. This 2 has one cell and needs 1 more. Its only open side is r10c9, so that cell is 2.

  6. This 4 has one cell and needs 3 more. Its only open side is r10c7, so that cell is 4.

  7. Try each number that fits in r2c1. 1 and 5 each lead to a broken rule. So it is 3.

  8. This 5 has one cell and needs 4 more. Its only open side is r3c2, so that cell is 5.

  9. This 5 has 2 cells and needs 3 more. Its only open side is r4c2, so that cell is 5.

  10. This 5 has 3 cells and needs 2 more. The only open side it can grow through is r4c3, so that cell is 5.

  11. This 3 has one cell and needs 2 more. Its only open side is r5c1, so that cell is 3.

  12. Try each number that fits in r1c2. A 1 leads to a broken rule: a region grows too big or runs out of room. So it is 4.

  13. This 4 has 2 cells and needs 2 more. Its only open side is r2c3, so that cell is 4.

  14. This 4 has 3 cells and needs 1 more. Its only open side is r2c4, so that cell is 4.

  15. This 7 has one cell and needs 6 more. Its only open side is r1c5, so that cell is 7.

  16. This 2 has one cell and needs 1 more. Its only open side is r3c4, so that cell is 2.

  17. Each other number either has no room to fit around r1c6 or would touch a region of its own size. Only 7 is left.

  18. Try each number that fits in r2c5. 1 and 6 each lead to a broken rule. So it is 7.

  19. This 7 has 6 cells and needs 1 more. Its only open side is r2c7, so that cell is 7.

  20. This 6 has one cell and needs 5 more. Its only open side is r4c5, so that cell is 6.

  21. Try each number that fits in r4c7. 1, 4 and 9 each lead to a broken rule. So it is 6.

  22. Try each number that fits in r8c7. 2, 4 and 5 each lead to a broken rule. So it is 6.

  23. Try each number that fits in r9c7. 1, 4 and 5 each lead to a broken rule. So it is 6.

  24. This 6 has 3 cells and needs 3 more. Its only open side is r8c9, so that cell is 6.

  25. This 6 has 4 cells and needs 2 more. Its only open side is r7c9, so that cell is 6.

  26. This 4 has one cell and needs 3 more. Its only open side is r6c8, so that cell is 4.

  27. This 4 has one cell and needs 3 more. Its only open side is r7c10, so that cell is 4.

  28. This 6 has 5 cells and needs 1 more. Its only open side is r6c9, so that cell is 6.

  29. This 4 has 2 cells and needs 2 more. Its only open side is r6c10, so that cell is 4.

  30. This 4 has 3 cells and needs 1 more. Its only open side is r5c10, so that cell is 4.

  31. This 4 has 2 cells and needs 2 more. Its only open side is r10c6, so that cell is 4.

  32. This 4 has 3 cells and needs 1 more. Its only open side is r10c5, so that cell is 4.

  33. This 9 needs 8 more cells, and exactly that many cells around it could join. So r3c8, r4c9, r2c8, r3c9, r4c10, r5c9, r1c8 and r3c10 are 9.

  34. This 5 needs 3 more cells, and exactly that many cells around it could join. So r8c5, r9c5 and r9c4 are 5.

  35. This 3 has 2 cells and needs 1 more. Its only open side is r9c2, so that cell is 3.

  36. Try each number that fits in r5c7. A 1 leads to a broken rule: a region grows too big or runs out of room. So it is 6.

  37. Try each number that fits in r6c5. 1 and 7 each lead to a broken rule. So it is 4.

  38. Try each number that fits in r4c4. 1, 3 and 7 each lead to a broken rule. So it is 5.

  39. This 7 needs 6 more cells, and exactly that many cells around it could join. So r5c4, r6c3, r7c4, r5c3, r7c3 and r5c2 are 7.

  40. This 3 has 2 cells and needs 1 more. Its only open side is r6c1, so that cell is 3.

  41. This 5 has 2 cells and needs 3 more. Its only open side is r8c2, so that cell is 5.

  42. This 5 has 4 cells and needs 1 more. Its only open side is r8c1, so that cell is 5.

  43. Each other number either has no room to fit around r10c1 or would touch a region of its own size. Only 2 is left.

  44. This 2 has one cell and needs 1 more. Its only open side is r9c1, so that cell is 2.