Cats & Dogs #113: 8x8 Grid Puzzle (Medium)

medium

Tap a square: 🐱 cat → 🐶 dog → clear

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🐱 4 cats and 🐶 4 dogs in every row and column = same   × different

A 8x8 logic grid: 4 cats and 4 dogs in every row and column, no three of a kind in a row, and a few = and × clues to point the way.

  • Exactly 4 cats and 4 dogs in every row and every column.
  • Never three of the same animal in a row, across or down.
  • An = between two squares means the same animal; a × means different animals.

Step-by-step solution

Squares are written as R<row>C<column>, counting from the top-left.

  1. The = clue between R8C7 and R7C7 means they are the same. R8C7 is a cat, so R7C7 is a cat.
  2. The × clue between R8C7 and R8C8 means they are different. R8C7 is a cat, so R8C8 is a dog.
  3. R7C7 and R8C7 are both cats, so R6C7 must be a dog (no three in a row).
  4. The = clue between R6C7 and R6C6 means they are the same. R6C7 is a dog, so R6C6 is a dog.
  5. R6C6 and R6C7 are both dogs, so R6C5 must be a cat (no three in a row).
  6. The = clue between R6C5 and R6C4 means they are the same. R6C5 is a cat, so R6C4 is a cat.
  7. R6C4 and R6C5 are both cats, so R6C3 must be a dog (no three in a row).
  8. R6C6 and R6C7 are both dogs, so R6C8 must be a cat (no three in a row).
  9. The = clue between R6C8 and R5C8 means they are the same. R6C8 is a cat, so R5C8 is a cat.
  10. R5C4 and R6C4 are both cats, so R4C4 must be a dog (no three in a row).
  11. The = clue between R4C4 and R4C5 means they are the same. R4C4 is a dog, so R4C5 is a dog.
  12. R4C4 and R4C5 are both dogs, so R4C3 must be a cat (no three in a row).
  13. The × clue between R4C3 and R3C3 means they are different. R4C3 is a cat, so R3C3 is a dog.
  14. The × clue between R3C3 and R3C4 means they are different. R3C3 is a dog, so R3C4 is a cat.
  15. R4C4 and R4C5 are both dogs, so R4C6 must be a cat (no three in a row).
  16. The = clue between R4C6 and R3C6 means they are the same. R4C6 is a cat, so R3C6 is a cat.
  17. R3C4 and R3C6 are both cats with one square between them, so R3C5 must be a dog.
  18. R5C4 and R6C4 are both cats, so R7C4 must be a dog (no three in a row).
  19. R3C5 and R4C5 are both dogs, so R2C5 must be a cat (no three in a row).
  20. R3C5 and R4C5 are both dogs, so R5C5 must be a cat (no three in a row).
  21. R5C4 and R5C5 are both cats, so R5C3 must be a dog (no three in a row).
  22. The = clue between R5C3 and R5C2 means they are the same. R5C3 is a dog, so R5C2 is a dog.
  23. R5C2 and R5C3 are both dogs, so R5C1 must be a cat (no three in a row).
  24. R5C4 and R5C5 are both cats, so R5C6 must be a dog (no three in a row).
  25. R5C3 and R6C3 are both dogs, so R7C3 must be a cat (no three in a row).
  26. The = clue between R7C3 and R7C2 means they are the same. R7C3 is a cat, so R7C2 is a cat.
  27. The × clue between R7C3 and R8C3 means they are different. R7C3 is a cat, so R8C3 is a dog.
  28. R7C2 and R7C3 are both cats, so R7C1 must be a dog (no three in a row).
  29. R5C5 and R6C5 are both cats, so R7C5 must be a dog (no three in a row).
  30. R7C4 and R7C5 are both dogs, so R7C6 must be a cat (no three in a row).
  31. R7C6 and R7C7 are both cats, so R7C8 must be a dog (no three in a row).
  32. R3C6 and R4C6 are both cats, so R2C6 must be a dog (no three in a row).
  33. R5C8 and R6C8 are both cats, so R4C8 must be a dog (no three in a row).
  34. R3C8 and R4C8 are both dogs, so R2C8 must be a cat (no three in a row).
  35. Row 5 already has its 4 cats, so R5C7 must be dogs.
  36. R5C7 and R6C7 are both dogs, so R4C7 must be a cat (no three in a row).
  37. Column 3 already has its 4 dogs, so R1C3 must be cats.
  38. R1C2 and R1C3 are both cats, so R1C1 must be a dog (no three in a row).
  39. R1C2 and R1C3 are both cats, so R1C4 must be a dog (no three in a row).
  40. Column 3 already has its 4 dogs, so R2C3 must be cats.
  41. R2C3 and R2C5 are both cats with one square between them, so R2C4 must be a dog.
  42. Column 4 already has its 4 dogs, so R8C4 must be cats.
  43. The × clue between R8C4 and R8C5 means they are different. R8C4 is a cat, so R8C5 is a dog.
  44. Column 5 already has its 4 dogs, so R1C5 must be cats.
  45. Column 8 already has its 4 dogs, so R1C8 must be cats.
  46. Row 1 already has its 4 cats, so R1C6 and R1C7 must be dogs.
  47. The × clue between R1C7 and R2C7 means they are different. R1C7 is a dog, so R2C7 is a cat.
  48. R2C7 and R4C7 are both cats with one square between them, so R3C7 must be a dog.
  49. Row 2 already has its 4 cats, so R2C1 must be dogs.
  50. R1C1 and R2C1 are both dogs, so R3C1 must be a cat (no three in a row).
  51. R3C1 and R5C1 are both cats with one square between them, so R4C1 must be a dog.
  52. Row 2 already has its 4 cats, so R2C2 must be dogs.
  53. Row 3 already has its 4 dogs, so R3C2 must be cats.
  54. Row 4 already has its 4 dogs, so R4C2 must be cats.
  55. Column 1 already has its 4 dogs, so R6C1 must be cats.
  56. Row 6 already has its 4 cats, so R6C2 must be dogs.
  57. Column 1 already has its 4 dogs, so R8C1 must be cats.
  58. Column 2 already has its 4 cats, so R8C2 must be dogs.
  59. Row 8 already has its 4 dogs, so R8C6 must be cats.

About this puzzle

This 8×8 grid starts with 4 filled squares and 14 = / × clues. It can be solved in 59 steps using pairs, gaps, counts and clues.

Whenever two of the same animal sit side by side, the squares on both ends must be the other animal. Look for these pairs first.

Every puzzle on this site has exactly one solution that can be reached by deduction. If you are guessing, look again at the rows and columns that are nearly full.

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