Cats & Dogs #193: 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 R6C6 and R6C5 means they are the same. R6C6 is a dog, so R6C5 is a dog.
  2. The × clue between R6C5 and R5C5 means they are different. R6C5 is a dog, so R5C5 is a cat.
  3. The × clue between R5C5 and R4C5 means they are different. R5C5 is a cat, so R4C5 is a dog.
  4. The × clue between R4C5 and R3C5 means they are different. R4C5 is a dog, so R3C5 is a cat.
  5. R3C5 and R3C6 are both cats, so R3C4 must be a dog (no three in a row).
  6. The = clue between R3C4 and R3C3 means they are the same. R3C4 is a dog, so R3C3 is a dog.
  7. The = clue between R3C4 and R4C4 means they are the same. R3C4 is a dog, so R4C4 is a dog.
  8. R3C3 and R3C4 are both dogs, so R3C2 must be a cat (no three in a row).
  9. The × clue between R3C2 and R2C2 means they are different. R3C2 is a cat, so R2C2 is a dog.
  10. R3C5 and R3C6 are both cats, so R3C7 must be a dog (no three in a row).
  11. R4C4 and R4C5 are both dogs, so R4C3 must be a cat (no three in a row).
  12. R4C4 and R4C5 are both dogs, so R4C6 must be a cat (no three in a row).
  13. R6C5 and R6C6 are both dogs, so R6C4 must be a cat (no three in a row).
  14. R6C5 and R6C6 are both dogs, so R6C7 must be a cat (no three in a row).
  15. R8C6 and R8C8 are both dogs with one square between them, so R8C7 must be a cat.
  16. R3C2 and R5C2 are both cats with one square between them, so R4C2 must be a dog.
  17. R3C4 and R4C4 are both dogs, so R2C4 must be a cat (no three in a row).
  18. R2C4 and R2C5 are both cats, so R2C3 must be a dog (no three in a row).
  19. R2C2 and R2C3 are both dogs, so R2C1 must be a cat (no three in a row).
  20. The = clue between R2C1 and R1C1 means they are the same. R2C1 is a cat, so R1C1 is a cat.
  21. R2C4 and R2C5 are both cats, so R2C6 must be a dog (no three in a row).
  22. R1C1 and R2C1 are both cats, so R3C1 must be a dog (no three in a row).
  23. R2C3 and R3C3 are both dogs, so R1C3 must be a cat (no three in a row).
  24. R1C1 and R1C3 are both cats with one square between them, so R1C2 must be a dog.
  25. R3C4 and R4C4 are both dogs, so R5C4 must be a cat (no three in a row).
  26. R5C2 and R5C4 are both cats with one square between them, so R5C3 must be a dog.
  27. The = clue between R5C3 and R6C3 means they are the same. R5C3 is a dog, so R6C3 is a dog.
  28. The × clue between R6C3 and R6C2 means they are different. R6C3 is a dog, so R6C2 is a cat.
  29. The × clue between R6C2 and R6C1 means they are different. R6C2 is a cat, so R6C1 is a dog.
  30. R5C4 and R5C5 are both cats, so R5C6 must be a dog (no three in a row).
  31. R5C2 and R6C2 are both cats, so R7C2 must be a dog (no three in a row).
  32. R5C3 and R6C3 are both dogs, so R7C3 must be a cat (no three in a row).
  33. R5C4 and R6C4 are both cats, so R7C4 must be a dog (no three in a row).
  34. R2C5 and R3C5 are both cats, so R1C5 must be a dog (no three in a row).
  35. R5C6 and R6C6 are both dogs, so R7C6 must be a cat (no three in a row).
  36. R6C7 and R8C7 are both cats with one square between them, so R7C7 must be a dog.
  37. Row 3 already has its 4 dogs, so R3C8 must be cats.
  38. Row 6 already has its 4 dogs, so R6C8 must be cats.
  39. Column 2 already has its 4 dogs, so R8C2 must be cats.
  40. Column 3 already has its 4 dogs, so R8C3 must be cats.
  41. R8C2 and R8C3 are both cats, so R8C1 must be a dog (no three in a row).
  42. R8C2 and R8C3 are both cats, so R8C4 must be a dog (no three in a row).
  43. R8C4 and R8C6 are both dogs with one square between them, so R8C5 must be a cat.
  44. R6C1 and R8C1 are both dogs with one square between them, so R7C1 must be a cat.
  45. Column 4 already has its 4 dogs, so R1C4 must be cats.
  46. Column 5 already has its 4 cats, so R7C5 must be dogs.
  47. Row 7 already has its 4 dogs, so R7C8 must be cats.
  48. R6C8 and R7C8 are both cats, so R5C8 must be a dog (no three in a row).
  49. R5C6 and R5C8 are both dogs with one square between them, so R5C7 must be a cat.
  50. R5C7 and R6C7 are both cats, so R4C7 must be a dog (no three in a row).
  51. R3C7 and R4C7 are both dogs, so R2C7 must be a cat (no three in a row).
  52. Row 2 already has its 4 cats, so R2C8 must be dogs.
  53. Row 4 already has its 4 dogs, so R4C1 and R4C8 must be cats.
  54. Row 5 already has its 4 cats, so R5C1 must be dogs.
  55. Column 6 already has its 4 dogs, so R1C6 must be cats.
  56. Row 1 already has its 4 cats, so R1C7 and R1C8 must be dogs.

About this puzzle

This 8×8 grid starts with 6 filled squares and 11 = / × clues. It can be solved in 56 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.

This kind of puzzle is known as a binary or Takuzu puzzle, here with cats and dogs and extra = / × clues.

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