Cats & Dogs #106: 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

Use pure logic to place every cat and dog. Each row and column holds 4 of each animal, three in a row is never allowed, and the clues between squares settle the rest.

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

About this puzzle

This 8×8 grid starts with 5 filled squares and 10 = / × 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.

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

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