Cats & Dogs #185: 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

Fill the 8x8 grid with cats and dogs so that every row and every column has exactly 4 of each, and never more than two of the same animal side by side.

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

About this puzzle

This 8×8 grid starts with 4 filled squares and 15 = / × clues. It can be solved in 60 steps using pairs, gaps, counts and clues.

Watch for a gap: if the squares on either side of an empty square match, the empty one must be different.

When every square is filled, press Check Answer. The grid is verified against the stored solution and any broken rule is named.

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