Cats & Dogs #123: 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 R3C5 and R2C5 means they are the same. R3C5 is a cat, so R2C5 is a cat.
  2. The × clue between R2C5 and R2C6 means they are different. R2C5 is a cat, so R2C6 is a dog.
  3. The = clue between R3C2 and R3C1 means they are the same. R3C2 is a dog, so R3C1 is a dog.
  4. The = clue between R3C1 and R2C1 means they are the same. R3C1 is a dog, so R2C1 is a dog.
  5. The = clue between R2C1 and R2C2 means they are the same. R2C1 is a dog, so R2C2 is a dog.
  6. R2C1 and R2C2 are both dogs, so R2C3 must be a cat (no three in a row).
  7. R2C3 and R2C5 are both cats with one square between them, so R2C4 must be a dog.
  8. R3C1 and R3C2 are both dogs, so R3C3 must be a cat (no three in a row).
  9. R3C3 and R3C5 are both cats with one square between them, so R3C4 must be a dog.
  10. R7C4 and R7C5 are both cats, so R7C3 must be a dog (no three in a row).
  11. The = clue between R7C3 and R7C2 means they are the same. R7C3 is a dog, so R7C2 is a dog.
  12. R7C2 and R7C3 are both dogs, so R7C1 must be a cat (no three in a row).
  13. R7C4 and R7C5 are both cats, so R7C6 must be a dog (no three in a row).
  14. R7C6 and R7C8 are both dogs with one square between them, so R7C7 must be a cat.
  15. The × clue between R7C7 and R6C7 means they are different. R7C7 is a cat, so R6C7 is a dog.
  16. R2C1 and R3C1 are both dogs, so R1C1 must be a cat (no three in a row).
  17. R2C1 and R3C1 are both dogs, so R4C1 must be a cat (no three in a row).
  18. R2C2 and R3C2 are both dogs, so R1C2 must be a cat (no three in a row).
  19. R1C1 and R1C2 are both cats, so R1C3 must be a dog (no three in a row).
  20. R2C2 and R3C2 are both dogs, so R4C2 must be a cat (no three in a row).
  21. R4C1 and R4C2 are both cats, so R4C3 must be a dog (no three in a row).
  22. R5C2 and R7C2 are both dogs with one square between them, so R6C2 must be a cat.
  23. R2C4 and R3C4 are both dogs, so R1C4 must be a cat (no three in a row).
  24. R2C4 and R3C4 are both dogs, so R4C4 must be a cat (no three in a row).
  25. R4C4 and R4C6 are both cats with one square between them, so R4C5 must be a dog.
  26. R2C5 and R3C5 are both cats, so R1C5 must be a dog (no three in a row).
  27. Row 2 already has its 4 dogs, so R2C7 and R2C8 must be cats.
  28. Row 4 already has its 4 cats, so R4C7 must be dogs.
  29. The × clue between R4C7 and R3C7 means they are different. R4C7 is a dog, so R3C7 is a cat.
  30. R3C5 and R3C7 are both cats with one square between them, so R3C6 must be a dog.
  31. R2C6 and R3C6 are both dogs, so R1C6 must be a cat (no three in a row).
  32. R2C7 and R3C7 are both cats, so R1C7 must be a dog (no three in a row).
  33. R4C7 and R6C7 are both dogs with one square between them, so R5C7 must be a cat.
  34. Row 1 already has its 4 cats, so R1C8 must be dogs.
  35. Row 3 already has its 4 dogs, so R3C8 must be cats.
  36. R2C8 and R3C8 are both cats, so R4C8 must be a dog (no three in a row).
  37. Column 2 already has its 4 dogs, so R8C2 must be cats.
  38. The = clue between R8C2 and R8C1 means they are the same. R8C2 is a cat, so R8C1 is a cat.
  39. R8C1 and R8C2 are both cats, so R8C3 must be a dog (no three in a row).
  40. R8C3 and R8C5 are both dogs with one square between them, so R8C4 must be a cat.
  41. R7C1 and R8C1 are both cats, so R6C1 must be a dog (no three in a row).
  42. R7C3 and R8C3 are both dogs, so R6C3 must be a cat (no three in a row).
  43. R6C2 and R6C3 are both cats, so R6C4 must be a dog (no three in a row).
  44. Column 1 already has its 4 cats, so R5C1 must be dogs.
  45. R5C1 and R5C2 are both dogs, so R5C3 must be a cat (no three in a row).
  46. Column 4 already has its 4 cats, so R5C4 must be dogs.
  47. Column 7 already has its 4 cats, so R8C7 must be dogs.
  48. R8C5 and R8C7 are both dogs with one square between them, so R8C6 must be a cat.
  49. Row 8 already has its 4 cats, so R8C8 must be dogs.
  50. R7C8 and R8C8 are both dogs, so R6C8 must be a cat (no three in a row).
  51. Column 8 already has its 4 dogs, so R5C8 must be cats.
  52. R5C7 and R5C8 are both cats, so R5C6 must be a dog (no three in a row).
  53. R5C4 and R5C6 are both dogs with one square between them, so R5C5 must be a cat.
  54. R5C5 and R7C5 are both cats with one square between them, so R6C5 must be a dog.
  55. R6C4 and R6C5 are both dogs, so R6C6 must be a cat (no three in a row).

About this puzzle

This 8×8 grid starts with 8 filled squares and 9 = / × clues. It can be solved in 55 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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