Cats & Dogs #137: 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 R2C8 and R3C8 means they are different. R2C8 is a cat, so R3C8 is a dog.
  2. The = clue between R3C5 and R3C6 means they are the same. R3C5 is a cat, so R3C6 is a cat.
  3. The × clue between R6C7 and R5C7 means they are different. R6C7 is a dog, so R5C7 is a cat.
  4. R3C5 and R3C6 are both cats, so R3C4 must be a dog (no three in a row).
  5. R3C3 and R3C4 are both dogs, so R3C2 must be a cat (no three in a row).
  6. R3C5 and R3C6 are both cats, so R3C7 must be a dog (no three in a row).
  7. R5C7 and R5C8 are both cats, so R5C6 must be a dog (no three in a row).
  8. The × clue between R5C6 and R4C6 means they are different. R5C6 is a dog, so R4C6 is a cat.
  9. R5C5 and R5C6 are both dogs, so R5C4 must be a cat (no three in a row).
  10. R6C7 and R6C8 are both dogs, so R6C6 must be a cat (no three in a row).
  11. R6C4 and R6C6 are both cats with one square between them, so R6C5 must be a dog.
  12. R5C4 and R6C4 are both cats, so R4C4 must be a dog (no three in a row).
  13. R4C2 and R4C4 are both dogs with one square between them, so R4C3 must be a cat.
  14. R3C4 and R4C4 are both dogs, so R2C4 must be a cat (no three in a row).
  15. The = clue between R2C4 and R1C4 means they are the same. R2C4 is a cat, so R1C4 is a cat.
  16. R5C4 and R6C4 are both cats, so R7C4 must be a dog (no three in a row).
  17. R5C5 and R6C5 are both dogs, so R4C5 must be a cat (no three in a row).
  18. R4C5 and R4C6 are both cats, so R4C7 must be a dog (no three in a row).
  19. R3C5 and R4C5 are both cats, so R2C5 must be a dog (no three in a row).
  20. R5C5 and R6C5 are both dogs, so R7C5 must be a cat (no three in a row).
  21. R3C6 and R4C6 are both cats, so R2C6 must be a dog (no three in a row).
  22. R2C5 and R2C6 are both dogs, so R2C7 must be a cat (no three in a row).
  23. Row 3 already has its 4 dogs, so R3C1 must be cats.
  24. Column 4 already has its 4 cats, so R8C4 must be dogs.
  25. The = clue between R8C4 and R8C3 means they are the same. R8C4 is a dog, so R8C3 is a dog.
  26. R8C3 and R8C4 are both dogs, so R8C2 must be a cat (no three in a row).
  27. The = clue between R8C2 and R8C1 means they are the same. R8C2 is a cat, so R8C1 is a cat.
  28. R8C3 and R8C4 are both dogs, so R8C5 must be a cat (no three in a row).
  29. R8C5 and R8C7 are both cats with one square between them, so R8C6 must be a dog.
  30. R7C2 and R8C2 are both cats, so R6C2 must be a dog (no three in a row).
  31. R4C2 and R6C2 are both dogs with one square between them, so R5C2 must be a cat.
  32. R5C2 and R5C4 are both cats with one square between them, so R5C3 must be a dog.
  33. Row 5 already has its 4 cats, so R5C1 must be dogs.
  34. The × clue between R5C1 and R4C1 means they are different. R5C1 is a dog, so R4C1 is a cat.
  35. R3C1 and R4C1 are both cats, so R2C1 must be a dog (no three in a row).
  36. Row 4 already has its 4 cats, so R4C8 must be dogs.
  37. Row 6 already has its 4 dogs, so R6C1 must be cats.
  38. R6C1 and R8C1 are both cats with one square between them, so R7C1 must be a dog.
  39. Row 6 already has its 4 dogs, so R6C3 must be cats.
  40. Row 8 already has its 4 cats, so R8C8 must be dogs.
  41. R6C8 and R8C8 are both dogs with one square between them, so R7C8 must be a cat.
  42. Column 1 already has its 4 cats, so R1C1 must be dogs.
  43. Column 2 already has its 4 cats, so R1C2 must be dogs.
  44. R1C1 and R1C2 are both dogs, so R1C3 must be a cat (no three in a row).
  45. R1C3 and R1C4 are both cats, so R1C5 must be a dog (no three in a row).
  46. Column 2 already has its 4 cats, so R2C2 must be dogs.
  47. R2C1 and R2C2 are both dogs, so R2C3 must be a cat (no three in a row).
  48. Column 3 already has its 4 cats, so R7C3 must be dogs.
  49. Column 8 already has its 4 dogs, so R1C8 must be cats.
  50. The = clue between R1C8 and R1C7 means they are the same. R1C8 is a cat, so R1C7 is a cat.
  51. R1C7 and R1C8 are both cats, so R1C6 must be a dog (no three in a row).
  52. Column 6 already has its 4 dogs, so R7C6 must be cats.
  53. R7C5 and R7C6 are both cats, so R7C7 must be a dog (no three in a row).

About this puzzle

This 8×8 grid starts with 11 filled squares and 9 = / × clues. It can be solved in 53 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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