Cats & Dogs #105: 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 R1C7 and R1C6 means they are different. R1C7 is a dog, so R1C6 is a cat.
  2. The = clue between R5C5 and R6C5 means they are the same. R5C5 is a cat, so R6C5 is a cat.
  3. R1C5 and R1C6 are both cats, so R1C4 must be a dog (no three in a row).
  4. R8C3 and R8C4 are both cats, so R8C2 must be a dog (no three in a row).
  5. R8C3 and R8C4 are both cats, so R8C5 must be a dog (no three in a row).
  6. The × clue between R8C5 and R8C6 means they are different. R8C5 is a dog, so R8C6 is a cat.
  7. R8C6 and R8C7 are both cats, so R8C8 must be a dog (no three in a row).
  8. R7C3 and R8C3 are both cats, so R6C3 must be a dog (no three in a row).
  9. The × clue between R6C3 and R5C3 means they are different. R6C3 is a dog, so R5C3 is a cat.
  10. R5C3 and R5C5 are both cats with one square between them, so R5C4 must be a dog.
  11. R3C3 and R5C3 are both cats with one square between them, so R4C3 must be a dog.
  12. R5C5 and R6C5 are both cats, so R4C5 must be a dog (no three in a row).
  13. The × clue between R4C5 and R4C6 means they are different. R4C5 is a dog, so R4C6 is a cat.
  14. The = clue between R4C6 and R5C6 means they are the same. R4C6 is a cat, so R5C6 is a cat.
  15. R4C3 and R4C5 are both dogs with one square between them, so R4C4 must be a cat.
  16. R5C5 and R5C6 are both cats, so R5C7 must be a dog (no three in a row).
  17. R5C5 and R6C5 are both cats, so R7C5 must be a dog (no three in a row).
  18. R4C6 and R5C6 are both cats, so R3C6 must be a dog (no three in a row).
  19. R4C6 and R5C6 are both cats, so R6C6 must be a dog (no three in a row).
  20. Row 8 already has its 4 cats, so R8C1 must be dogs.
  21. Column 3 already has its 4 cats, so R1C3 must be dogs.
  22. R1C3 and R1C4 are both dogs, so R1C2 must be a cat (no three in a row).
  23. Column 3 already has its 4 cats, so R2C3 must be dogs.
  24. Column 6 already has its 4 cats, so R2C6 and R7C6 must be dogs.
  25. R7C5 and R7C6 are both dogs, so R7C4 must be a cat (no three in a row).
  26. R7C3 and R7C4 are both cats, so R7C2 must be a dog (no three in a row).
  27. R7C5 and R7C6 are both dogs, so R7C7 must be a cat (no three in a row).
  28. R7C2 and R8C2 are both dogs, so R6C2 must be a cat (no three in a row).
  29. R7C4 and R8C4 are both cats, so R6C4 must be a dog (no three in a row).
  30. R7C7 and R8C7 are both cats, so R6C7 must be a dog (no three in a row).
  31. R6C6 and R6C7 are both dogs, so R6C8 must be a cat (no three in a row).
  32. R5C7 and R6C7 are both dogs, so R4C7 must be a cat (no three in a row).
  33. R4C6 and R4C7 are both cats, so R4C8 must be a dog (no three in a row).
  34. R3C7 and R4C7 are both cats, so R2C7 must be a dog (no three in a row).
  35. R2C6 and R2C7 are both dogs, so R2C5 must be a cat (no three in a row).
  36. R2C6 and R2C7 are both dogs, so R2C8 must be a cat (no three in a row).
  37. R1C5 and R2C5 are both cats, so R3C5 must be a dog (no three in a row).
  38. R3C5 and R3C6 are both dogs, so R3C4 must be a cat (no three in a row).
  39. R3C3 and R3C4 are both cats, so R3C2 must be a dog (no three in a row).
  40. The = clue between R3C2 and R4C2 means they are the same. R3C2 is a dog, so R4C2 is a dog.
  41. R4C2 and R4C3 are both dogs, so R4C1 must be a cat (no three in a row).
  42. R3C2 and R4C2 are both dogs, so R2C2 must be a cat (no three in a row).
  43. R3C2 and R4C2 are both dogs, so R5C2 must be a cat (no three in a row).
  44. R5C2 and R5C3 are both cats, so R5C1 must be a dog (no three in a row).
  45. R3C4 and R4C4 are both cats, so R2C4 must be a dog (no three in a row).
  46. Row 2 already has its 4 dogs, so R2C1 must be cats.
  47. R2C1 and R4C1 are both cats with one square between them, so R3C1 must be a dog.
  48. Row 3 already has its 4 dogs, so R3C8 must be cats.
  49. R2C8 and R3C8 are both cats, so R1C8 must be a dog (no three in a row).
  50. Row 1 already has its 4 dogs, so R1C1 must be cats.
  51. Row 5 already has its 4 cats, so R5C8 must be dogs.
  52. Row 6 already has its 4 dogs, so R6C1 must be cats.
  53. Column 1 already has its 4 cats, so R7C1 must be dogs.
  54. Row 7 already has its 4 dogs, so R7C8 must be cats.

About this puzzle

This 8×8 grid starts with 9 filled squares and 7 = / × clues. It can be solved in 54 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.

Stuck? Open the step-by-step solution below -- each step names the squares involved, so you can use it as a hint and finish the puzzle yourself.

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