Cats & Dogs #109: 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 R2C1 and R2C2 means they are the same. R2C1 is a cat, so R2C2 is a cat.
  2. The × clue between R4C6 and R3C6 means they are different. R4C6 is a dog, so R3C6 is a cat.
  3. The = clue between R4C6 and R4C7 means they are the same. R4C6 is a dog, so R4C7 is a dog.
  4. The = clue between R7C2 and R7C1 means they are the same. R7C2 is a dog, so R7C1 is a dog.
  5. The × clue between R7C1 and R8C1 means they are different. R7C1 is a dog, so R8C1 is a cat.
  6. The = clue between R7C6 and R8C6 means they are the same. R7C6 is a cat, so R8C6 is a cat.
  7. R2C1 and R2C2 are both cats, so R2C3 must be a dog (no three in a row).
  8. R4C6 and R4C7 are both dogs, so R4C5 must be a cat (no three in a row).
  9. R4C6 and R4C7 are both dogs, so R4C8 must be a cat (no three in a row).
  10. R7C1 and R7C2 are both dogs, so R7C3 must be a cat (no three in a row).
  11. R7C3 and R7C5 are both cats with one square between them, so R7C4 must be a dog.
  12. The = clue between R7C4 and R8C4 means they are the same. R7C4 is a dog, so R8C4 is a dog.
  13. R7C5 and R7C6 are both cats, so R7C7 must be a dog (no three in a row).
  14. R7C4 and R8C4 are both dogs, so R6C4 must be a cat (no three in a row).
  15. R7C6 and R8C6 are both cats, so R6C6 must be a dog (no three in a row).
  16. R4C6 and R6C6 are both dogs with one square between them, so R5C6 must be a cat.
  17. R4C7 and R5C7 are both dogs, so R3C7 must be a cat (no three in a row).
  18. R3C6 and R3C7 are both cats, so R3C5 must be a dog (no three in a row).
  19. R3C6 and R3C7 are both cats, so R3C8 must be a dog (no three in a row).
  20. R4C7 and R5C7 are both dogs, so R6C7 must be a cat (no three in a row).
  21. Row 7 already has its 4 dogs, so R7C8 must be cats.
  22. Column 6 already has its 4 cats, so R1C6 must be dogs.
  23. The = clue between R1C6 and R1C5 means they are the same. R1C6 is a dog, so R1C5 is a dog.
  24. R1C5 and R1C6 are both dogs, so R1C4 must be a cat (no three in a row).
  25. R1C5 and R1C6 are both dogs, so R1C7 must be a cat (no three in a row).
  26. R1C5 and R3C5 are both dogs with one square between them, so R2C5 must be a cat.
  27. R1C7 and R3C7 are both cats with one square between them, so R2C7 must be a dog.
  28. Column 6 already has its 4 cats, so R2C6 must be dogs.
  29. R2C6 and R2C7 are both dogs, so R2C8 must be a cat (no three in a row).
  30. Row 2 already has its 4 cats, so R2C4 must be dogs.
  31. Column 7 already has its 4 dogs, so R8C7 must be cats.
  32. R8C6 and R8C7 are both cats, so R8C5 must be a dog (no three in a row).
  33. R8C4 and R8C5 are both dogs, so R8C3 must be a cat (no three in a row).
  34. R8C1 and R8C3 are both cats with one square between them, so R8C2 must be a dog.
  35. R8C6 and R8C7 are both cats, so R8C8 must be a dog (no three in a row).
  36. R7C2 and R8C2 are both dogs, so R6C2 must be a cat (no three in a row).
  37. The = clue between R6C2 and R5C2 means they are the same. R6C2 is a cat, so R5C2 is a cat.
  38. The × clue between R5C2 and R5C1 means they are different. R5C2 is a cat, so R5C1 is a dog.
  39. R6C2 and R6C4 are both cats with one square between them, so R6C3 must be a dog.
  40. R5C1 and R7C1 are both dogs with one square between them, so R6C1 must be a cat.
  41. R5C2 and R6C2 are both cats, so R4C2 must be a dog (no three in a row).
  42. Row 6 already has its 4 cats, so R6C5 and R6C8 must be dogs.
  43. Column 5 already has its 4 dogs, so R5C5 must be cats.
  44. R5C5 and R5C6 are both cats, so R5C4 must be a dog (no three in a row).
  45. Column 4 already has its 4 dogs, so R3C4 and R4C4 must be cats.
  46. R4C4 and R4C5 are both cats, so R4C3 must be a dog (no three in a row).
  47. R4C2 and R4C3 are both dogs, so R4C1 must be a cat (no three in a row).
  48. R2C1 and R4C1 are both cats with one square between them, so R3C1 must be a dog.
  49. R2C3 and R4C3 are both dogs with one square between them, so R3C3 must be a cat.
  50. R3C3 and R3C4 are both cats, so R3C2 must be a dog (no three in a row).
  51. R4C3 and R6C3 are both dogs with one square between them, so R5C3 must be a cat.
  52. Row 5 already has its 4 cats, so R5C8 must be dogs.
  53. Column 1 already has its 4 cats, so R1C1 must be dogs.
  54. Column 2 already has its 4 dogs, so R1C2 must be cats.
  55. R1C2 and R1C4 are both cats with one square between them, so R1C3 must be a dog.
  56. Row 1 already has its 4 dogs, so R1C8 must be cats.

About this puzzle

This 8×8 grid starts with 6 filled squares and 10 = / × clues. It can be solved in 56 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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