Cats & Dogs #107: 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 R8C2 and R7C2 means they are the same. R8C2 is a cat, so R7C2 is a cat.
  2. The × clue between R7C2 and R7C3 means they are different. R7C2 is a cat, so R7C3 is a dog.
  3. R7C2 and R8C2 are both cats, so R6C2 must be a dog (no three in a row).
  4. R3C6 and R4C6 are both cats, so R2C6 must be a dog (no three in a row).
  5. R3C6 and R4C6 are both cats, so R5C6 must be a dog (no three in a row).
  6. The × clue between R5C6 and R5C5 means they are different. R5C6 is a dog, so R5C5 is a cat.
  7. The = clue between R5C5 and R4C5 means they are the same. R5C5 is a cat, so R4C5 is a cat.
  8. R4C5 and R4C6 are both cats, so R4C4 must be a dog (no three in a row).
  9. The = clue between R4C4 and R5C4 means they are the same. R4C4 is a dog, so R5C4 is a dog.
  10. R4C5 and R4C6 are both cats, so R4C7 must be a dog (no three in a row).
  11. R4C4 and R5C4 are both dogs, so R3C4 must be a cat (no three in a row).
  12. The × clue between R3C4 and R3C3 means they are different. R3C4 is a cat, so R3C3 is a dog.
  13. The = clue between R3C3 and R2C3 means they are the same. R3C3 is a dog, so R2C3 is a dog.
  14. R2C1 and R2C3 are both dogs with one square between them, so R2C2 must be a cat.
  15. R3C4 and R3C6 are both cats with one square between them, so R3C5 must be a dog.
  16. R2C3 and R3C3 are both dogs, so R1C3 must be a cat (no three in a row).
  17. R2C3 and R3C3 are both dogs, so R4C3 must be a cat (no three in a row).
  18. R4C4 and R5C4 are both dogs, so R6C4 must be a cat (no three in a row).
  19. The × clue between R6C4 and R6C3 means they are different. R6C4 is a cat, so R6C3 is a dog.
  20. R6C2 and R6C3 are both dogs, so R6C1 must be a cat (no three in a row).
  21. R6C3 and R7C3 are both dogs, so R5C3 must be a cat (no three in a row).
  22. R6C3 and R7C3 are both dogs, so R8C3 must be a cat (no three in a row).
  23. R8C2 and R8C3 are both cats, so R8C1 must be a dog (no three in a row).
  24. The × clue between R8C1 and R7C1 means they are different. R8C1 is a dog, so R7C1 is a cat.
  25. R8C2 and R8C3 are both cats, so R8C4 must be a dog (no three in a row).
  26. R6C1 and R7C1 are both cats, so R5C1 must be a dog (no three in a row).
  27. The × clue between R5C1 and R5C2 means they are different. R5C1 is a dog, so R5C2 is a cat.
  28. R4C5 and R5C5 are both cats, so R6C5 must be a dog (no three in a row).
  29. Row 5 already has its 4 cats, so R5C7 must be dogs.
  30. R4C7 and R5C7 are both dogs, so R3C7 must be a cat (no three in a row).
  31. R3C6 and R3C7 are both cats, so R3C8 must be a dog (no three in a row).
  32. R4C7 and R5C7 are both dogs, so R6C7 must be a cat (no three in a row).
  33. The × clue between R6C7 and R6C6 means they are different. R6C7 is a cat, so R6C6 is a dog.
  34. R5C6 and R6C6 are both dogs, so R7C6 must be a cat (no three in a row).
  35. The × clue between R7C6 and R8C6 means they are different. R7C6 is a cat, so R8C6 is a dog.
  36. R8C4 and R8C6 are both dogs with one square between them, so R8C5 must be a cat.
  37. Row 6 already has its 4 dogs, so R6C8 must be cats.
  38. R5C8 and R6C8 are both cats, so R4C8 must be a dog (no three in a row).
  39. R3C8 and R4C8 are both dogs, so R2C8 must be a cat (no three in a row).
  40. R5C8 and R6C8 are both cats, so R7C8 must be a dog (no three in a row).
  41. Column 2 already has its 4 cats, so R1C2 and R3C2 must be dogs.
  42. R3C2 and R3C3 are both dogs, so R3C1 must be a cat (no three in a row).
  43. Column 2 already has its 4 cats, so R4C2 must be dogs.
  44. Row 4 already has its 4 dogs, so R4C1 must be cats.
  45. Column 1 already has its 4 cats, so R1C1 must be dogs.
  46. Column 6 already has its 4 dogs, so R1C6 must be cats.
  47. The = clue between R1C6 and R1C5 means they are the same. R1C6 is a cat, so R1C5 is a cat.
  48. R1C3 and R1C5 are both cats with one square between them, so R1C4 must be a dog.
  49. R1C5 and R1C6 are both cats, so R1C7 must be a dog (no three in a row).
  50. Row 1 already has its 4 dogs, so R1C8 must be cats.
  51. Column 4 already has its 4 dogs, so R2C4 and R7C4 must be cats.
  52. R7C4 and R7C6 are both cats with one square between them, so R7C5 must be a dog.
  53. Row 7 already has its 4 cats, so R7C7 must be dogs.
  54. Column 5 already has its 4 cats, so R2C5 must be dogs.
  55. R2C5 and R2C6 are both dogs, so R2C7 must be a cat (no three in a row).
  56. Column 7 already has its 4 dogs, so R8C7 must be cats.
  57. Row 8 already has its 4 cats, so R8C8 must be dogs.

About this puzzle

This 8×8 grid starts with 5 filled squares and 13 = / × clues. It can be solved in 57 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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