Cats & Dogs #121: 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. R2C3 and R2C4 are both dogs, so R2C2 must be a cat (no three in a row).
  2. R2C3 and R2C4 are both dogs, so R2C5 must be a cat (no three in a row).
  3. R1C3 and R2C3 are both dogs, so R3C3 must be a cat (no three in a row).
  4. The = clue between R3C3 and R3C4 means they are the same. R3C3 is a cat, so R3C4 is a cat.
  5. R3C3 and R3C4 are both cats, so R3C2 must be a dog (no three in a row).
  6. The × clue between R3C2 and R4C2 means they are different. R3C2 is a dog, so R4C2 is a cat.
  7. The × clue between R4C2 and R5C2 means they are different. R4C2 is a cat, so R5C2 is a dog.
  8. The × clue between R5C2 and R5C1 means they are different. R5C2 is a dog, so R5C1 is a cat.
  9. The × clue between R5C2 and R5C3 means they are different. R5C2 is a dog, so R5C3 is a cat.
  10. R3C3 and R3C4 are both cats, so R3C5 must be a dog (no three in a row).
  11. R3C3 and R5C3 are both cats with one square between them, so R4C3 must be a dog.
  12. The = clue between R4C3 and R4C4 means they are the same. R4C3 is a dog, so R4C4 is a dog.
  13. R4C3 and R4C4 are both dogs, so R4C5 must be a cat (no three in a row).
  14. The × clue between R4C5 and R4C6 means they are different. R4C5 is a cat, so R4C6 is a dog.
  15. The × clue between R4C6 and R4C7 means they are different. R4C6 is a dog, so R4C7 is a cat.
  16. R5C3 and R6C3 are both cats, so R7C3 must be a dog (no three in a row).
  17. The = clue between R7C3 and R7C4 means they are the same. R7C3 is a dog, so R7C4 is a dog.
  18. R7C3 and R7C4 are both dogs, so R7C2 must be a cat (no three in a row).
  19. R7C3 and R7C4 are both dogs, so R7C5 must be a cat (no three in a row).
  20. The = clue between R7C5 and R7C6 means they are the same. R7C5 is a cat, so R7C6 is a cat.
  21. R7C5 and R7C6 are both cats, so R7C7 must be a dog (no three in a row).
  22. R3C7 and R4C7 are both cats, so R2C7 must be a dog (no three in a row).
  23. R2C7 and R2C8 are both dogs, so R2C6 must be a cat (no three in a row).
  24. R3C7 and R4C7 are both cats, so R5C7 must be a dog (no three in a row).
  25. R5C7 and R7C7 are both dogs with one square between them, so R6C7 must be a cat.
  26. Row 2 already has its 4 dogs, so R2C1 must be cats.
  27. Column 3 already has its 4 dogs, so R8C3 must be cats.
  28. The = clue between R8C3 and R8C4 means they are the same. R8C3 is a cat, so R8C4 is a cat.
  29. R8C3 and R8C4 are both cats, so R8C2 must be a dog (no three in a row).
  30. R8C3 and R8C4 are both cats, so R8C5 must be a dog (no three in a row).
  31. The × clue between R8C5 and R8C6 means they are different. R8C5 is a dog, so R8C6 is a cat.
  32. R8C6 and R8C7 are both cats, so R8C8 must be a dog (no three in a row).
  33. R7C6 and R8C6 are both cats, so R6C6 must be a dog (no three in a row).
  34. R4C6 and R6C6 are both dogs with one square between them, so R5C6 must be a cat.
  35. Row 8 already has its 4 cats, so R8C1 must be dogs.
  36. The × clue between R8C1 and R7C1 means they are different. R8C1 is a dog, so R7C1 is a cat.
  37. R5C1 and R7C1 are both cats with one square between them, so R6C1 must be a dog.
  38. Row 7 already has its 4 cats, so R7C8 must be dogs.
  39. R7C8 and R8C8 are both dogs, so R6C8 must be a cat (no three in a row).
  40. Column 6 already has its 4 cats, so R1C6 and R3C6 must be dogs.
  41. Column 7 already has its 4 cats, so R1C7 must be dogs.
  42. R1C6 and R1C7 are both dogs, so R1C5 must be a cat (no three in a row).
  43. R1C6 and R1C7 are both dogs, so R1C8 must be a cat (no three in a row).
  44. Column 5 already has its 4 cats, so R5C5 and R6C5 must be dogs.
  45. R6C5 and R6C6 are both dogs, so R6C4 must be a cat (no three in a row).
  46. The = clue between R6C4 and R5C4 means they are the same. R6C4 is a cat, so R5C4 is a cat.
  47. R6C3 and R6C4 are both cats, so R6C2 must be a dog (no three in a row).
  48. Row 5 already has its 4 cats, so R5C8 must be dogs.
  49. Column 2 already has its 4 dogs, so R1C2 must be cats.
  50. Column 4 already has its 4 cats, so R1C4 must be dogs.
  51. Row 1 already has its 4 dogs, so R1C1 must be cats.
  52. R1C1 and R2C1 are both cats, so R3C1 must be a dog (no three in a row).
  53. Row 3 already has its 4 dogs, so R3C8 must be cats.
  54. Column 1 already has its 4 cats, so R4C1 must be dogs.
  55. Row 4 already has its 4 dogs, so R4C8 must be cats.

About this puzzle

This 8×8 grid starts with 7 filled squares and 14 = / × 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.

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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