Cats & Dogs #164: 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 R1C5 and R1C6 means they are different. R1C5 is a dog, so R1C6 is a cat.
  2. The × clue between R5C1 and R4C1 means they are different. R5C1 is a dog, so R4C1 is a cat.
  3. The = clue between R4C1 and R3C1 means they are the same. R4C1 is a cat, so R3C1 is a cat.
  4. The × clue between R4C4 and R4C3 means they are different. R4C4 is a dog, so R4C3 is a cat.
  5. The × clue between R8C4 and R8C5 means they are different. R8C4 is a cat, so R8C5 is a dog.
  6. The = clue between R8C5 and R7C5 means they are the same. R8C5 is a dog, so R7C5 is a dog.
  7. R4C1 and R4C3 are both cats with one square between them, so R4C2 must be a dog.
  8. R4C6 and R4C8 are both cats with one square between them, so R4C7 must be a dog.
  9. R3C1 and R4C1 are both cats, so R2C1 must be a dog (no three in a row).
  10. R7C5 and R8C5 are both dogs, so R6C5 must be a cat (no three in a row).
  11. The = clue between R6C5 and R6C4 means they are the same. R6C5 is a cat, so R6C4 is a cat.
  12. R6C4 and R6C5 are both cats, so R6C3 must be a dog (no three in a row).
  13. R6C4 and R6C5 are both cats, so R6C6 must be a dog (no three in a row).
  14. R6C4 and R8C4 are both cats with one square between them, so R7C4 must be a dog.
  15. R7C4 and R7C5 are both dogs, so R7C3 must be a cat (no three in a row).
  16. The = clue between R7C3 and R7C2 means they are the same. R7C3 is a cat, so R7C2 is a cat.
  17. R7C2 and R7C3 are both cats, so R7C1 must be a dog (no three in a row).
  18. R7C4 and R7C5 are both dogs, so R7C6 must be a cat (no three in a row).
  19. R7C6 and R7C8 are both cats with one square between them, so R7C7 must be a dog.
  20. R5C1 and R7C1 are both dogs with one square between them, so R6C1 must be a cat.
  21. R1C6 and R2C6 are both cats, so R3C6 must be a dog (no three in a row).
  22. Row 4 already has its 4 cats, so R4C5 must be dogs.
  23. Column 1 already has its 4 dogs, so R1C1 must be cats.
  24. Column 5 already has its 4 dogs, so R2C5 must be cats.
  25. R2C5 and R2C6 are both cats, so R2C4 must be a dog (no three in a row).
  26. R2C5 and R2C6 are both cats, so R2C7 must be a dog (no three in a row).
  27. R2C4 and R4C4 are both dogs with one square between them, so R3C4 must be a cat.
  28. R2C7 and R4C7 are both dogs with one square between them, so R3C7 must be a cat.
  29. Column 5 already has its 4 dogs, so R3C5 must be cats.
  30. R3C4 and R3C5 are both cats, so R3C3 must be a dog (no three in a row).
  31. Row 3 already has its 4 cats, so R3C2 must be dogs.
  32. R3C2 and R4C2 are both dogs, so R2C2 must be a cat (no three in a row).
  33. The × clue between R2C2 and R2C3 means they are different. R2C2 is a cat, so R2C3 is a dog.
  34. R3C2 and R4C2 are both dogs, so R5C2 must be a cat (no three in a row).
  35. R5C2 and R7C2 are both cats with one square between them, so R6C2 must be a dog.
  36. R2C3 and R3C3 are both dogs, so R1C3 must be a cat (no three in a row).
  37. R1C1 and R1C3 are both cats with one square between them, so R1C2 must be a dog.
  38. Row 2 already has its 4 dogs, so R2C8 must be cats.
  39. R2C8 and R4C8 are both cats with one square between them, so R3C8 must be a dog.
  40. Column 2 already has its 4 dogs, so R8C2 must be cats.
  41. R8C2 and R8C4 are both cats with one square between them, so R8C3 must be a dog.
  42. Column 3 already has its 4 dogs, so R5C3 must be cats.
  43. R5C2 and R5C3 are both cats, so R5C4 must be a dog (no three in a row).
  44. Column 4 already has its 4 dogs, so R1C4 must be cats.
  45. Row 1 already has its 4 cats, so R1C7 and R1C8 must be dogs.
  46. Column 5 already has its 4 dogs, so R5C5 must be cats.
  47. Column 6 already has its 4 cats, so R5C6 and R8C6 must be dogs.
  48. R8C5 and R8C6 are both dogs, so R8C7 must be a cat (no three in a row).
  49. Row 8 already has its 4 dogs, so R8C8 must be cats.
  50. R7C8 and R8C8 are both cats, so R6C8 must be a dog (no three in a row).
  51. R6C6 and R6C8 are both dogs with one square between them, so R6C7 must be a cat.
  52. Column 7 already has its 4 dogs, so R5C7 must be cats.
  53. Row 5 already has its 4 cats, so R5C8 must be dogs.

About this puzzle

This 8×8 grid starts with 9 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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