Cats & Dogs #130: 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 R4C2 and R3C2 means they are different. R4C2 is a dog, so R3C2 is a cat.
  2. The × clue between R3C7 and R3C6 means they are different. R3C7 is a dog, so R3C6 is a cat.
  3. The = clue between R3C6 and R4C6 means they are the same. R3C6 is a cat, so R4C6 is a cat.
  4. R3C2 and R3C4 are both cats with one square between them, so R3C3 must be a dog.
  5. R3C4 and R3C6 are both cats with one square between them, so R3C5 must be a dog.
  6. R1C2 and R3C2 are both cats with one square between them, so R2C2 must be a dog.
  7. R3C5 and R4C5 are both dogs, so R2C5 must be a cat (no three in a row).
  8. R3C5 and R4C5 are both dogs, so R5C5 must be a cat (no three in a row).
  9. R3C6 and R4C6 are both cats, so R2C6 must be a dog (no three in a row).
  10. R3C6 and R4C6 are both cats, so R5C6 must be a dog (no three in a row).
  11. The × clue between R5C6 and R5C7 means they are different. R5C6 is a dog, so R5C7 is a cat.
  12. R5C7 and R6C7 are both cats, so R4C7 must be a dog (no three in a row).
  13. R3C7 and R4C7 are both dogs, so R2C7 must be a cat (no three in a row).
  14. R5C7 and R6C7 are both cats, so R7C7 must be a dog (no three in a row).
  15. Row 4 already has its 4 dogs, so R4C1, R4C3 and R4C4 must be cats.
  16. R3C4 and R4C4 are both cats, so R2C4 must be a dog (no three in a row).
  17. R2C2 and R2C4 are both dogs with one square between them, so R2C3 must be a cat.
  18. The = clue between R2C3 and R1C3 means they are the same. R2C3 is a cat, so R1C3 is a cat.
  19. R1C2 and R1C3 are both cats, so R1C1 must be a dog (no three in a row).
  20. The = clue between R1C1 and R2C1 means they are the same. R1C1 is a dog, so R2C1 is a dog.
  21. R1C2 and R1C3 are both cats, so R1C4 must be a dog (no three in a row).
  22. R1C1 and R2C1 are both dogs, so R3C1 must be a cat (no three in a row).
  23. R3C1 and R4C1 are both cats, so R5C1 must be a dog (no three in a row).
  24. R5C1 and R6C1 are both dogs, so R7C1 must be a cat (no three in a row).
  25. R3C4 and R4C4 are both cats, so R5C4 must be a dog (no three in a row).
  26. The = clue between R5C4 and R6C4 means they are the same. R5C4 is a dog, so R6C4 is a dog.
  27. R5C4 and R6C4 are both dogs, so R7C4 must be a cat (no three in a row).
  28. The = clue between R7C4 and R7C3 means they are the same. R7C4 is a cat, so R7C3 is a cat.
  29. R7C1 and R7C3 are both cats with one square between them, so R7C2 must be a dog.
  30. R7C3 and R7C4 are both cats, so R7C5 must be a dog (no three in a row).
  31. R7C5 and R7C7 are both dogs with one square between them, so R7C6 must be a cat.
  32. Row 2 already has its 4 dogs, so R2C8 must be cats.
  33. Row 3 already has its 4 cats, so R3C8 must be dogs.
  34. R3C8 and R4C8 are both dogs, so R5C8 must be a cat (no three in a row).
  35. Row 7 already has its 4 cats, so R7C8 must be dogs.
  36. The = clue between R7C8 and R8C8 means they are the same. R7C8 is a dog, so R8C8 is a dog.
  37. R7C8 and R8C8 are both dogs, so R6C8 must be a cat (no three in a row).
  38. R6C7 and R6C8 are both cats, so R6C6 must be a dog (no three in a row).
  39. R6C4 and R6C6 are both dogs with one square between them, so R6C5 must be a cat.
  40. Column 1 already has its 4 dogs, so R8C1 must be cats.
  41. Column 3 already has its 4 cats, so R5C3 must be dogs.
  42. R5C1 and R5C3 are both dogs with one square between them, so R5C2 must be a cat.
  43. Column 3 already has its 4 cats, so R6C3 must be dogs.
  44. R6C1 and R6C3 are both dogs with one square between them, so R6C2 must be a cat.
  45. Column 2 already has its 4 cats, so R8C2 must be dogs.
  46. Column 3 already has its 4 cats, so R8C3 must be dogs.
  47. R8C2 and R8C3 are both dogs, so R8C4 must be a cat (no three in a row).
  48. The × clue between R8C4 and R8C5 means they are different. R8C4 is a cat, so R8C5 is a dog.
  49. Row 8 already has its 4 dogs, so R8C6 and R8C7 must be cats.
  50. Column 5 already has its 4 dogs, so R1C5 must be cats.
  51. Column 6 already has its 4 cats, so R1C6 must be dogs.
  52. Column 7 already has its 4 cats, so R1C7 must be dogs.
  53. R1C6 and R1C7 are both dogs, so R1C8 must be a cat (no three in a row).

About this puzzle

This 8×8 grid starts with 8 filled squares and 10 = / × 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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