Cats & Dogs #149: 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

Can you finish the grid? Cats and dogs must balance in every line, no animal may appear three times in a row, and = / × signs tell you whether two neighbors match.

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

About this puzzle

This 8×8 grid starts with 7 filled squares and 11 = / × clues. It can be solved in 56 steps using pairs, gaps, counts and clues.

Start with the clues and the squares already filled in. An = or × next to a known animal gives you its neighbor immediately.

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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