Cats & Dogs #131: 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 R1C8 and R1C7 means they are different. R1C8 is a cat, so R1C7 is a dog.
  2. The = clue between R2C5 and R2C6 means they are the same. R2C5 is a cat, so R2C6 is a cat.
  3. The × clue between R4C2 and R4C3 means they are different. R4C2 is a dog, so R4C3 is a cat.
  4. The × clue between R4C3 and R4C4 means they are different. R4C3 is a cat, so R4C4 is a dog.
  5. The × clue between R4C4 and R4C5 means they are different. R4C4 is a dog, so R4C5 is a cat.
  6. The × clue between R4C5 and R5C5 means they are different. R4C5 is a cat, so R5C5 is a dog.
  7. The = clue between R5C5 and R5C6 means they are the same. R5C5 is a dog, so R5C6 is a dog.
  8. The = clue between R5C6 and R6C6 means they are the same. R5C6 is a dog, so R6C6 is a dog.
  9. R2C5 and R2C6 are both cats, so R2C4 must be a dog (no three in a row).
  10. R2C5 and R2C6 are both cats, so R2C7 must be a dog (no three in a row).
  11. R5C5 and R5C6 are both dogs, so R5C4 must be a cat (no three in a row).
  12. R5C5 and R5C6 are both dogs, so R5C7 must be a cat (no three in a row).
  13. The × clue between R5C7 and R6C7 means they are different. R5C7 is a cat, so R6C7 is a dog.
  14. R6C6 and R6C7 are both dogs, so R6C5 must be a cat (no three in a row).
  15. R6C6 and R6C7 are both dogs, so R6C8 must be a cat (no three in a row).
  16. R3C3 and R4C3 are both cats, so R2C3 must be a dog (no three in a row).
  17. R2C3 and R2C4 are both dogs, so R2C2 must be a cat (no three in a row).
  18. The × clue between R2C2 and R2C1 means they are different. R2C2 is a cat, so R2C1 is a dog.
  19. R3C3 and R4C3 are both cats, so R5C3 must be a dog (no three in a row).
  20. R2C4 and R4C4 are both dogs with one square between them, so R3C4 must be a cat.
  21. R3C3 and R3C4 are both cats, so R3C2 must be a dog (no three in a row).
  22. R3C3 and R3C4 are both cats, so R3C5 must be a dog (no three in a row).
  23. R3C2 and R4C2 are both dogs, so R5C2 must be a cat (no three in a row).
  24. R5C6 and R6C6 are both dogs, so R4C6 must be a cat (no three in a row).
  25. R4C5 and R4C6 are both cats, so R4C7 must be a dog (no three in a row).
  26. R2C6 and R4C6 are both cats with one square between them, so R3C6 must be a dog.
  27. R3C5 and R3C6 are both dogs, so R3C7 must be a cat (no three in a row).
  28. R5C6 and R6C6 are both dogs, so R7C6 must be a cat (no three in a row).
  29. R4C8 and R6C8 are both cats with one square between them, so R5C8 must be a dog.
  30. Row 2 already has its 4 dogs, so R2C8 must be cats.
  31. R1C8 and R2C8 are both cats, so R3C8 must be a dog (no three in a row).
  32. Row 3 already has its 4 dogs, so R3C1 must be cats.
  33. Row 4 already has its 4 cats, so R4C1 must be dogs.
  34. Row 5 already has its 4 dogs, so R5C1 must be cats.
  35. R5C1 and R7C1 are both cats with one square between them, so R6C1 must be a dog.
  36. Column 5 already has its 4 cats, so R7C5 must be dogs.
  37. The × clue between R7C5 and R7C4 means they are different. R7C5 is a dog, so R7C4 is a cat.
  38. R5C4 and R7C4 are both cats with one square between them, so R6C4 must be a dog.
  39. Row 6 already has its 4 dogs, so R6C2 must be cats.
  40. R5C2 and R6C2 are both cats, so R7C2 must be a dog (no three in a row).
  41. Row 6 already has its 4 dogs, so R6C3 must be cats.
  42. Column 5 already has its 4 cats, so R8C5 must be dogs.
  43. Column 7 already has its 4 dogs, so R7C7 must be cats.
  44. R7C6 and R7C7 are both cats, so R7C8 must be a dog (no three in a row).
  45. Row 7 already has its 4 cats, so R7C3 must be dogs.
  46. The × clue between R7C3 and R8C3 means they are different. R7C3 is a dog, so R8C3 is a cat.
  47. Column 3 already has its 4 cats, so R1C3 must be dogs.
  48. The × clue between R1C3 and R1C2 means they are different. R1C3 is a dog, so R1C2 is a cat.
  49. The × clue between R1C3 and R1C4 means they are different. R1C3 is a dog, so R1C4 is a cat.
  50. R1C4 and R1C5 are both cats, so R1C6 must be a dog (no three in a row).
  51. Row 1 already has its 4 cats, so R1C1 must be dogs.
  52. Column 1 already has its 4 dogs, so R8C1 must be cats.
  53. R8C1 and R8C3 are both cats with one square between them, so R8C2 must be a dog.
  54. Column 4 already has its 4 cats, so R8C4 must be dogs.
  55. R8C4 and R8C5 are both dogs, so R8C6 must be a cat (no three in a row).
  56. Column 7 already has its 4 dogs, so R8C7 must be cats.
  57. R8C6 and R8C7 are both cats, so R8C8 must be a dog (no three in a row).

About this puzzle

This 8×8 grid starts with 7 filled squares and 14 = / × clues. It can be solved in 57 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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