Cats & Dogs #135: 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 R7C6 and R7C5 means they are the same. R7C6 is a dog, so R7C5 is a dog.
  2. R3C1 and R3C2 are both cats, so R3C3 must be a dog (no three in a row).
  3. The = clue between R3C3 and R3C4 means they are the same. R3C3 is a dog, so R3C4 is a dog.
  4. The × clue between R3C4 and R2C4 means they are different. R3C4 is a dog, so R2C4 is a cat.
  5. R2C3 and R2C4 are both cats, so R2C2 must be a dog (no three in a row).
  6. R2C3 and R2C4 are both cats, so R2C5 must be a dog (no three in a row).
  7. The = clue between R2C5 and R1C5 means they are the same. R2C5 is a dog, so R1C5 is a dog.
  8. The = clue between R1C5 and R1C6 means they are the same. R1C5 is a dog, so R1C6 is a dog.
  9. The = clue between R2C5 and R2C6 means they are the same. R2C5 is a dog, so R2C6 is a dog.
  10. R1C5 and R1C6 are both dogs, so R1C4 must be a cat (no three in a row).
  11. The = clue between R1C4 and R1C3 means they are the same. R1C4 is a cat, so R1C3 is a cat.
  12. R1C3 and R1C4 are both cats, so R1C2 must be a dog (no three in a row).
  13. R1C5 and R1C6 are both dogs, so R1C7 must be a cat (no three in a row).
  14. R2C5 and R2C6 are both dogs, so R2C7 must be a cat (no three in a row).
  15. R3C3 and R3C4 are both dogs, so R3C5 must be a cat (no three in a row).
  16. R7C5 and R7C6 are both dogs, so R7C4 must be a cat (no three in a row).
  17. R7C5 and R7C6 are both dogs, so R7C7 must be a cat (no three in a row).
  18. R3C3 and R5C3 are both dogs with one square between them, so R4C3 must be a cat.
  19. R1C6 and R2C6 are both dogs, so R3C6 must be a cat (no three in a row).
  20. R3C5 and R3C6 are both cats, so R3C7 must be a dog (no three in a row).
  21. R3C7 and R5C7 are both dogs with one square between them, so R4C7 must be a cat.
  22. R6C8 and R8C8 are both dogs with one square between them, so R7C8 must be a cat.
  23. Row 2 already has its 4 dogs, so R2C8 must be cats.
  24. The = clue between R2C8 and R1C8 means they are the same. R2C8 is a cat, so R1C8 is a cat.
  25. R1C8 and R2C8 are both cats, so R3C8 must be a dog (no three in a row).
  26. The × clue between R3C8 and R4C8 means they are different. R3C8 is a dog, so R4C8 is a cat.
  27. R4C7 and R4C8 are both cats, so R4C6 must be a dog (no three in a row).
  28. Row 1 already has its 4 cats, so R1C1 must be dogs.
  29. Column 6 already has its 4 dogs, so R5C6 must be cats.
  30. The × clue between R5C6 and R5C5 means they are different. R5C6 is a cat, so R5C5 is a dog.
  31. R5C3 and R5C5 are both dogs with one square between them, so R5C4 must be a cat.
  32. R5C4 and R7C4 are both cats with one square between them, so R6C4 must be a dog.
  33. R5C5 and R7C5 are both dogs with one square between them, so R6C5 must be a cat.
  34. Column 4 already has its 4 cats, so R4C4 must be dogs.
  35. R4C4 and R4C6 are both dogs with one square between them, so R4C5 must be a cat.
  36. Row 4 already has its 4 cats, so R4C1 and R4C2 must be dogs.
  37. Column 4 already has its 4 cats, so R8C4 must be dogs.
  38. Column 5 already has its 4 dogs, so R8C5 must be cats.
  39. Column 6 already has its 4 dogs, so R6C6 must be cats.
  40. R6C5 and R6C6 are both cats, so R6C7 must be a dog (no three in a row).
  41. Column 6 already has its 4 dogs, so R8C6 must be cats.
  42. R8C5 and R8C6 are both cats, so R8C7 must be a dog (no three in a row).
  43. Column 8 already has its 4 cats, so R5C8 must be dogs.
  44. Row 5 already has its 4 dogs, so R5C1 must be cats.
  45. The × clue between R5C1 and R6C1 means they are different. R5C1 is a cat, so R6C1 is a dog.
  46. Row 5 already has its 4 dogs, so R5C2 must be cats.
  47. Row 6 already has its 4 dogs, so R6C2 must be cats.
  48. R5C2 and R6C2 are both cats, so R7C2 must be a dog (no three in a row).
  49. Row 6 already has its 4 dogs, so R6C3 must be cats.
  50. Column 1 already has its 4 dogs, so R7C1 must be cats.
  51. Row 7 already has its 4 cats, so R7C3 must be dogs.
  52. Column 1 already has its 4 dogs, so R8C1 must be cats.
  53. Column 2 already has its 4 dogs, so R8C2 must be cats.
  54. R8C1 and R8C2 are both cats, so R8C3 must be a dog (no three in a row).

About this puzzle

This 8×8 grid starts with 9 filled squares and 11 = / × clues. It can be solved in 54 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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