Cats & Dogs #181: 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 R2C4 and R3C4 means they are the same. R2C4 is a dog, so R3C4 is a dog.
  2. The = clue between R2C8 and R2C7 means they are the same. R2C8 is a cat, so R2C7 is a cat.
  3. The = clue between R3C4 and R3C3 means they are the same. R3C4 is a dog, so R3C3 is a dog.
  4. The × clue between R8C8 and R7C8 means they are different. R8C8 is a dog, so R7C8 is a cat.
  5. R2C7 and R2C8 are both cats, so R2C6 must be a dog (no three in a row).
  6. R2C4 and R2C6 are both dogs with one square between them, so R2C5 must be a cat.
  7. R3C3 and R3C4 are both dogs, so R3C2 must be a cat (no three in a row).
  8. R3C3 and R3C4 are both dogs, so R3C5 must be a cat (no three in a row).
  9. R3C2 and R4C2 are both cats, so R2C2 must be a dog (no three in a row).
  10. R2C2 and R2C4 are both dogs with one square between them, so R2C3 must be a cat.
  11. R3C2 and R4C2 are both cats, so R5C2 must be a dog (no three in a row).
  12. R2C4 and R3C4 are both dogs, so R1C4 must be a cat (no three in a row).
  13. R2C4 and R3C4 are both dogs, so R4C4 must be a cat (no three in a row).
  14. R4C2 and R4C4 are both cats with one square between them, so R4C3 must be a dog.
  15. R3C3 and R4C3 are both dogs, so R5C3 must be a cat (no three in a row).
  16. R2C5 and R3C5 are both cats, so R1C5 must be a dog (no three in a row).
  17. R2C5 and R3C5 are both cats, so R4C5 must be a dog (no three in a row).
  18. The × clue between R4C5 and R5C5 means they are different. R4C5 is a dog, so R5C5 is a cat.
  19. The = clue between R5C5 and R6C5 means they are the same. R5C5 is a cat, so R6C5 is a cat.
  20. R5C3 and R5C5 are both cats with one square between them, so R5C4 must be a dog.
  21. R6C5 and R6C6 are both cats, so R6C4 must be a dog (no three in a row).
  22. The = clue between R6C4 and R6C3 means they are the same. R6C4 is a dog, so R6C3 is a dog.
  23. The = clue between R6C3 and R7C3 means they are the same. R6C3 is a dog, so R7C3 is a dog.
  24. R6C3 and R6C4 are both dogs, so R6C2 must be a cat (no three in a row).
  25. R6C5 and R6C6 are both cats, so R6C7 must be a dog (no three in a row).
  26. The × clue between R6C7 and R7C7 means they are different. R6C7 is a dog, so R7C7 is a cat.
  27. R7C7 and R7C8 are both cats, so R7C6 must be a dog (no three in a row).
  28. The × clue between R7C6 and R8C6 means they are different. R7C6 is a dog, so R8C6 is a cat.
  29. R6C3 and R7C3 are both dogs, so R8C3 must be a cat (no three in a row).
  30. R5C4 and R6C4 are both dogs, so R7C4 must be a cat (no three in a row).
  31. R5C5 and R6C5 are both cats, so R7C5 must be a dog (no three in a row).
  32. R5C8 and R7C8 are both cats with one square between them, so R6C8 must be a dog.
  33. Row 2 already has its 4 cats, so R2C1 must be dogs.
  34. The = clue between R2C1 and R1C1 means they are the same. R2C1 is a dog, so R1C1 is a dog.
  35. R1C1 and R2C1 are both dogs, so R3C1 must be a cat (no three in a row).
  36. Row 6 already has its 4 dogs, so R6C1 must be cats.
  37. Column 3 already has its 4 dogs, so R1C3 must be cats.
  38. R1C3 and R1C4 are both cats, so R1C2 must be a dog (no three in a row).
  39. Column 4 already has its 4 dogs, so R8C4 must be cats.
  40. R8C3 and R8C4 are both cats, so R8C2 must be a dog (no three in a row).
  41. R8C3 and R8C4 are both cats, so R8C5 must be a dog (no three in a row).
  42. Column 2 already has its 4 dogs, so R7C2 must be cats.
  43. Row 7 already has its 4 cats, so R7C1 must be dogs.
  44. Column 1 already has its 4 dogs, so R5C1 must be cats.
  45. Row 5 already has its 4 cats, so R5C6 and R5C7 must be dogs.
  46. R5C7 and R6C7 are both dogs, so R4C7 must be a cat (no three in a row).
  47. R2C7 and R4C7 are both cats with one square between them, so R3C7 must be a dog.
  48. Column 1 already has its 4 dogs, so R8C1 must be cats.
  49. Row 8 already has its 4 cats, so R8C7 must be dogs.
  50. Column 7 already has its 4 dogs, so R1C7 must be cats.
  51. The × clue between R1C7 and R1C6 means they are different. R1C7 is a cat, so R1C6 is a dog.
  52. R1C6 and R2C6 are both dogs, so R3C6 must be a cat (no three in a row).
  53. Row 1 already has its 4 dogs, so R1C8 must be cats.
  54. R1C8 and R2C8 are both cats, so R3C8 must be a dog (no three in a row).
  55. Column 6 already has its 4 dogs, so R4C6 must be cats.
  56. R4C6 and R4C7 are both cats, so R4C8 must be a dog (no three in a row).

About this puzzle

This 8×8 grid starts with 7 filled squares and 12 = / × 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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