Cats & Dogs #134: 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 R1C6 and R1C5 means they are the same. R1C6 is a dog, so R1C5 is a dog.
  2. The × clue between R8C7 and R7C7 means they are different. R8C7 is a cat, so R7C7 is a dog.
  3. R1C5 and R1C6 are both dogs, so R1C4 must be a cat (no three in a row).
  4. R1C5 and R1C6 are both dogs, so R1C7 must be a cat (no three in a row).
  5. R1C5 and R3C5 are both dogs with one square between them, so R2C5 must be a cat.
  6. The = clue between R2C5 and R2C4 means they are the same. R2C5 is a cat, so R2C4 is a cat.
  7. R2C4 and R2C5 are both cats, so R2C3 must be a dog (no three in a row).
  8. R2C4 and R2C5 are both cats, so R2C6 must be a dog (no three in a row).
  9. R1C4 and R2C4 are both cats, so R3C4 must be a dog (no three in a row).
  10. R3C4 and R3C5 are both dogs, so R3C3 must be a cat (no three in a row).
  11. The = clue between R3C3 and R3C2 means they are the same. R3C3 is a cat, so R3C2 is a cat.
  12. R3C2 and R3C3 are both cats, so R3C1 must be a dog (no three in a row).
  13. R3C4 and R3C5 are both dogs, so R3C6 must be a cat (no three in a row).
  14. R3C3 and R5C3 are both cats with one square between them, so R4C3 must be a dog.
  15. The × clue between R4C3 and R4C4 means they are different. R4C3 is a dog, so R4C4 is a cat.
  16. R6C7 and R7C7 are both dogs, so R5C7 must be a cat (no three in a row).
  17. R5C7 and R5C8 are both cats, so R5C6 must be a dog (no three in a row).
  18. Column 4 already has its 4 cats, so R5C4 must be dogs.
  19. R5C4 and R5C6 are both dogs with one square between them, so R5C5 must be a cat.
  20. Row 5 already has its 4 cats, so R5C1 must be dogs.
  21. R3C1 and R5C1 are both dogs with one square between them, so R4C1 must be a cat.
  22. Row 5 already has its 4 cats, so R5C2 must be dogs.
  23. The × clue between R5C2 and R4C2 means they are different. R5C2 is a dog, so R4C2 is a cat.
  24. R3C2 and R4C2 are both cats, so R2C2 must be a dog (no three in a row).
  25. The = clue between R2C2 and R1C2 means they are the same. R2C2 is a dog, so R1C2 is a dog.
  26. R2C2 and R2C3 are both dogs, so R2C1 must be a cat (no three in a row).
  27. Column 4 already has its 4 cats, so R6C4 must be dogs.
  28. R6C3 and R6C4 are both dogs, so R6C2 must be a cat (no three in a row).
  29. The × clue between R6C2 and R6C1 means they are different. R6C2 is a cat, so R6C1 is a dog.
  30. R6C3 and R6C4 are both dogs, so R6C5 must be a cat (no three in a row).
  31. R5C1 and R6C1 are both dogs, so R7C1 must be a cat (no three in a row).
  32. The × clue between R7C1 and R7C2 means they are different. R7C1 is a cat, so R7C2 is a dog.
  33. R5C5 and R6C5 are both cats, so R4C5 must be a dog (no three in a row).
  34. R5C5 and R6C5 are both cats, so R7C5 must be a dog (no three in a row).
  35. R7C5 and R7C7 are both dogs with one square between them, so R7C6 must be a cat.
  36. Row 6 already has its 4 dogs, so R6C6 must be cats.
  37. R6C6 and R7C6 are both cats, so R8C6 must be a dog (no three in a row).
  38. Row 6 already has its 4 dogs, so R6C8 must be cats.
  39. R5C8 and R6C8 are both cats, so R4C8 must be a dog (no three in a row).
  40. The × clue between R4C8 and R3C8 means they are different. R4C8 is a dog, so R3C8 is a cat.
  41. R3C6 and R3C8 are both cats with one square between them, so R3C7 must be a dog.
  42. R5C8 and R6C8 are both cats, so R7C8 must be a dog (no three in a row).
  43. Row 7 already has its 4 dogs, so R7C3 must be cats.
  44. Column 2 already has its 4 dogs, so R8C2 must be cats.
  45. Column 4 already has its 4 cats, so R8C4 must be dogs.
  46. The × clue between R8C4 and R8C3 means they are different. R8C4 is a dog, so R8C3 is a cat.
  47. R8C2 and R8C3 are both cats, so R8C1 must be a dog (no three in a row).
  48. R8C4 and R8C6 are both dogs with one square between them, so R8C5 must be a cat.
  49. Row 8 already has its 4 cats, so R8C8 must be dogs.
  50. Column 1 already has its 4 dogs, so R1C1 must be cats.
  51. Column 3 already has its 4 cats, so R1C3 must be dogs.
  52. Row 1 already has its 4 dogs, so R1C8 must be cats.
  53. R1C8 and R3C8 are both cats with one square between them, so R2C8 must be a dog.
  54. R2C6 and R2C8 are both dogs with one square between them, so R2C7 must be a cat.
  55. Column 6 already has its 4 dogs, so R4C6 must be cats.
  56. Row 4 already has its 4 cats, so R4C7 must be dogs.

About this puzzle

This 8×8 grid starts with 8 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.

Stuck? Open the step-by-step solution below -- each step names the squares involved, so you can use it as a hint and finish the puzzle yourself.

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