Cats & Dogs #102: 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 R3C2 and R2C2 means they are the same. R3C2 is a cat, so R2C2 is a cat.
  2. The × clue between R6C6 and R6C7 means they are different. R6C6 is a dog, so R6C7 is a cat.
  3. The = clue between R7C4 and R8C4 means they are the same. R7C4 is a cat, so R8C4 is a cat.
  4. The × clue between R8C4 and R8C3 means they are different. R8C4 is a cat, so R8C3 is a dog.
  5. R3C6 and R3C7 are both cats, so R3C5 must be a dog (no three in a row).
  6. R3C3 and R3C5 are both dogs with one square between them, so R3C4 must be a cat.
  7. R3C6 and R3C7 are both cats, so R3C8 must be a dog (no three in a row).
  8. The = clue between R3C8 and R2C8 means they are the same. R3C8 is a dog, so R2C8 is a dog.
  9. R7C2 and R7C4 are both cats with one square between them, so R7C3 must be a dog.
  10. R2C2 and R3C2 are both cats, so R1C2 must be a dog (no three in a row).
  11. R2C2 and R3C2 are both cats, so R4C2 must be a dog (no three in a row).
  12. R7C3 and R8C3 are both dogs, so R6C3 must be a cat (no three in a row).
  13. R7C4 and R8C4 are both cats, so R6C4 must be a dog (no three in a row).
  14. R6C4 and R6C6 are both dogs with one square between them, so R6C5 must be a cat.
  15. R3C6 and R5C6 are both cats with one square between them, so R4C6 must be a dog.
  16. The × clue between R4C6 and R4C5 means they are different. R4C6 is a dog, so R4C5 is a cat.
  17. R4C5 and R6C5 are both cats with one square between them, so R5C5 must be a dog.
  18. The × clue between R5C5 and R5C4 means they are different. R5C5 is a dog, so R5C4 is a cat.
  19. R3C4 and R5C4 are both cats with one square between them, so R4C4 must be a dog.
  20. R4C2 and R4C4 are both dogs with one square between them, so R4C3 must be a cat.
  21. R4C3 and R6C3 are both cats with one square between them, so R5C3 must be a dog.
  22. The = clue between R5C3 and R5C2 means they are the same. R5C3 is a dog, so R5C2 is a dog.
  23. R5C2 and R5C3 are both dogs, so R5C1 must be a cat (no three in a row).
  24. R4C2 and R5C2 are both dogs, so R6C2 must be a cat (no three in a row).
  25. R6C2 and R6C3 are both cats, so R6C1 must be a dog (no three in a row).
  26. R6C2 and R7C2 are both cats, so R8C2 must be a dog (no three in a row).
  27. R8C2 and R8C3 are both dogs, so R8C1 must be a cat (no three in a row).
  28. R2C8 and R3C8 are both dogs, so R1C8 must be a cat (no three in a row).
  29. R2C8 and R3C8 are both dogs, so R4C8 must be a cat (no three in a row).
  30. Row 3 already has its 4 cats, so R3C1 must be dogs.
  31. Row 6 already has its 4 cats, so R6C8 must be dogs.
  32. R6C8 and R8C8 are both dogs with one square between them, so R7C8 must be a cat.
  33. Column 3 already has its 4 dogs, so R1C3 and R2C3 must be cats.
  34. R2C2 and R2C3 are both cats, so R2C1 must be a dog (no three in a row).
  35. R2C2 and R2C3 are both cats, so R2C4 must be a dog (no three in a row).
  36. R2C1 and R3C1 are both dogs, so R1C1 must be a cat (no three in a row).
  37. R2C1 and R3C1 are both dogs, so R4C1 must be a cat (no three in a row).
  38. Row 4 already has its 4 cats, so R4C7 must be dogs.
  39. Column 1 already has its 4 cats, so R7C1 must be dogs.
  40. Column 4 already has its 4 cats, so R1C4 must be dogs.
  41. R1C4 and R1C6 are both dogs with one square between them, so R1C5 must be a cat.
  42. Row 1 already has its 4 cats, so R1C7 must be dogs.
  43. Column 5 already has its 4 cats, so R7C5 and R8C5 must be dogs.
  44. Row 8 already has its 4 dogs, so R8C6 and R8C7 must be cats.
  45. R6C7 and R8C7 are both cats with one square between them, so R7C7 must be a dog.
  46. R7C5 and R7C7 are both dogs with one square between them, so R7C6 must be a cat.
  47. Column 6 already has its 4 cats, so R2C6 must be dogs.
  48. R2C6 and R2C8 are both dogs with one square between them, so R2C7 must be a cat.
  49. Column 7 already has its 4 cats, so R5C7 must be dogs.
  50. Row 5 already has its 4 dogs, so R5C8 must be cats.

About this puzzle

This 8×8 grid starts with 11 filled squares and 8 = / × clues. It can be solved in 50 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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