Cats & Dogs #168: 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 R3C8 and R4C8 means they are the same. R3C8 is a cat, so R4C8 is a cat.
  2. The = clue between R6C3 and R6C2 means they are the same. R6C3 is a cat, so R6C2 is a cat.
  3. R6C2 and R6C3 are both cats, so R6C1 must be a dog (no three in a row).
  4. R6C2 and R6C3 are both cats, so R6C4 must be a dog (no three in a row).
  5. R6C7 and R6C8 are both dogs, so R6C6 must be a cat (no three in a row).
  6. The × clue between R6C6 and R5C6 means they are different. R6C6 is a cat, so R5C6 is a dog.
  7. The × clue between R6C6 and R7C6 means they are different. R6C6 is a cat, so R7C6 is a dog.
  8. R3C8 and R4C8 are both cats, so R2C8 must be a dog (no three in a row).
  9. R3C8 and R4C8 are both cats, so R5C8 must be a dog (no three in a row).
  10. R5C6 and R5C8 are both dogs with one square between them, so R5C7 must be a cat.
  11. R5C8 and R6C8 are both dogs, so R7C8 must be a cat (no three in a row).
  12. Row 6 already has its 4 dogs, so R6C5 must be cats.
  13. Column 8 already has its 4 dogs, so R8C8 must be cats.
  14. R8C7 and R8C8 are both cats, so R8C6 must be a dog (no three in a row).
  15. R8C5 and R8C6 are both dogs, so R8C4 must be a cat (no three in a row).
  16. Column 4 already has its 4 cats, so R1C4 must be dogs.
  17. R1C3 and R1C4 are both dogs, so R1C2 must be a cat (no three in a row).
  18. R1C3 and R1C4 are both dogs, so R1C5 must be a cat (no three in a row).
  19. R1C5 and R1C6 are both cats, so R1C7 must be a dog (no three in a row).
  20. Row 1 already has its 4 dogs, so R1C1 must be cats.
  21. Column 4 already has its 4 cats, so R3C4 must be dogs.
  22. R3C4 and R3C5 are both dogs, so R3C3 must be a cat (no three in a row).
  23. The = clue between R3C3 and R3C2 means they are the same. R3C3 is a cat, so R3C2 is a cat.
  24. R3C2 and R3C3 are both cats, so R3C1 must be a dog (no three in a row).
  25. R3C4 and R3C5 are both dogs, so R3C6 must be a cat (no three in a row).
  26. R3C6 and R3C8 are both cats with one square between them, so R3C7 must be a dog.
  27. R1C2 and R3C2 are both cats with one square between them, so R2C2 must be a dog.
  28. R1C6 and R3C6 are both cats with one square between them, so R2C6 must be a dog.
  29. R2C6 and R2C8 are both dogs with one square between them, so R2C7 must be a cat.
  30. Column 4 already has its 4 cats, so R4C4 must be dogs.
  31. The × clue between R4C4 and R4C5 means they are different. R4C4 is a dog, so R4C5 is a cat.
  32. R4C2 and R4C4 are both dogs with one square between them, so R4C3 must be a cat.
  33. R3C3 and R4C3 are both cats, so R2C3 must be a dog (no three in a row).
  34. R2C2 and R2C3 are both dogs, so R2C1 must be a cat (no three in a row).
  35. R3C3 and R4C3 are both cats, so R5C3 must be a dog (no three in a row).
  36. R4C5 and R6C5 are both cats with one square between them, so R5C5 must be a dog.
  37. Row 2 already has its 4 dogs, so R2C5 must be cats.
  38. Row 5 already has its 4 dogs, so R5C1 and R5C2 must be cats.
  39. R5C2 and R6C2 are both cats, so R7C2 must be a dog (no three in a row).
  40. The × clue between R7C2 and R7C1 means they are different. R7C2 is a dog, so R7C1 is a cat.
  41. Column 1 already has its 4 cats, so R4C1 and R8C1 must be dogs.
  42. Column 2 already has its 4 cats, so R8C2 must be dogs.
  43. R8C1 and R8C2 are both dogs, so R8C3 must be a cat (no three in a row).
  44. R6C3 and R8C3 are both cats with one square between them, so R7C3 must be a dog.
  45. Column 5 already has its 4 cats, so R7C5 must be dogs.
  46. R7C5 and R7C6 are both dogs, so R7C7 must be a cat (no three in a row).
  47. Column 6 already has its 4 dogs, so R4C6 must be cats.
  48. R4C5 and R4C6 are both cats, so R4C7 must be a dog (no three in a row).

About this puzzle

This 8×8 grid starts with 14 filled squares and 7 = / × clues. It can be solved in 48 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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