Cats & Dogs #136: 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

A 8x8 logic grid: 4 cats and 4 dogs in every row and column, no three of a kind in a row, and a few = and × clues to point the way.

  • 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 R5C6 and R6C6 means they are the same. R5C6 is a cat, so R6C6 is a cat.
  3. The = clue between R6C3 and R6C4 means they are the same. R6C3 is a dog, so R6C4 is a dog.
  4. The × clue between R6C4 and R5C4 means they are different. R6C4 is a dog, so R5C4 is a cat.
  5. R1C5 and R1C6 are both dogs, so R1C4 must be a cat (no three in a row).
  6. The × clue between R1C4 and R1C3 means they are different. R1C4 is a cat, so R1C3 is a dog.
  7. The × clue between R1C4 and R2C4 means they are different. R1C4 is a cat, so R2C4 is a dog.
  8. R1C5 and R1C6 are both dogs, so R1C7 must be a cat (no three in a row).
  9. R5C4 and R5C6 are both cats with one square between them, so R5C5 must be a dog.
  10. R6C3 and R6C4 are both dogs, so R6C2 must be a cat (no three in a row).
  11. The × clue between R6C2 and R7C2 means they are different. R6C2 is a cat, so R7C2 is a dog.
  12. The × clue between R7C2 and R8C2 means they are different. R7C2 is a dog, so R8C2 is a cat.
  13. R6C3 and R6C4 are both dogs, so R6C5 must be a cat (no three in a row).
  14. R6C5 and R6C6 are both cats, so R6C7 must be a dog (no three in a row).
  15. R8C2 and R8C4 are both cats with one square between them, so R8C3 must be a dog.
  16. R6C3 and R8C3 are both dogs with one square between them, so R7C3 must be a cat.
  17. R2C4 and R3C4 are both dogs, so R4C4 must be a cat (no three in a row).
  18. The × clue between R4C4 and R4C3 means they are different. R4C4 is a cat, so R4C3 is a dog.
  19. R4C3 and R6C3 are both dogs with one square between them, so R5C3 must be a cat.
  20. R5C3 and R5C4 are both cats, so R5C2 must be a dog (no three in a row).
  21. R5C6 and R6C6 are both cats, so R4C6 must be a dog (no three in a row).
  22. R5C6 and R6C6 are both cats, so R7C6 must be a dog (no three in a row).
  23. R7C6 and R7C8 are both dogs with one square between them, so R7C7 must be a cat.
  24. R1C7 and R2C7 are both cats, so R3C7 must be a dog (no three in a row).
  25. Column 3 already has its 4 dogs, so R2C3 and R3C3 must be cats.
  26. The = clue between R3C3 and R3C2 means they are the same. R3C3 is a cat, so R3C2 is a cat.
  27. The = clue between R3C2 and R4C2 means they are the same. R3C2 is a cat, so R4C2 is a cat.
  28. R3C2 and R3C3 are both cats, so R3C1 must be a dog (no three in a row).
  29. R3C2 and R4C2 are both cats, so R2C2 must be a dog (no three in a row).
  30. Column 2 already has its 4 cats, so R1C2 must be dogs.
  31. R1C2 and R1C3 are both dogs, so R1C1 must be a cat (no three in a row).
  32. Row 1 already has its 4 dogs, so R1C8 must be cats.
  33. Column 4 already has its 4 cats, so R7C4 must be dogs.
  34. R7C4 and R7C6 are both dogs with one square between them, so R7C5 must be a cat.
  35. R6C5 and R7C5 are both cats, so R8C5 must be a dog (no three in a row).
  36. Row 7 already has its 4 dogs, so R7C1 must be cats.
  37. The = clue between R7C1 and R6C1 means they are the same. R7C1 is a cat, so R6C1 is a cat.
  38. R6C1 and R7C1 are both cats, so R5C1 must be a dog (no three in a row).
  39. R3C1 and R5C1 are both dogs with one square between them, so R4C1 must be a cat.
  40. R6C1 and R7C1 are both cats, so R8C1 must be a dog (no three in a row).
  41. Row 6 already has its 4 cats, so R6C8 must be dogs.
  42. R6C8 and R7C8 are both dogs, so R5C8 must be a cat (no three in a row).
  43. R5C6 and R5C8 are both cats with one square between them, so R5C7 must be a dog.
  44. R3C7 and R5C7 are both dogs with one square between them, so R4C7 must be a cat.
  45. R6C8 and R7C8 are both dogs, so R8C8 must be a cat (no three in a row).
  46. Row 4 already has its 4 cats, so R4C5 must be dogs.
  47. R4C5 and R5C5 are both dogs, so R3C5 must be a cat (no three in a row).
  48. Row 4 already has its 4 cats, so R4C8 must be dogs.
  49. Column 1 already has its 4 cats, so R2C1 must be dogs.
  50. Column 5 already has its 4 dogs, so R2C5 must be cats.
  51. R2C5 and R2C7 are both cats with one square between them, so R2C6 must be a dog.
  52. R1C6 and R2C6 are both dogs, so R3C6 must be a cat (no three in a row).
  53. Row 2 already has its 4 dogs, so R2C8 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 R8C6 must be cats.
  56. R8C6 and R8C8 are both cats with one square between them, so R8C7 must be a dog.

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.

Count as you go. Once a row or column has all of one animal, every remaining empty square in it must be the other.

Every puzzle on this site has exactly one solution that can be reached by deduction. If you are guessing, look again at the rows and columns that are nearly full.

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