Cats & Dogs #128: 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 R2C1 and R1C1 means they are the same. R2C1 is a dog, so R1C1 is a dog.
  2. The = clue between R3C7 and R3C6 means they are the same. R3C7 is a cat, so R3C6 is a cat.
  3. The = clue between R4C3 and R4C4 means they are the same. R4C3 is a cat, so R4C4 is a cat.
  4. The × clue between R4C4 and R5C4 means they are different. R4C4 is a cat, so R5C4 is a dog.
  5. R3C6 and R3C7 are both cats, so R3C5 must be a dog (no three in a row).
  6. R3C6 and R3C7 are both cats, so R3C8 must be a dog (no three in a row).
  7. R4C3 and R4C4 are both cats, so R4C2 must be a dog (no three in a row).
  8. R4C3 and R4C4 are both cats, so R4C5 must be a dog (no three in a row).
  9. R1C1 and R2C1 are both dogs, so R3C1 must be a cat (no three in a row).
  10. The = clue between R3C1 and R4C1 means they are the same. R3C1 is a cat, so R4C1 is a cat.
  11. R3C1 and R4C1 are both cats, so R5C1 must be a dog (no three in a row).
  12. R5C1 and R6C1 are both dogs, so R7C1 must be a cat (no three in a row).
  13. R5C4 and R6C4 are both dogs, so R7C4 must be a cat (no three in a row).
  14. R3C5 and R4C5 are both dogs, so R2C5 must be a cat (no three in a row).
  15. R2C5 and R2C7 are both cats with one square between them, so R2C6 must be a dog.
  16. R3C5 and R4C5 are both dogs, so R5C5 must be a cat (no three in a row).
  17. R2C7 and R3C7 are both cats, so R1C7 must be a dog (no three in a row).
  18. R2C7 and R3C7 are both cats, so R4C7 must be a dog (no three in a row).
  19. R4C5 and R4C7 are both dogs with one square between them, so R4C6 must be a cat.
  20. R3C6 and R4C6 are both cats, so R5C6 must be a dog (no three in a row).
  21. R5C6 and R5C7 are both dogs, so R5C8 must be a cat (no three in a row).
  22. R4C7 and R5C7 are both dogs, so R6C7 must be a cat (no three in a row).
  23. Row 4 already has its 4 cats, so R4C8 must be dogs.
  24. R3C8 and R4C8 are both dogs, so R2C8 must be a cat (no three in a row).
  25. Row 5 already has its 4 dogs, so R5C2 and R5C3 must be cats.
  26. R4C3 and R5C3 are both cats, so R3C3 must be a dog (no three in a row).
  27. R3C3 and R3C5 are both dogs with one square between them, so R3C4 must be a cat.
  28. R4C3 and R5C3 are both cats, so R6C3 must be a dog (no three in a row).
  29. R6C1 and R6C3 are both dogs with one square between them, so R6C2 must be a cat.
  30. R6C3 and R6C4 are both dogs, so R6C5 must be a cat (no three in a row).
  31. R6C5 and R6C7 are both cats with one square between them, so R6C6 must be a dog.
  32. R5C2 and R6C2 are both cats, so R7C2 must be a dog (no three in a row).
  33. R6C3 and R7C3 are both dogs, so R8C3 must be a cat (no three in a row).
  34. R3C4 and R4C4 are both cats, so R2C4 must be a dog (no three in a row).
  35. R5C5 and R6C5 are both cats, so R7C5 must be a dog (no three in a row).
  36. R5C6 and R6C6 are both dogs, so R7C6 must be a cat (no three in a row).
  37. Row 3 already has its 4 cats, so R3C2 must be dogs.
  38. R3C2 and R4C2 are both dogs, so R2C2 must be a cat (no three in a row).
  39. Row 2 already has its 4 cats, so R2C3 must be dogs.
  40. R2C3 and R3C3 are both dogs, so R1C3 must be a cat (no three in a row).
  41. Row 6 already has its 4 dogs, so R6C8 must be cats.
  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 R7C7 must be cats.
  44. R6C7 and R7C7 are both cats, so R8C7 must be a dog (no three in a row).
  45. Column 1 already has its 4 dogs, so R8C1 must be cats.
  46. R8C1 and R8C3 are both cats with one square between them, so R8C2 must be a dog.
  47. Column 2 already has its 4 dogs, so R1C2 must be cats.
  48. R1C2 and R1C3 are both cats, so R1C4 must be a dog (no three in a row).
  49. Column 4 already has its 4 dogs, so R8C4 must be cats.
  50. R8C3 and R8C4 are both cats, so R8C5 must be a dog (no three in a row).
  51. R8C5 and R8C7 are both dogs with one square between them, so R8C6 must be a cat.
  52. Row 8 already has its 4 cats, so R8C8 must be dogs.
  53. Column 5 already has its 4 dogs, so R1C5 must be cats.
  54. Column 6 already has its 4 cats, so R1C6 must be dogs.
  55. R1C6 and R1C7 are both dogs, so R1C8 must be a cat (no three in a row).

About this puzzle

This 8×8 grid starts with 8 filled squares and 5 = / × clues. It can be solved in 55 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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