Cats & Dogs #146: 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 R2C2 and R3C2 means they are different. R2C2 is a dog, so R3C2 is a cat.
  2. The × clue between R8C6 and R8C7 means they are different. R8C6 is a dog, so R8C7 is a cat.
  3. R3C2 and R4C2 are both cats, so R5C2 must be a dog (no three in a row).
  4. R3C6 and R4C6 are both cats, so R2C6 must be a dog (no three in a row).
  5. R2C6 and R2C8 are both dogs with one square between them, so R2C7 must be a cat.
  6. R3C6 and R4C6 are both cats, so R5C6 must be a dog (no three in a row).
  7. The = clue between R5C6 and R5C7 means they are the same. R5C6 is a dog, so R5C7 is a dog.
  8. R5C6 and R5C7 are both dogs, so R5C5 must be a cat (no three in a row).
  9. R5C6 and R5C7 are both dogs, so R5C8 must be a cat (no three in a row).
  10. R2C8 and R3C8 are both dogs, so R1C8 must be a cat (no three in a row).
  11. R2C8 and R3C8 are both dogs, so R4C8 must be a cat (no three in a row).
  12. R4C6 and R4C8 are both cats with one square between them, so R4C7 must be a dog.
  13. R4C7 and R5C7 are both dogs, so R3C7 must be a cat (no three in a row).
  14. R3C6 and R3C7 are both cats, so R3C5 must be a dog (no three in a row).
  15. The = clue between R3C5 and R3C4 means they are the same. R3C5 is a dog, so R3C4 is a dog.
  16. R3C4 and R3C5 are both dogs, so R3C3 must be a cat (no three in a row).
  17. R3C2 and R3C3 are both cats, so R3C1 must be a dog (no three in a row).
  18. R2C7 and R3C7 are both cats, so R1C7 must be a dog (no three in a row).
  19. R1C6 and R1C7 are both dogs, so R1C5 must be a cat (no three in a row).
  20. R4C7 and R5C7 are both dogs, so R6C7 must be a cat (no three in a row).
  21. R6C7 and R8C7 are both cats with one square between them, so R7C7 must be a dog.
  22. The = clue between R7C7 and R7C8 means they are the same. R7C7 is a dog, so R7C8 is a dog.
  23. R7C7 and R7C8 are both dogs, so R7C6 must be a cat (no three in a row).
  24. R4C8 and R5C8 are both cats, so R6C8 must be a dog (no three in a row).
  25. R6C8 and R7C8 are both dogs, so R8C8 must be a cat (no three in a row).
  26. Column 6 already has its 4 dogs, so R6C6 must be cats.
  27. R6C6 and R6C7 are both cats, so R6C5 must be a dog (no three in a row).
  28. R6C4 and R6C5 are both dogs, so R6C3 must be a cat (no three in a row).
  29. The = clue between R6C3 and R7C3 means they are the same. R6C3 is a cat, so R7C3 is a cat.
  30. The × clue between R7C3 and R7C4 means they are different. R7C3 is a cat, so R7C4 is a dog.
  31. R6C3 and R7C3 are both cats, so R5C3 must be a dog (no three in a row).
  32. R5C2 and R5C3 are both dogs, so R5C1 must be a cat (no three in a row).
  33. The × clue between R5C1 and R6C1 means they are different. R5C1 is a cat, so R6C1 is a dog.
  34. The = clue between R6C1 and R7C1 means they are the same. R6C1 is a dog, so R7C1 is a dog.
  35. R5C2 and R5C3 are both dogs, so R5C4 must be a cat (no three in a row).
  36. The × clue between R5C4 and R4C4 means they are different. R5C4 is a cat, so R4C4 is a dog.
  37. R6C1 and R7C1 are both dogs, so R8C1 must be a cat (no three in a row).
  38. R6C3 and R7C3 are both cats, so R8C3 must be a dog (no three in a row).
  39. R3C4 and R4C4 are both dogs, so R2C4 must be a cat (no three in a row).
  40. The × clue between R2C4 and R2C3 means they are different. R2C4 is a cat, so R2C3 is a dog.
  41. R2C2 and R2C3 are both dogs, so R2C1 must be a cat (no three in a row).
  42. R6C4 and R7C4 are both dogs, so R8C4 must be a cat (no three in a row).
  43. Row 2 already has its 4 dogs, so R2C5 must be cats.
  44. Row 6 already has its 4 dogs, so R6C2 must be cats.
  45. Row 7 already has its 4 dogs, so R7C2 must be cats.
  46. R6C2 and R7C2 are both cats, so R8C2 must be a dog (no three in a row).
  47. Row 7 already has its 4 dogs, so R7C5 must be cats.
  48. Row 8 already has its 4 cats, so R8C5 must be dogs.
  49. Column 2 already has its 4 cats, so R1C2 must be dogs.
  50. Column 4 already has its 4 dogs, so R1C4 must be cats.
  51. R1C4 and R1C5 are both cats, so R1C3 must be a dog (no three in a row).
  52. R1C2 and R1C3 are both dogs, so R1C1 must be a cat (no three in a row).
  53. Column 1 already has its 4 cats, so R4C1 must be dogs.
  54. Column 3 already has its 4 dogs, so R4C3 must be cats.
  55. Row 4 already has its 4 cats, so R4C5 must be dogs.

About this puzzle

This 8×8 grid starts with 9 filled squares and 11 = / × 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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