Cats & Dogs #174: 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 R1C2 means they are the same. R2C2 is a dog, so R1C2 is a dog.
  2. The = clue between R1C7 and R2C7 means they are the same. R1C7 is a dog, so R2C7 is a dog.
  3. The × clue between R5C2 and R5C3 means they are different. R5C2 is a cat, so R5C3 is a dog.
  4. The = clue between R5C8 and R5C7 means they are the same. R5C8 is a dog, so R5C7 is a dog.
  5. The × clue between R6C7 and R6C6 means they are different. R6C7 is a cat, so R6C6 is a dog.
  6. The × clue between R6C7 and R6C8 means they are different. R6C7 is a cat, so R6C8 is a dog.
  7. The × clue between R6C7 and R7C7 means they are different. R6C7 is a cat, so R7C7 is a dog.
  8. R5C7 and R5C8 are both dogs, so R5C6 must be a cat (no three in a row).
  9. R1C2 and R2C2 are both dogs, so R3C2 must be a cat (no three in a row).
  10. R3C2 and R5C2 are both cats with one square between them, so R4C2 must be a dog.
  11. R1C7 and R2C7 are both dogs, so R3C7 must be a cat (no three in a row).
  12. The × clue between R3C7 and R3C6 means they are different. R3C7 is a cat, so R3C6 is a dog.
  13. The = clue between R3C6 and R3C5 means they are the same. R3C6 is a dog, so R3C5 is a dog.
  14. R3C5 and R3C6 are both dogs, so R3C4 must be a cat (no three in a row).
  15. The = clue between R3C4 and R4C4 means they are the same. R3C4 is a cat, so R4C4 is a cat.
  16. R3C2 and R3C4 are both cats with one square between them, so R3C3 must be a dog.
  17. R3C3 and R5C3 are both dogs with one square between them, so R4C3 must be a cat.
  18. R4C3 and R4C4 are both cats, so R4C5 must be a dog (no three in a row).
  19. R3C4 and R4C4 are both cats, so R2C4 must be a dog (no three in a row).
  20. R2C2 and R2C4 are both dogs with one square between them, so R2C3 must be a cat.
  21. R3C4 and R4C4 are both cats, so R5C4 must be a dog (no three in a row).
  22. R5C3 and R5C4 are both dogs, so R5C5 must be a cat (no three in a row).
  23. R5C4 and R7C4 are both dogs with one square between them, so R6C4 must be a cat.
  24. The = clue between R6C4 and R6C3 means they are the same. R6C4 is a cat, so R6C3 is a cat.
  25. R6C3 and R6C4 are both cats, so R6C2 must be a dog (no three in a row).
  26. R6C3 and R6C4 are both cats, so R6C5 must be a dog (no three in a row).
  27. R3C5 and R4C5 are both dogs, so R2C5 must be a cat (no three in a row).
  28. R3C8 and R5C8 are both dogs with one square between them, so R4C8 must be a cat.
  29. R5C8 and R6C8 are both dogs, so R7C8 must be a cat (no three in a row).
  30. Row 3 already has its 4 dogs, so R3C1 must be cats.
  31. Row 5 already has its 4 dogs, so R5C1 must be cats.
  32. R3C1 and R5C1 are both cats with one square between them, so R4C1 must be a dog.
  33. Row 6 already has its 4 dogs, so R6C1 must be cats.
  34. R5C1 and R6C1 are both cats, so R7C1 must be a dog (no three in a row).
  35. The × clue between R7C1 and R8C1 means they are different. R7C1 is a dog, so R8C1 is a cat.
  36. Column 1 already has its 4 cats, so R1C1 must be dogs.
  37. R1C1 and R1C2 are both dogs, so R1C3 must be a cat (no three in a row).
  38. Column 1 already has its 4 cats, so R2C1 must be dogs.
  39. Row 2 already has its 4 dogs, so R2C6 and R2C8 must be cats.
  40. Column 2 already has its 4 dogs, so R7C2 and R8C2 must be cats.
  41. R8C1 and R8C2 are both cats, so R8C3 must be a dog (no three in a row).
  42. Column 3 already has its 4 cats, so R7C3 must be dogs.
  43. R7C3 and R7C4 are both dogs, so R7C5 must be a cat (no three in a row).
  44. The = clue between R7C5 and R8C5 means they are the same. R7C5 is a cat, so R8C5 is a cat.
  45. Row 7 already has its 4 dogs, so R7C6 must be cats.
  46. Column 5 already has its 4 cats, so R1C5 must be dogs.
  47. R1C5 and R1C7 are both dogs with one square between them, so R1C6 must be a cat.
  48. Row 1 already has its 4 dogs, so R1C4 and R1C8 must be cats.
  49. Column 4 already has its 4 cats, so R8C4 must be dogs.
  50. Column 6 already has its 4 cats, so R4C6 must be dogs.
  51. R4C5 and R4C6 are both dogs, so R4C7 must be a cat (no three in a row).
  52. Column 6 already has its 4 cats, so R8C6 must be dogs.
  53. Column 7 already has its 4 dogs, so R8C7 must be cats.
  54. Row 8 already has its 4 cats, so R8C8 must be dogs.

About this puzzle

This 8×8 grid starts with 7 filled squares and 13 = / × clues. It can be solved in 54 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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