Cats & Dogs #103: 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 R1C3 and R1C2 means they are different. R1C3 is a cat, so R1C2 is a dog.
  2. The × clue between R1C2 and R2C2 means they are different. R1C2 is a dog, so R2C2 is a cat.
  3. The × clue between R1C3 and R1C4 means they are different. R1C3 is a cat, so R1C4 is a dog.
  4. The × clue between R6C5 and R6C4 means they are different. R6C5 is a dog, so R6C4 is a cat.
  5. R7C3 and R7C4 are both cats, so R7C2 must be a dog (no three in a row).
  6. R7C3 and R7C4 are both cats, so R7C5 must be a dog (no three in a row).
  7. R6C4 and R7C4 are both cats, so R5C4 must be a dog (no three in a row).
  8. R4C4 and R5C4 are both dogs, so R3C4 must be a cat (no three in a row).
  9. R6C4 and R7C4 are both cats, so R8C4 must be a dog (no three in a row).
  10. R6C5 and R7C5 are both dogs, so R5C5 must be a cat (no three in a row).
  11. The × clue between R5C5 and R5C6 means they are different. R5C5 is a cat, so R5C6 is a dog.
  12. R6C5 and R7C5 are both dogs, so R8C5 must be a cat (no three in a row).
  13. Column 4 already has its 4 dogs, so R2C4 must be cats.
  14. The × clue between R2C4 and R2C5 means they are different. R2C4 is a cat, so R2C5 is a dog.
  15. The = clue between R2C5 and R3C5 means they are the same. R2C5 is a dog, so R3C5 is a dog.
  16. R2C2 and R2C4 are both cats with one square between them, so R2C3 must be a dog.
  17. The = clue between R2C3 and R3C3 means they are the same. R2C3 is a dog, so R3C3 is a dog.
  18. R2C3 and R3C3 are both dogs, so R4C3 must be a cat (no three in a row).
  19. The × clue between R4C3 and R4C2 means they are different. R4C3 is a cat, so R4C2 is a dog.
  20. The = clue between R4C3 and R5C3 means they are the same. R4C3 is a cat, so R5C3 is a cat.
  21. The × clue between R5C3 and R5C2 means they are different. R5C3 is a cat, so R5C2 is a dog.
  22. The = clue between R5C2 and R5C1 means they are the same. R5C2 is a dog, so R5C1 is a dog.
  23. R4C2 and R5C2 are both dogs, so R3C2 must be a cat (no three in a row).
  24. R4C2 and R5C2 are both dogs, so R6C2 must be a cat (no three in a row).
  25. R6C2 and R6C4 are both cats with one square between them, so R6C3 must be a dog.
  26. R2C5 and R3C5 are both dogs, so R1C5 must be a cat (no three in a row).
  27. R2C5 and R3C5 are both dogs, so R4C5 must be a cat (no three in a row).
  28. Row 5 already has its 4 dogs, so R5C7 must be cats.
  29. The × clue between R5C7 and R4C7 means they are different. R5C7 is a cat, so R4C7 is a dog.
  30. The × clue between R4C7 and R4C6 means they are different. R4C7 is a dog, so R4C6 is a cat.
  31. The × clue between R4C6 and R3C6 means they are different. R4C6 is a cat, so R3C6 is a dog.
  32. R3C5 and R3C6 are both dogs, so R3C7 must be a cat (no three in a row).
  33. Row 3 already has its 4 cats, so R3C8 must be dogs.
  34. R2C8 and R3C8 are both dogs, so R1C8 must be a cat (no three in a row).
  35. The × clue between R1C8 and R1C7 means they are different. R1C8 is a cat, so R1C7 is a dog.
  36. R2C8 and R3C8 are both dogs, so R4C8 must be a cat (no three in a row).
  37. Row 1 already has its 4 dogs, so R1C6 must be cats.
  38. Row 4 already has its 4 cats, so R4C1 must be dogs.
  39. R4C1 and R5C1 are both dogs, so R6C1 must be a cat (no three in a row).
  40. R6C1 and R8C1 are both cats with one square between them, so R7C1 must be a dog.
  41. Row 5 already has its 4 dogs, so R5C8 must be cats.
  42. R4C8 and R5C8 are both cats, so R6C8 must be a dog (no three in a row).
  43. R6C8 and R7C8 are both dogs, so R8C8 must be a cat (no three in a row).
  44. Row 7 already has its 4 dogs, so R7C6 and R7C7 must be cats.
  45. R5C7 and R7C7 are both cats with one square between them, so R6C7 must be a dog.
  46. R6C5 and R6C7 are both dogs with one square between them, so R6C6 must be a cat.
  47. R6C6 and R7C6 are both cats, so R8C6 must be a dog (no three in a row).
  48. Column 1 already has its 4 dogs, so R2C1 must be cats.
  49. Column 2 already has its 4 dogs, so R8C2 must be cats.
  50. R8C1 and R8C2 are both cats, so R8C3 must be a dog (no three in a row).
  51. Row 8 already has its 4 cats, so R8C7 must be dogs.
  52. Column 6 already has its 4 cats, so R2C6 must be dogs.
  53. R2C5 and R2C6 are both dogs, so R2C7 must be a cat (no three in a row).

About this puzzle

This 8×8 grid starts with 10 filled squares and 16 = / × clues. It can be solved in 53 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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