Cats & Dogs #108: 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 R2C3 and R1C3 means they are the same. R2C3 is a cat, so R1C3 is a cat.
  2. The × clue between R4C3 and R4C4 means they are different. R4C3 is a dog, so R4C4 is a cat.
  3. The = clue between R6C7 and R5C7 means they are the same. R6C7 is a dog, so R5C7 is a dog.
  4. The = clue between R5C7 and R5C8 means they are the same. R5C7 is a dog, so R5C8 is a dog.
  5. R2C6 and R2C8 are both dogs with one square between them, so R2C7 must be a cat.
  6. The × clue between R2C7 and R1C7 means they are different. R2C7 is a cat, so R1C7 is a dog.
  7. R1C7 and R1C8 are both dogs, so R1C6 must be a cat (no three in a row).
  8. R5C7 and R5C8 are both dogs, so R5C6 must be a cat (no three in a row).
  9. R6C7 and R6C8 are both dogs, so R6C6 must be a cat (no three in a row).
  10. R6C5 and R6C6 are both cats, so R6C4 must be a dog (no three in a row).
  11. R1C3 and R2C3 are both cats, so R3C3 must be a dog (no three in a row).
  12. R3C3 and R4C3 are both dogs, so R5C3 must be a cat (no three in a row).
  13. R5C6 and R6C6 are both cats, so R4C6 must be a dog (no three in a row).
  14. R2C6 and R4C6 are both dogs with one square between them, so R3C6 must be a cat.
  15. R3C5 and R3C6 are both cats, so R3C4 must be a dog (no three in a row).
  16. R3C3 and R3C4 are both dogs, so R3C2 must be a cat (no three in a row).
  17. R3C5 and R3C6 are both cats, so R3C7 must be a dog (no three in a row).
  18. R5C6 and R6C6 are both cats, so R7C6 must be a dog (no three in a row).
  19. R3C7 and R5C7 are both dogs with one square between them, so R4C7 must be a cat.
  20. R5C7 and R6C7 are both dogs, so R7C7 must be a cat (no three in a row).
  21. R1C8 and R2C8 are both dogs, so R3C8 must be a cat (no three in a row).
  22. R5C8 and R6C8 are both dogs, so R4C8 must be a cat (no three in a row).
  23. R5C8 and R6C8 are both dogs, so R7C8 must be a cat (no three in a row).
  24. Row 3 already has its 4 cats, so R3C1 must be dogs.
  25. R2C1 and R3C1 are both dogs, so R1C1 must be a cat (no three in a row).
  26. R1C1 and R1C3 are both cats with one square between them, so R1C2 must be a dog.
  27. R2C1 and R3C1 are both dogs, so R4C1 must be a cat (no three in a row).
  28. Row 4 already has its 4 cats, so R4C2 must be dogs.
  29. R4C2 and R5C2 are both dogs, so R6C2 must be a cat (no three in a row).
  30. The × clue between R6C2 and R6C1 means they are different. R6C2 is a cat, so R6C1 is a dog.
  31. The × clue between R6C1 and R7C1 means they are different. R6C1 is a dog, so R7C1 is a cat.
  32. The × clue between R7C1 and R7C2 means they are different. R7C1 is a cat, so R7C2 is a dog.
  33. Row 4 already has its 4 cats, so R4C5 must be dogs.
  34. Row 6 already has its 4 dogs, so R6C3 must be cats.
  35. R5C3 and R6C3 are both cats, so R7C3 must be a dog (no three in a row).
  36. R7C2 and R7C3 are both dogs, so R7C4 must be a cat (no three in a row).
  37. Row 7 already has its 4 cats, so R7C5 must be dogs.
  38. The × clue between R7C5 and R8C5 means they are different. R7C5 is a dog, so R8C5 is a cat.
  39. Column 2 already has its 4 dogs, so R2C2 must be cats.
  40. R2C2 and R2C3 are both cats, so R2C4 must be a dog (no three in a row).
  41. R2C4 and R2C6 are both dogs with one square between them, so R2C5 must be a cat.
  42. R2C4 and R3C4 are both dogs, so R1C4 must be a cat (no three in a row).
  43. R1C3 and R1C4 are both cats, so R1C5 must be a dog (no three in a row).
  44. Column 2 already has its 4 dogs, so R8C2 must be cats.
  45. Column 3 already has its 4 cats, so R8C3 must be dogs.
  46. Column 5 already has its 4 cats, so R5C5 must be dogs.
  47. Row 5 already has its 4 dogs, so R5C1 and R5C4 must be cats.
  48. Column 1 already has its 4 cats, so R8C1 must be dogs.
  49. Column 4 already has its 4 cats, so R8C4 must be dogs.
  50. Column 6 already has its 4 cats, so R8C6 must be dogs.
  51. Row 8 already has its 4 dogs, so R8C7 and R8C8 must be cats.

About this puzzle

This 8×8 grid starts with 11 filled squares and 9 = / × clues. It can be solved in 51 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.

This kind of puzzle is known as a binary or Takuzu puzzle, here with cats and dogs and extra = / × clues.

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