Cats & Dogs #157: 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 R4C2 and R3C2 means they are the same. R4C2 is a dog, so R3C2 is a dog.
  2. The = clue between R3C2 and R3C3 means they are the same. R3C2 is a dog, so R3C3 is a dog.
  3. R3C2 and R3C3 are both dogs, so R3C1 must be a cat (no three in a row).
  4. R3C2 and R3C3 are both dogs, so R3C4 must be a cat (no three in a row).
  5. R3C4 and R3C5 are both cats, so R3C6 must be a dog (no three in a row).
  6. The × clue between R3C6 and R2C6 means they are different. R3C6 is a dog, so R2C6 is a cat.
  7. R6C4 and R6C6 are both cats with one square between them, so R6C5 must be a dog.
  8. The × clue between R6C5 and R5C5 means they are different. R6C5 is a dog, so R5C5 is a cat.
  9. The = clue between R5C5 and R5C4 means they are the same. R5C5 is a cat, so R5C4 is a cat.
  10. R5C4 and R5C5 are both cats, so R5C3 must be a dog (no three in a row).
  11. The = clue between R5C3 and R6C3 means they are the same. R5C3 is a dog, so R6C3 is a dog.
  12. The × clue between R6C3 and R6C2 means they are different. R6C3 is a dog, so R6C2 is a cat.
  13. R5C4 and R5C5 are both cats, so R5C6 must be a dog (no three in a row).
  14. R3C2 and R4C2 are both dogs, so R2C2 must be a cat (no three in a row).
  15. R3C2 and R4C2 are both dogs, so R5C2 must be a cat (no three in a row).
  16. R5C2 and R6C2 are both cats, so R7C2 must be a dog (no three in a row).
  17. R3C3 and R5C3 are both dogs with one square between them, so R4C3 must be a cat.
  18. R5C3 and R6C3 are both dogs, so R7C3 must be a cat (no three in a row).
  19. R3C4 and R5C4 are both cats with one square between them, so R4C4 must be a dog.
  20. R5C4 and R6C4 are both cats, so R7C4 must be a dog (no three in a row).
  21. R3C5 and R5C5 are both cats with one square between them, so R4C5 must be a dog.
  22. R4C4 and R4C5 are both dogs, so R4C6 must be a cat (no three in a row).
  23. Row 4 already has its 4 dogs, so R4C1 must be cats.
  24. R3C1 and R4C1 are both cats, so R2C1 must be a dog (no three in a row).
  25. R3C1 and R4C1 are both cats, so R5C1 must be a dog (no three in a row).
  26. The × clue between R5C1 and R6C1 means they are different. R5C1 is a dog, so R6C1 is a cat.
  27. Row 4 already has its 4 dogs, so R4C8 must be cats.
  28. The × clue between R4C8 and R3C8 means they are different. R4C8 is a cat, so R3C8 is a dog.
  29. R3C6 and R3C8 are both dogs with one square between them, so R3C7 must be a cat.
  30. Row 6 already has its 4 cats, so R6C7 must be dogs.
  31. R4C7 and R6C7 are both dogs with one square between them, so R5C7 must be a cat.
  32. Row 5 already has its 4 cats, so R5C8 must be dogs.
  33. Row 6 already has its 4 cats, so R6C8 must be dogs.
  34. R5C8 and R6C8 are both dogs, so R7C8 must be a cat (no three in a row).
  35. The × clue between R7C8 and R8C8 means they are different. R7C8 is a cat, so R8C8 is a dog.
  36. Column 3 already has its 4 dogs, so R1C3 must be cats.
  37. The × clue between R1C3 and R1C2 means they are different. R1C3 is a cat, so R1C2 is a dog.
  38. The × clue between R1C3 and R1C4 means they are different. R1C3 is a cat, so R1C4 is a dog.
  39. Column 2 already has its 4 dogs, so R8C2 must be cats.
  40. Column 3 already has its 4 dogs, so R2C3 must be cats.
  41. R2C2 and R2C3 are both cats, so R2C4 must be a dog (no three in a row).
  42. Column 4 already has its 4 dogs, so R8C4 must be cats.
  43. Column 8 already has its 4 dogs, so R1C8 and R2C8 must be cats.
  44. R2C6 and R2C8 are both cats with one square between them, so R2C7 must be a dog.
  45. Row 2 already has its 4 cats, so R2C5 must be dogs.
  46. The = clue between R2C5 and R1C5 means they are the same. R2C5 is a dog, so R1C5 is a dog.
  47. R1C4 and R1C5 are both dogs, so R1C6 must be a cat (no three in a row).
  48. R1C6 and R1C8 are both cats with one square between them, so R1C7 must be a dog.
  49. Row 1 already has its 4 dogs, so R1C1 must be cats.
  50. Column 1 already has its 4 cats, so R7C1 and R8C1 must be dogs.
  51. Column 5 already has its 4 dogs, so R7C5 and R8C5 must be cats.
  52. R8C4 and R8C5 are both cats, so R8C6 must be a dog (no three in a row).
  53. R8C6 and R8C8 are both dogs with one square between them, so R8C7 must be a cat.
  54. Column 6 already has its 4 cats, so R7C6 must be dogs.
  55. Row 7 already has its 4 dogs, so R7C7 must be cats.

About this puzzle

This 8×8 grid starts with 6 filled squares and 13 = / × 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.

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

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