Cats & Dogs #196: 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 R6C4 and R5C4 means they are the same. R6C4 is a dog, so R5C4 is a dog.
  3. The × clue between R5C4 and R5C3 means they are different. R5C4 is a dog, so R5C3 is a cat.
  4. The × clue between R7C1 and R6C1 means they are different. R7C1 is a dog, so R6C1 is a cat.
  5. The × clue between R6C1 and R5C1 means they are different. R6C1 is a cat, so R5C1 is a dog.
  6. The × clue between R5C1 and R5C2 means they are different. R5C1 is a dog, so R5C2 is a cat.
  7. The = clue between R7C7 and R8C7 means they are the same. R7C7 is a cat, so R8C7 is a cat.
  8. R7C1 and R7C3 are both dogs with one square between them, so R7C2 must be a cat.
  9. R5C2 and R7C2 are both cats with one square between them, so R6C2 must be a dog.
  10. R6C2 and R6C4 are both dogs with one square between them, so R6C3 must be a cat.
  11. R1C3 and R2C3 are both cats, so R3C3 must be a dog (no three in a row).
  12. R5C3 and R6C3 are both cats, so R4C3 must be a dog (no three in a row).
  13. R5C4 and R6C4 are both dogs, so R4C4 must be a cat (no three in a row).
  14. The × clue between R4C4 and R3C4 means they are different. R4C4 is a cat, so R3C4 is a dog.
  15. R3C3 and R3C4 are both dogs, so R3C2 must be a cat (no three in a row).
  16. R3C3 and R3C4 are both dogs, so R3C5 must be a cat (no three in a row).
  17. The = clue between R3C5 and R2C5 means they are the same. R3C5 is a cat, so R2C5 is a cat.
  18. R2C3 and R2C5 are both cats with one square between them, so R2C4 must be a dog.
  19. R3C2 and R5C2 are both cats with one square between them, so R4C2 must be a dog.
  20. R4C2 and R4C3 are both dogs, so R4C1 must be a cat (no three in a row).
  21. R2C4 and R3C4 are both dogs, so R1C4 must be a cat (no three in a row).
  22. R1C3 and R1C4 are both cats, so R1C2 must be a dog (no three in a row).
  23. R1C3 and R1C4 are both cats, so R1C5 must be a dog (no three in a row).
  24. R5C4 and R6C4 are both dogs, so R7C4 must be a cat (no three in a row).
  25. R2C5 and R3C5 are both cats, so R4C5 must be a dog (no three in a row).
  26. R7C7 and R8C7 are both cats, so R6C7 must be a dog (no three in a row).
  27. The × clue between R6C7 and R6C8 means they are different. R6C7 is a dog, so R6C8 is a cat.
  28. R5C8 and R6C8 are both cats, so R4C8 must be a dog (no three in a row).
  29. R5C8 and R6C8 are both cats, so R7C8 must be a dog (no three in a row).
  30. Row 4 already has its 4 dogs, so R4C6 and R4C7 must be cats.
  31. Column 3 already has its 4 cats, so R8C3 must be dogs.
  32. The × clue between R8C3 and R8C2 means they are different. R8C3 is a dog, so R8C2 is a cat.
  33. Column 2 already has its 4 cats, so R2C2 must be dogs.
  34. Column 4 already has its 4 dogs, so R8C4 must be cats.
  35. Row 8 already has its 4 cats, so R8C5 must be dogs.
  36. The = clue between R8C5 and R7C5 means they are the same. R8C5 is a dog, so R7C5 is a dog.
  37. R7C5 and R8C5 are both dogs, so R6C5 must be a cat (no three in a row).
  38. Row 6 already has its 4 cats, so R6C6 must be dogs.
  39. Row 7 already has its 4 dogs, so R7C6 must be cats.
  40. Row 8 already has its 4 cats, so R8C6 and R8C8 must be dogs.
  41. Column 5 already has its 4 dogs, so R5C5 must be cats.
  42. Row 5 already has its 4 cats, so R5C6 and R5C7 must be dogs.
  43. Column 6 already has its 4 dogs, so R1C6 and R3C6 must be cats.
  44. R3C5 and R3C6 are both cats, so R3C7 must be a dog (no three in a row).
  45. The × clue between R3C7 and R2C7 means they are different. R3C7 is a dog, so R2C7 is a cat.
  46. Column 7 already has its 4 cats, so R1C7 must be dogs.
  47. Row 1 already has its 4 dogs, so R1C1 must be cats.
  48. Column 1 already has its 4 cats, so R2C1 must be dogs.
  49. Row 2 already has its 4 dogs, so R2C8 must be cats.
  50. Column 1 already has its 4 cats, so R3C1 must be dogs.
  51. Row 3 already has its 4 dogs, so R3C8 must be cats.

About this puzzle

This 8×8 grid starts with 9 filled squares and 13 = / × 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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