Cats & Dogs #119: 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

Use pure logic to place every cat and dog. Each row and column holds 4 of each animal, three in a row is never allowed, and the clues between squares settle the rest.

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

About this puzzle

This 8×8 grid starts with 6 filled squares and 13 = / × clues. It can be solved in 54 steps using pairs, gaps, counts and clues.

Whenever two of the same animal sit side by side, the squares on both ends must be the other animal. Look for these pairs first.

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

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