Cats & Dogs #120: 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 R1C1 and R1C2 means they are the same. R1C1 is a cat, so R1C2 is a cat.
  2. The × clue between R5C6 and R6C6 means they are different. R5C6 is a dog, so R6C6 is a cat.
  3. The = clue between R8C2 and R7C2 means they are the same. R8C2 is a dog, so R7C2 is a dog.
  4. R1C1 and R1C2 are both cats, so R1C3 must be a dog (no three in a row).
  5. R2C4 and R2C5 are both cats, so R2C3 must be a dog (no three in a row).
  6. R2C2 and R2C3 are both dogs, so R2C1 must be a cat (no three in a row).
  7. R2C4 and R2C5 are both cats, so R2C6 must be a dog (no three in a row).
  8. The = clue between R2C6 and R2C7 means they are the same. R2C6 is a dog, so R2C7 is a dog.
  9. R2C6 and R2C7 are both dogs, so R2C8 must be a cat (no three in a row).
  10. R6C4 and R6C6 are both cats with one square between them, so R6C5 must be a dog.
  11. The × clue between R6C5 and R5C5 means they are different. R6C5 is a dog, so R5C5 is a cat.
  12. The × clue between R5C5 and R4C5 means they are different. R5C5 is a cat, so R4C5 is a dog.
  13. R4C4 and R4C5 are both dogs, so R4C3 must be a cat (no three in a row).
  14. R4C4 and R4C5 are both dogs, so R4C6 must be a cat (no three in a row).
  15. R7C1 and R7C2 are both dogs, so R7C3 must be a cat (no three in a row).
  16. R1C1 and R2C1 are both cats, so R3C1 must be a dog (no three in a row).
  17. R7C2 and R8C2 are both dogs, so R6C2 must be a cat (no three in a row).
  18. R6C2 and R6C4 are both cats with one square between them, so R6C3 must be a dog.
  19. R1C3 and R2C3 are both dogs, so R3C3 must be a cat (no three in a row).
  20. R3C3 and R4C3 are both cats, so R5C3 must be a dog (no three in a row).
  21. The = clue between R5C3 and R5C2 means they are the same. R5C3 is a dog, so R5C2 is a dog.
  22. R5C2 and R5C3 are both dogs, so R5C1 must be a cat (no three in a row).
  23. R5C2 and R5C3 are both dogs, so R5C4 must be a cat (no three in a row).
  24. R5C4 and R6C4 are both cats, so R7C4 must be a dog (no three in a row).
  25. The × clue between R7C4 and R8C4 means they are different. R7C4 is a dog, so R8C4 is a cat.
  26. R1C8 and R2C8 are both cats, so R3C8 must be a dog (no three in a row).
  27. The = clue between R3C8 and R4C8 means they are the same. R3C8 is a dog, so R4C8 is a dog.
  28. R3C8 and R4C8 are both dogs, so R5C8 must be a cat (no three in a row).
  29. Row 5 already has its 4 cats, so R5C7 must be dogs.
  30. The = clue between R5C7 and R6C7 means they are the same. R5C7 is a dog, so R6C7 is a dog.
  31. R5C7 and R6C7 are both dogs, so R4C7 must be a cat (no three in a row).
  32. R5C7 and R6C7 are both dogs, so R7C7 must be a cat (no three in a row).
  33. Column 2 already has its 4 dogs, so R3C2 must be cats.
  34. R3C2 and R3C3 are both cats, so R3C4 must be a dog (no three in a row).
  35. Column 2 already has its 4 dogs, so R4C2 must be cats.
  36. R4C2 and R4C3 are both cats, so R4C1 must be a dog (no three in a row).
  37. Column 3 already has its 4 dogs, so R8C3 must be cats.
  38. R8C3 and R8C4 are both cats, so R8C5 must be a dog (no three in a row).
  39. R6C5 and R8C5 are both dogs with one square between them, so R7C5 must be a cat.
  40. R7C5 and R7C7 are both cats with one square between them, so R7C6 must be a dog.
  41. Row 7 already has its 4 dogs, so R7C8 must be cats.
  42. R5C8 and R7C8 are both cats with one square between them, so R6C8 must be a dog.
  43. Row 6 already has its 4 dogs, so R6C1 must be cats.
  44. Column 1 already has its 4 cats, so R8C1 must be dogs.
  45. Column 4 already has its 4 cats, so R1C4 must be dogs.
  46. R1C3 and R1C4 are both dogs, so R1C5 must be a cat (no three in a row).
  47. R1C5 and R2C5 are both cats, so R3C5 must be a dog (no three in a row).
  48. R3C4 and R3C5 are both dogs, so R3C6 must be a cat (no three in a row).
  49. Row 1 already has its 4 cats, so R1C6 and R1C7 must be dogs.
  50. R1C7 and R2C7 are both dogs, so R3C7 must be a cat (no three in a row).
  51. Column 6 already has its 4 dogs, so R8C6 must be cats.
  52. Column 7 already has its 4 dogs, so R8C7 must be cats.
  53. R8C6 and R8C7 are both cats, so R8C8 must be a dog (no three in a row).

About this puzzle

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