Cats & Dogs #167: 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 R2C4 and R2C3 means they are the same. R2C4 is a cat, so R2C3 is a cat.
  2. The = clue between R2C3 and R1C3 means they are the same. R2C3 is a cat, so R1C3 is a cat.
  3. The = clue between R8C4 and R8C3 means they are the same. R8C4 is a dog, so R8C3 is a dog.
  4. R2C3 and R2C4 are both cats, so R2C2 must be a dog (no three in a row).
  5. R2C3 and R2C4 are both cats, so R2C5 must be a dog (no three in a row).
  6. The = clue between R2C5 and R1C5 means they are the same. R2C5 is a dog, so R1C5 is a dog.
  7. The × clue between R1C5 and R1C4 means they are different. R1C5 is a dog, so R1C4 is a cat.
  8. R1C3 and R1C4 are both cats, so R1C2 must be a dog (no three in a row).
  9. R8C3 and R8C4 are both dogs, so R8C2 must be a cat (no three in a row).
  10. R8C3 and R8C4 are both dogs, so R8C5 must be a cat (no three in a row).
  11. R1C2 and R2C2 are both dogs, so R3C2 must be a cat (no three in a row).
  12. The × clue between R3C2 and R4C2 means they are different. R3C2 is a cat, so R4C2 is a dog.
  13. The × clue between R4C2 and R5C2 means they are different. R4C2 is a dog, so R5C2 is a cat.
  14. The = clue between R5C2 and R5C3 means they are the same. R5C2 is a cat, so R5C3 is a cat.
  15. The × clue between R5C3 and R6C3 means they are different. R5C3 is a cat, so R6C3 is a dog.
  16. R5C2 and R5C3 are both cats, so R5C1 must be a dog (no three in a row).
  17. R5C2 and R5C3 are both cats, so R5C4 must be a dog (no three in a row).
  18. R1C3 and R2C3 are both cats, so R3C3 must be a dog (no three in a row).
  19. R6C3 and R8C3 are both dogs with one square between them, so R7C3 must be a cat.
  20. The × clue between R7C3 and R7C2 means they are different. R7C3 is a cat, so R7C2 is a dog.
  21. R1C4 and R2C4 are both cats, so R3C4 must be a dog (no three in a row).
  22. R3C3 and R3C4 are both dogs, so R3C5 must be a cat (no three in a row).
  23. R3C4 and R5C4 are both dogs with one square between them, so R4C4 must be a cat.
  24. R4C4 and R4C6 are both cats with one square between them, so R4C5 must be a dog.
  25. The × clue between R4C5 and R5C5 means they are different. R4C5 is a dog, so R5C5 is a cat.
  26. The = clue between R5C5 and R5C6 means they are the same. R5C5 is a cat, so R5C6 is a cat.
  27. R5C5 and R5C6 are both cats, so R5C7 must be a dog (no three in a row).
  28. R4C6 and R5C6 are both cats, so R3C6 must be a dog (no three in a row).
  29. R3C6 and R3C8 are both dogs with one square between them, so R3C7 must be a cat.
  30. The = clue between R3C7 and R2C7 means they are the same. R3C7 is a cat, so R2C7 is a cat.
  31. R4C6 and R5C6 are both cats, so R6C6 must be a dog (no three in a row).
  32. R6C6 and R6C8 are both dogs with one square between them, so R6C7 must be a cat.
  33. R2C7 and R3C7 are both cats, so R1C7 must be a dog (no three in a row).
  34. R1C5 and R1C7 are both dogs with one square between them, so R1C6 must be a cat.
  35. R2C7 and R3C7 are both cats, so R4C7 must be a dog (no three in a row).
  36. Row 3 already has its 4 dogs, so R3C1 must be cats.
  37. Row 5 already has its 4 cats, so R5C8 must be dogs.
  38. R3C8 and R5C8 are both dogs with one square between them, so R4C8 must be a cat.
  39. R5C8 and R6C8 are both dogs, so R7C8 must be a cat (no three in a row).
  40. Column 2 already has its 4 dogs, so R6C2 must be cats.
  41. The × clue between R6C2 and R6C1 means they are different. R6C2 is a cat, so R6C1 is a dog.
  42. R5C1 and R6C1 are both dogs, so R4C1 must be a cat (no three in a row).
  43. R3C1 and R4C1 are both cats, so R2C1 must be a dog (no three in a row).
  44. R5C1 and R6C1 are both dogs, so R7C1 must be a cat (no three in a row).
  45. Row 4 already has its 4 cats, so R4C3 must be dogs.
  46. Row 6 already has its 4 dogs, so R6C4 and R6C5 must be cats.
  47. R5C5 and R6C5 are both cats, so R7C5 must be a dog (no three in a row).
  48. Column 4 already has its 4 cats, so R7C4 must be dogs.
  49. R7C4 and R7C5 are both dogs, so R7C6 must be a cat (no three in a row).
  50. R7C6 and R7C8 are both cats with one square between them, so R7C7 must be a dog.
  51. Column 6 already has its 4 cats, so R2C6 must be dogs.
  52. Row 2 already has its 4 dogs, so R2C8 must be cats.
  53. The = clue between R2C8 and R1C8 means they are the same. R2C8 is a cat, so R1C8 is a cat.
  54. Row 1 already has its 4 cats, so R1C1 must be dogs.
  55. Column 1 already has its 4 dogs, so R8C1 must be cats.
  56. Column 6 already has its 4 cats, so R8C6 must be dogs.
  57. Column 7 already has its 4 dogs, so R8C7 must be cats.
  58. Row 8 already has its 4 cats, so R8C8 must be dogs.

About this puzzle

This 8×8 grid starts with 5 filled squares and 15 = / × clues. It can be solved in 58 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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