Cats & Dogs #117: 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 R3C1 and R4C1 means they are different. R3C1 is a cat, so R4C1 is a dog.
  2. The = clue between R4C1 and R4C2 means they are the same. R4C1 is a dog, so R4C2 is a dog.
  3. The = clue between R7C3 and R7C2 means they are the same. R7C3 is a dog, so R7C2 is a dog.
  4. The = clue between R8C5 and R7C5 means they are the same. R8C5 is a dog, so R7C5 is a dog.
  5. R4C1 and R4C2 are both dogs, so R4C3 must be a cat (no three in a row).
  6. R7C2 and R7C3 are both dogs, so R7C1 must be a cat (no three in a row).
  7. The = clue between R7C1 and R8C1 means they are the same. R7C1 is a cat, so R8C1 is a cat.
  8. The = clue between R8C1 and R8C2 means they are the same. R8C1 is a cat, so R8C2 is a cat.
  9. R7C2 and R7C3 are both dogs, so R7C4 must be a cat (no three in a row).
  10. R7C5 and R7C6 are both dogs, so R7C7 must be a cat (no three in a row).
  11. The × clue between R7C7 and R6C7 means they are different. R7C7 is a cat, so R6C7 is a dog.
  12. The × clue between R6C7 and R5C7 means they are different. R6C7 is a dog, so R5C7 is a cat.
  13. R8C1 and R8C2 are both cats, so R8C3 must be a dog (no three in a row).
  14. R8C3 and R8C5 are both dogs with one square between them, so R8C4 must be a cat.
  15. R7C1 and R8C1 are both cats, so R6C1 must be a dog (no three in a row).
  16. R4C1 and R6C1 are both dogs with one square between them, so R5C1 must be a cat.
  17. R7C3 and R8C3 are both dogs, so R6C3 must be a cat (no three in a row).
  18. R4C3 and R6C3 are both cats with one square between them, so R5C3 must be a dog.
  19. R7C4 and R8C4 are both cats, so R6C4 must be a dog (no three in a row).
  20. R7C5 and R8C5 are both dogs, so R6C5 must be a cat (no three in a row).
  21. Row 7 already has its 4 dogs, so R7C8 must be cats.
  22. The × clue between R7C8 and R6C8 means they are different. R7C8 is a cat, so R6C8 is a dog.
  23. R6C7 and R6C8 are both dogs, so R6C6 must be a cat (no three in a row).
  24. Row 6 already has its 4 dogs, so R6C2 must be cats.
  25. The × clue between R6C2 and R5C2 means they are different. R6C2 is a cat, so R5C2 is a dog.
  26. R5C2 and R5C3 are both dogs, so R5C4 must be a cat (no three in a row).
  27. R4C2 and R5C2 are both dogs, so R3C2 must be a cat (no three in a row).
  28. R3C1 and R3C2 are both cats, so R3C3 must be a dog (no three in a row).
  29. R3C3 and R3C5 are both dogs with one square between them, so R3C4 must be a cat.
  30. R3C4 and R5C4 are both cats with one square between them, so R4C4 must be a dog.
  31. Column 1 already has its 4 cats, so R1C1 and R2C1 must be dogs.
  32. Column 3 already has its 4 dogs, so R1C3 must be cats.
  33. The = clue between R1C3 and R1C2 means they are the same. R1C3 is a cat, so R1C2 is a cat.
  34. R1C2 and R1C3 are both cats, so R1C4 must be a dog (no three in a row).
  35. R1C2 and R3C2 are both cats with one square between them, so R2C2 must be a dog.
  36. R2C1 and R2C2 are both dogs, so R2C3 must be a cat (no three in a row).
  37. Column 4 already has its 4 cats, so R2C4 must be dogs.
  38. The × clue between R2C4 and R2C5 means they are different. R2C4 is a dog, so R2C5 is a cat.
  39. The = clue between R2C5 and R2C6 means they are the same. R2C5 is a cat, so R2C6 is a cat.
  40. The × clue between R2C6 and R3C6 means they are different. R2C6 is a cat, so R3C6 is a dog.
  41. R2C5 and R2C6 are both cats, so R2C7 must be a dog (no three in a row).
  42. R3C5 and R3C6 are both dogs, so R3C7 must be a cat (no three in a row).
  43. R3C7 and R5C7 are both cats with one square between them, so R4C7 must be a dog.
  44. Row 2 already has its 4 dogs, so R2C8 must be cats.
  45. Row 3 already has its 4 cats, so R3C8 must be dogs.
  46. Row 4 already has its 4 dogs, so R4C5 must be cats.
  47. R4C5 and R6C5 are both cats with one square between them, so R5C5 must be a dog.
  48. Row 4 already has its 4 dogs, so R4C6 must be cats.
  49. R4C6 and R6C6 are both cats with one square between them, so R5C6 must be a dog.
  50. Row 4 already has its 4 dogs, so R4C8 must be cats.
  51. Row 5 already has its 4 dogs, so R5C8 must be cats.
  52. Column 5 already has its 4 dogs, so R1C5 must be cats.
  53. Column 8 already has its 4 cats, so R1C8 must be dogs.
  54. The = clue between R1C8 and R1C7 means they are the same. R1C8 is a dog, so R1C7 is a dog.
  55. R1C7 and R1C8 are both dogs, so R1C6 must be a cat (no three in a row).
  56. Column 6 already has its 4 cats, so R8C6 must be dogs.
  57. R8C5 and R8C6 are both dogs, so R8C7 must be a cat (no three in a row).
  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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