Cats & Dogs #127: 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 R3C8 and R2C8 means they are different. R3C8 is a cat, so R2C8 is a dog.
  2. The × clue between R4C6 and R3C6 means they are different. R4C6 is a dog, so R3C6 is a cat.
  3. R2C7 and R2C8 are both dogs, so R2C6 must be a cat (no three in a row).
  4. R3C6 and R3C8 are both cats with one square between them, so R3C7 must be a dog.
  5. R6C5 and R6C6 are both cats, so R6C4 must be a dog (no three in a row).
  6. R6C5 and R6C6 are both cats, so R6C7 must be a dog (no three in a row).
  7. R7C1 and R7C2 are both dogs, so R7C3 must be a cat (no three in a row).
  8. R6C4 and R8C4 are both dogs with one square between them, so R7C4 must be a cat.
  9. R7C3 and R7C4 are both cats, so R7C5 must be a dog (no three in a row).
  10. R2C6 and R3C6 are both cats, so R1C6 must be a dog (no three in a row).
  11. The × clue between R1C6 and R1C5 means they are different. R1C6 is a dog, so R1C5 is a cat.
  12. The = clue between R1C5 and R2C5 means they are the same. R1C5 is a cat, so R2C5 is a cat.
  13. R2C5 and R2C6 are both cats, so R2C4 must be a dog (no three in a row).
  14. R2C2 and R2C4 are both dogs with one square between them, so R2C3 must be a cat.
  15. R1C5 and R2C5 are both cats, so R3C5 must be a dog (no three in a row).
  16. R3C5 and R5C5 are both dogs with one square between them, so R4C5 must be a cat.
  17. R2C7 and R3C7 are both dogs, so R1C7 must be a cat (no three in a row).
  18. R2C7 and R3C7 are both dogs, so R4C7 must be a cat (no three in a row).
  19. Row 2 already has its 4 dogs, so R2C1 must be cats.
  20. R1C1 and R2C1 are both cats, so R3C1 must be a dog (no three in a row).
  21. Column 5 already has its 4 cats, so R8C5 must be dogs.
  22. R8C4 and R8C5 are both dogs, so R8C3 must be a cat (no three in a row).
  23. R8C4 and R8C5 are both dogs, so R8C6 must be a cat (no three in a row).
  24. R7C3 and R8C3 are both cats, so R6C3 must be a dog (no three in a row).
  25. R6C3 and R6C4 are both dogs, so R6C2 must be a cat (no three in a row).
  26. R5C2 and R6C2 are both cats, so R4C2 must be a dog (no three in a row).
  27. The = clue between R4C2 and R4C1 means they are the same. R4C2 is a dog, so R4C1 is a dog.
  28. R4C1 and R4C2 are both dogs, so R4C3 must be a cat (no three in a row).
  29. R4C3 and R4C5 are both cats with one square between them, so R4C4 must be a dog.
  30. R3C1 and R4C1 are both dogs, so R5C1 must be a cat (no three in a row).
  31. R5C1 and R5C2 are both cats, so R5C3 must be a dog (no three in a row).
  32. R5C3 and R5C5 are both dogs with one square between them, so R5C4 must be a cat.
  33. R2C2 and R4C2 are both dogs with one square between them, so R3C2 must be a cat.
  34. R2C3 and R4C3 are both cats with one square between them, so R3C3 must be a dog.
  35. R3C3 and R3C5 are both dogs with one square between them, so R3C4 must be a cat.
  36. R6C6 and R8C6 are both cats with one square between them, so R7C6 must be a dog.
  37. R7C5 and R7C6 are both dogs, so R7C7 must be a cat (no three in a row).
  38. Row 4 already has its 4 dogs, so R4C8 must be cats.
  39. R3C8 and R4C8 are both cats, so R5C8 must be a dog (no three in a row).
  40. Row 7 already has its 4 dogs, so R7C8 must be cats.
  41. Column 3 already has its 4 cats, so R1C3 must be dogs.
  42. Column 4 already has its 4 dogs, so R1C4 must be cats.
  43. Row 1 already has its 4 cats, so R1C2 and R1C8 must be dogs.
  44. Column 2 already has its 4 dogs, so R8C2 must be cats.
  45. R8C2 and R8C3 are both cats, so R8C1 must be a dog (no three in a row).
  46. R7C1 and R8C1 are both dogs, so R6C1 must be a cat (no three in a row).
  47. Row 6 already has its 4 cats, so R6C8 must be dogs.
  48. Column 6 already has its 4 cats, so R5C6 must be dogs.
  49. R5C5 and R5C6 are both dogs, so R5C7 must be a cat (no three in a row).
  50. Column 7 already has its 4 cats, so R8C7 must be dogs.
  51. Row 8 already has its 4 dogs, so R8C8 must be cats.

About this puzzle

This 8×8 grid starts with 12 filled squares and 5 = / × clues. It can be solved in 51 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.

Every puzzle on this site has exactly one solution that can be reached by deduction. If you are guessing, look again at the rows and columns that are nearly full.

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