Cats & Dogs #169: 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 R5C7 and R6C7 means they are different. R5C7 is a dog, so R6C7 is a cat.
  2. The = clue between R6C6 and R7C6 means they are the same. R6C6 is a dog, so R7C6 is a dog.
  3. The × clue between R7C2 and R8C2 means they are different. R7C2 is a dog, so R8C2 is a cat.
  4. R4C1 and R4C3 are both cats with one square between them, so R4C2 must be a dog.
  5. R6C2 and R6C4 are both cats with one square between them, so R6C3 must be a dog.
  6. R7C5 and R7C6 are both dogs, so R7C4 must be a cat (no three in a row).
  7. R7C5 and R7C6 are both dogs, so R7C7 must be a cat (no three in a row).
  8. The × clue between R7C7 and R7C8 means they are different. R7C7 is a cat, so R7C8 is a dog.
  9. R2C1 and R4C1 are both cats with one square between them, so R3C1 must be a dog.
  10. R6C4 and R7C4 are both cats, so R5C4 must be a dog (no three in a row).
  11. R6C4 and R7C4 are both cats, so R8C4 must be a dog (no three in a row).
  12. R6C6 and R7C6 are both dogs, so R5C6 must be a cat (no three in a row).
  13. R6C6 and R7C6 are both dogs, so R8C6 must be a cat (no three in a row).
  14. R6C7 and R7C7 are both cats, so R8C7 must be a dog (no three in a row).
  15. Row 7 already has its 4 dogs, so R7C1 must be cats.
  16. The = clue between R7C1 and R6C1 means they are the same. R7C1 is a cat, so R6C1 is a cat.
  17. R4C1 and R6C1 are both cats with one square between them, so R5C1 must be a dog.
  18. R6C1 and R7C1 are both cats, so R8C1 must be a dog (no three in a row).
  19. Row 6 already has its 4 cats, so R6C5 must be dogs.
  20. R6C5 and R7C5 are both dogs, so R5C5 must be a cat (no three in a row).
  21. The = clue between R5C5 and R4C5 means they are the same. R5C5 is a cat, so R4C5 is a cat.
  22. The = clue between R4C5 and R4C6 means they are the same. R4C5 is a cat, so R4C6 is a cat.
  23. R4C3 and R4C5 are both cats with one square between them, so R4C4 must be a dog.
  24. R4C5 and R4C6 are both cats, so R4C7 must be a dog (no three in a row).
  25. R4C4 and R5C4 are both dogs, so R3C4 must be a cat (no three in a row).
  26. The = clue between R3C4 and R3C3 means they are the same. R3C4 is a cat, so R3C3 is a cat.
  27. R3C3 and R3C4 are both cats, so R3C2 must be a dog (no three in a row).
  28. R3C3 and R3C4 are both cats, so R3C5 must be a dog (no three in a row).
  29. R3C2 and R4C2 are both dogs, so R2C2 must be a cat (no three in a row).
  30. R2C1 and R2C2 are both cats, so R2C3 must be a dog (no three in a row).
  31. R3C2 and R4C2 are both dogs, so R5C2 must be a cat (no three in a row).
  32. R3C3 and R4C3 are both cats, so R5C3 must be a dog (no three in a row).
  33. R5C3 and R6C3 are both dogs, so R7C3 must be a cat (no three in a row).
  34. R6C5 and R7C5 are both dogs, so R8C5 must be a cat (no three in a row).
  35. R2C6 and R4C6 are both cats with one square between them, so R3C6 must be a dog.
  36. R3C5 and R3C6 are both dogs, so R3C7 must be a cat (no three in a row).
  37. Row 3 already has its 4 dogs, so R3C8 must be cats.
  38. Row 4 already has its 4 cats, so R4C8 must be dogs.
  39. Row 5 already has its 4 dogs, so R5C8 must be cats.
  40. Row 6 already has its 4 cats, so R6C8 must be dogs.
  41. R6C8 and R7C8 are both dogs, so R8C8 must be a cat (no three in a row).
  42. Row 8 already has its 4 cats, so R8C3 must be dogs.
  43. Column 1 already has its 4 cats, so R1C1 must be dogs.
  44. Column 2 already has its 4 cats, so R1C2 must be dogs.
  45. R1C1 and R1C2 are both dogs, so R1C3 must be a cat (no three in a row).
  46. The × clue between R1C3 and R1C4 means they are different. R1C3 is a cat, so R1C4 is a dog.
  47. Column 4 already has its 4 dogs, so R2C4 must be cats.
  48. R2C4 and R2C6 are both cats with one square between them, so R2C5 must be a dog.
  49. R2C5 and R3C5 are both dogs, so R1C5 must be a cat (no three in a row).
  50. Row 2 already has its 4 cats, so R2C7 and R2C8 must be dogs.
  51. Column 6 already has its 4 cats, so R1C6 must be dogs.
  52. Row 1 already has its 4 dogs, so R1C7 and R1C8 must be cats.

About this puzzle

This 8×8 grid starts with 10 filled squares and 9 = / × clues. It can be solved in 52 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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