Cats & Dogs #110: 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 R1C4 and R1C5 means they are the same. R1C4 is a cat, so R1C5 is a cat.
  2. The = clue between R5C1 and R4C1 means they are the same. R5C1 is a cat, so R4C1 is a cat.
  3. The × clue between R5C4 and R4C4 means they are different. R5C4 is a cat, so R4C4 is a dog.
  4. The = clue between R4C4 and R3C4 means they are the same. R4C4 is a dog, so R3C4 is a dog.
  5. The × clue between R6C8 and R6C7 means they are different. R6C8 is a cat, so R6C7 is a dog.
  6. The × clue between R6C7 and R6C6 means they are different. R6C7 is a dog, so R6C6 is a cat.
  7. R1C4 and R1C5 are both cats, so R1C3 must be a dog (no three in a row).
  8. R1C4 and R1C5 are both cats, so R1C6 must be a dog (no three in a row).
  9. R4C3 and R4C4 are both dogs, so R4C2 must be a cat (no three in a row).
  10. R4C3 and R4C4 are both dogs, so R4C5 must be a cat (no three in a row).
  11. R4C5 and R4C7 are both cats with one square between them, so R4C6 must be a dog.
  12. The = clue between R4C6 and R3C6 means they are the same. R4C6 is a dog, so R3C6 is a dog.
  13. R3C4 and R3C6 are both dogs with one square between them, so R3C5 must be a cat.
  14. R4C1 and R5C1 are both cats, so R3C1 must be a dog (no three in a row).
  15. R4C1 and R5C1 are both cats, so R6C1 must be a dog (no three in a row).
  16. R3C4 and R4C4 are both dogs, so R2C4 must be a cat (no three in a row).
  17. R1C5 and R3C5 are both cats with one square between them, so R2C5 must be a dog.
  18. R3C5 and R4C5 are both cats, so R5C5 must be a dog (no three in a row).
  19. The × clue between R5C5 and R6C5 means they are different. R5C5 is a dog, so R6C5 is a cat.
  20. R6C5 and R6C6 are both cats, so R6C4 must be a dog (no three in a row).
  21. R1C6 and R3C6 are both dogs with one square between them, so R2C6 must be a cat.
  22. R3C6 and R4C6 are both dogs, so R5C6 must be a cat (no three in a row).
  23. R5C6 and R6C6 are both cats, so R7C6 must be a dog (no three in a row).
  24. Row 4 already has its 4 cats, so R4C8 must be dogs.
  25. The = clue between R4C8 and R3C8 means they are the same. R4C8 is a dog, so R3C8 is a dog.
  26. R3C6 and R3C8 are both dogs with one square between them, so R3C7 must be a cat.
  27. R3C7 and R4C7 are both cats, so R2C7 must be a dog (no three in a row).
  28. R3C7 and R4C7 are both cats, so R5C7 must be a dog (no three in a row).
  29. R5C7 and R6C7 are both dogs, so R7C7 must be a cat (no three in a row).
  30. R3C8 and R4C8 are both dogs, so R2C8 must be a cat (no three in a row).
  31. R3C8 and R4C8 are both dogs, so R5C8 must be a cat (no three in a row).
  32. R5C8 and R6C8 are both cats, so R7C8 must be a dog (no three in a row).
  33. Row 3 already has its 4 dogs, so R3C2 must be cats.
  34. R3C2 and R4C2 are both cats, so R2C2 must be a dog (no three in a row).
  35. R3C2 and R4C2 are both cats, so R5C2 must be a dog (no three in a row).
  36. Row 3 already has its 4 dogs, so R3C3 must be cats.
  37. Row 5 already has its 4 cats, so R5C3 must be dogs.
  38. R4C3 and R5C3 are both dogs, so R6C3 must be a cat (no three in a row).
  39. Row 6 already has its 4 cats, so R6C2 must be dogs.
  40. R5C2 and R6C2 are both dogs, so R7C2 must be a cat (no three in a row).
  41. Column 5 already has its 4 cats, so R7C5 must be dogs.
  42. R7C5 and R7C6 are both dogs, so R7C4 must be a cat (no three in a row).
  43. R7C2 and R7C4 are both cats with one square between them, so R7C3 must be a dog.
  44. Row 7 already has its 4 dogs, so R7C1 must be cats.
  45. Column 3 already has its 4 dogs, so R2C3 must be cats.
  46. Row 2 already has its 4 cats, so R2C1 must be dogs.
  47. R2C1 and R3C1 are both dogs, so R1C1 must be a cat (no three in a row).
  48. Column 1 already has its 4 cats, so R8C1 must be dogs.
  49. Column 3 already has its 4 dogs, so R8C3 must be cats.
  50. Column 4 already has its 4 cats, so R8C4 must be dogs.
  51. Column 5 already has its 4 cats, so R8C5 must be dogs.
  52. R8C4 and R8C5 are both dogs, so R8C6 must be a cat (no three in a row).
  53. The = clue between R8C6 and R8C7 means they are the same. R8C6 is a cat, so R8C7 is a cat.
  54. R8C6 and R8C7 are both cats, so R8C8 must be a dog (no three in a row).
  55. Row 8 already has its 4 dogs, so R8C2 must be cats.
  56. Column 2 already has its 4 cats, so R1C2 must be dogs.
  57. Column 7 already has its 4 cats, so R1C7 must be dogs.
  58. R1C6 and R1C7 are both dogs, so R1C8 must be a cat (no three in a row).

About this puzzle

This 8×8 grid starts with 6 filled squares and 10 = / × clues. It can be solved in 58 steps using pairs, gaps, counts and clues.

Count as you go. Once a row or column has all of one animal, every remaining empty square in it must be the other.

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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