Cats & Dogs #82: 6x6 Grid Puzzle (Easy)

easy

Tap a square: 🐱 cat → 🐶 dog → clear

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🐱 3 cats and 🐶 3 dogs in every row and column = same   × different

Fill the 6x6 grid with cats and dogs so that every row and every column has exactly 3 of each, and never more than two of the same animal side by side.

  • Exactly 3 cats and 3 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 R3C3 and R4C3 means they are the same. R3C3 is a dog, so R4C3 is a dog.
  2. The × clue between R6C1 and R6C2 means they are different. R6C1 is a cat, so R6C2 is a dog.
  3. R4C5 and R4C6 are both cats, so R4C4 must be a dog (no three in a row).
  4. R4C3 and R4C4 are both dogs, so R4C2 must be a cat (no three in a row).
  5. R3C2 and R4C2 are both cats, so R2C2 must be a dog (no three in a row).
  6. R3C2 and R4C2 are both cats, so R5C2 must be a dog (no three in a row).
  7. R3C3 and R4C3 are both dogs, so R2C3 must be a cat (no three in a row).
  8. The = clue between R2C3 and R1C3 means they are the same. R2C3 is a cat, so R1C3 is a cat.
  9. R3C3 and R4C3 are both dogs, so R5C3 must be a cat (no three in a row).
  10. Row 4 already has its 3 cats, so R4C1 must be dogs.
  11. The × clue between R4C1 and R3C1 means they are different. R4C1 is a dog, so R3C1 is a cat.
  12. Column 2 already has its 3 dogs, so R1C2 must be cats.
  13. R1C2 and R1C3 are both cats, so R1C1 must be a dog (no three in a row).
  14. R1C2 and R1C3 are both cats, so R1C4 must be a dog (no three in a row).
  15. The × clue between R1C4 and R2C4 means they are different. R1C4 is a dog, so R2C4 is a cat.
  16. R2C3 and R2C4 are both cats, so R2C5 must be a dog (no three in a row).
  17. The × clue between R2C5 and R1C5 means they are different. R2C5 is a dog, so R1C5 is a cat.
  18. The × clue between R2C5 and R3C5 means they are different. R2C5 is a dog, so R3C5 is a cat.
  19. R3C5 and R4C5 are both cats, so R5C5 must be a dog (no three in a row).
  20. Row 1 already has its 3 cats, so R1C6 must be dogs.
  21. Row 3 already has its 3 cats, so R3C4 must be dogs.
  22. R3C4 and R4C4 are both dogs, so R5C4 must be a cat (no three in a row).
  23. Row 3 already has its 3 cats, so R3C6 must be dogs.
  24. R1C6 and R3C6 are both dogs with one square between them, so R2C6 must be a cat.
  25. Row 2 already has its 3 cats, so R2C1 must be dogs.
  26. Column 1 already has its 3 dogs, so R5C1 must be cats.
  27. Row 5 already has its 3 cats, so R5C6 must be dogs.
  28. Column 3 already has its 3 cats, so R6C3 must be dogs.
  29. R6C2 and R6C3 are both dogs, so R6C4 must be a cat (no three in a row).
  30. Column 5 already has its 3 cats, so R6C5 must be dogs.
  31. Row 6 already has its 3 dogs, so R6C6 must be cats.

About this puzzle

This 6×6 grid starts with 5 filled squares and 7 = / × clues. It can be solved in 31 steps using pairs, gaps, counts and clues.

Watch for a gap: if the squares on either side of an empty square match, the empty one must be different.

When every square is filled, press Check Answer. The grid is verified against the stored solution and any broken rule is named.

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