Cats & Dogs #83: 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 R2C3 and R1C3 means they are the same. R2C3 is a cat, so R1C3 is a cat.
  2. The × clue between R1C3 and R1C2 means they are different. R1C3 is a cat, so R1C2 is a dog.
  3. The = clue between R4C3 and R4C2 means they are the same. R4C3 is a cat, so R4C2 is a cat.
  4. R1C3 and R1C5 are both cats with one square between them, so R1C4 must be a dog.
  5. The × clue between R1C4 and R2C4 means they are different. R1C4 is a dog, so R2C4 is a cat.
  6. The × clue between R2C4 and R3C4 means they are different. R2C4 is a cat, so R3C4 is a dog.
  7. R2C3 and R2C4 are both cats, so R2C2 must be a dog (no three in a row).
  8. The = clue between R2C2 and R2C1 means they are the same. R2C2 is a dog, so R2C1 is a dog.
  9. R2C3 and R2C4 are both cats, so R2C5 must be a dog (no three in a row).
  10. R4C2 and R4C3 are both cats, so R4C1 must be a dog (no three in a row).
  11. R4C2 and R4C3 are both cats, so R4C4 must be a dog (no three in a row).
  12. R2C1 and R4C1 are both dogs with one square between them, so R3C1 must be a cat.
  13. R1C2 and R2C2 are both dogs, so R3C2 must be a cat (no three in a row).
  14. R3C1 and R3C2 are both cats, so R3C3 must be a dog (no three in a row).
  15. R3C3 and R3C4 are both dogs, so R3C5 must be a cat (no three in a row).
  16. R3C2 and R4C2 are both cats, so R5C2 must be a dog (no three in a row).
  17. R3C4 and R4C4 are both dogs, so R5C4 must be a cat (no three in a row).
  18. R5C4 and R5C6 are both cats with one square between them, so R5C5 must be a dog.
  19. Row 2 already has its 3 dogs, so R2C6 must be cats.
  20. Row 3 already has its 3 cats, so R3C6 must be dogs.
  21. Column 2 already has its 3 dogs, so R6C2 must be cats.
  22. The = clue between R6C2 and R6C1 means they are the same. R6C2 is a cat, so R6C1 is a cat.
  23. R6C1 and R6C2 are both cats, so R6C3 must be a dog (no three in a row).
  24. Column 3 already has its 3 cats, so R5C3 must be dogs.
  25. R5C2 and R5C3 are both dogs, so R5C1 must be a cat (no three in a row).
  26. Column 1 already has its 3 cats, so R1C1 must be dogs.
  27. Row 1 already has its 3 dogs, so R1C6 must be cats.
  28. Column 4 already has its 3 dogs, so R6C4 must be cats.
  29. Row 6 already has its 3 cats, so R6C5 must be dogs.
  30. R5C5 and R6C5 are both dogs, so R4C5 must be a cat (no three in a row).
  31. Row 4 already has its 3 cats, so R4C6 must be dogs.
  32. Row 6 already has its 3 cats, so R6C6 must be dogs.

About this puzzle

This 6×6 grid starts with 4 filled squares and 7 = / × clues. It can be solved in 32 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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