Cats & Dogs #38: 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 R3C4 and R3C3 means they are the same. R3C4 is a cat, so R3C3 is a cat.
  2. R3C3 and R3C4 are both cats, so R3C2 must be a dog (no three in a row).
  3. The = clue between R3C2 and R2C2 means they are the same. R3C2 is a dog, so R2C2 is a dog.
  4. The × clue between R3C2 and R3C1 means they are different. R3C2 is a dog, so R3C1 is a cat.
  5. R3C3 and R3C4 are both cats, so R3C5 must be a dog (no three in a row).
  6. R2C2 and R3C2 are both dogs, so R1C2 must be a cat (no three in a row).
  7. R2C2 and R3C2 are both dogs, so R4C2 must be a cat (no three in a row).
  8. R4C2 and R6C2 are both cats with one square between them, so R5C2 must be a dog.
  9. R5C2 and R5C4 are both dogs with one square between them, so R5C3 must be a cat.
  10. R3C3 and R5C3 are both cats with one square between them, so R4C3 must be a dog.
  11. Row 3 already has its 3 cats, so R3C6 must be dogs.
  12. The = clue between R3C6 and R4C6 means they are the same. R3C6 is a dog, so R4C6 is a dog.
  13. R3C6 and R4C6 are both dogs, so R2C6 must be a cat (no three in a row).
  14. R3C6 and R4C6 are both dogs, so R5C6 must be a cat (no three in a row).
  15. The × clue between R5C6 and R5C5 means they are different. R5C6 is a cat, so R5C5 is a dog.
  16. R3C5 and R5C5 are both dogs with one square between them, so R4C5 must be a cat.
  17. Row 5 already has its 3 dogs, so R5C1 must be cats.
  18. R3C1 and R5C1 are both cats with one square between them, so R4C1 must be a dog.
  19. Row 4 already has its 3 dogs, so R4C4 must be cats.
  20. R3C4 and R4C4 are both cats, so R2C4 must be a dog (no three in a row).
  21. R2C2 and R2C4 are both dogs with one square between them, so R2C3 must be a cat.
  22. R2C3 and R3C3 are both cats, so R1C3 must be a dog (no three in a row).
  23. The = clue between R1C3 and R1C4 means they are the same. R1C3 is a dog, so R1C4 is a dog.
  24. R1C3 and R1C4 are both dogs, so R1C5 must be a cat (no three in a row).
  25. The × clue between R1C5 and R2C5 means they are different. R1C5 is a cat, so R2C5 is a dog.
  26. Row 2 already has its 3 dogs, so R2C1 must be cats.
  27. R2C1 and R3C1 are both cats, so R1C1 must be a dog (no three in a row).
  28. Row 1 already has its 3 dogs, so R1C6 must be cats.
  29. Column 1 already has its 3 cats, so R6C1 must be dogs.
  30. Column 3 already has its 3 cats, so R6C3 must be dogs.
  31. Column 4 already has its 3 dogs, so R6C4 must be cats.
  32. Column 5 already has its 3 dogs, so R6C5 must be cats.
  33. R6C4 and R6C5 are both cats, so R6C6 must be a dog (no three in a row).

About this puzzle

This 6×6 grid starts with 3 filled squares and 7 = / × clues. It can be solved in 33 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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