Cats & Dogs #16: 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

A 6x6 logic grid: 3 cats and 3 dogs in every row and column, no three of a kind in a row, and a few = and × clues to point the way.

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

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.

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.

This kind of puzzle is known as a binary or Takuzu puzzle, here with cats and dogs and extra = / × clues.

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