Cats & Dogs #71: 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. The = clue between R1C3 and R1C2 means they are the same. R1C3 is a cat, so R1C2 is a cat.
  2. The = clue between R5C1 and R5C2 means they are the same. R5C1 is a dog, so R5C2 is a dog.
  3. R1C2 and R1C3 are both cats, so R1C1 must be a dog (no three in a row).
  4. R1C2 and R1C3 are both cats, so R1C4 must be a dog (no three in a row).
  5. R2C2 and R2C3 are both cats, so R2C1 must be a dog (no three in a row).
  6. R2C2 and R2C3 are both cats, so R2C4 must be a dog (no three in a row).
  7. R2C4 and R2C6 are both dogs with one square between them, so R2C5 must be a cat.
  8. R5C1 and R5C2 are both dogs, so R5C3 must be a cat (no three in a row).
  9. R1C1 and R2C1 are both dogs, so R3C1 must be a cat (no three in a row).
  10. R1C2 and R2C2 are both cats, so R3C2 must be a dog (no three in a row).
  11. R3C2 and R5C2 are both dogs with one square between them, so R4C2 must be a cat.
  12. R1C3 and R2C3 are both cats, so R3C3 must be a dog (no three in a row).
  13. R3C2 and R3C3 are both dogs, so R3C4 must be a cat (no three in a row).
  14. R1C5 and R2C5 are both cats, so R3C5 must be a dog (no three in a row).
  15. Row 1 already has its 3 cats, so R1C6 must be dogs.
  16. R1C6 and R2C6 are both dogs, so R3C6 must be a cat (no three in a row).
  17. Row 5 already has its 3 dogs, so R5C5 and R5C6 must be cats.
  18. R3C6 and R5C6 are both cats with one square between them, so R4C6 must be a dog.
  19. Column 1 already has its 3 dogs, so R4C1 must be cats.
  20. R4C1 and R4C2 are both cats, so R4C3 must be a dog (no three in a row).
  21. Column 1 already has its 3 dogs, so R6C1 must be cats.
  22. Column 2 already has its 3 cats, so R6C2 must be dogs.
  23. Column 3 already has its 3 cats, so R6C3 must be dogs.
  24. R6C2 and R6C3 are both dogs, so R6C4 must be a cat (no three in a row).
  25. Column 4 already has its 3 dogs, so R4C4 must be cats.
  26. Row 4 already has its 3 cats, so R4C5 must be dogs.
  27. Column 5 already has its 3 cats, so R6C5 must be dogs.
  28. Row 6 already has its 3 dogs, so R6C6 must be cats.

About this puzzle

This 6×6 grid starts with 7 filled squares and 2 = / × clues. It can be solved in 28 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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