Cats & Dogs #84: 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 R4C6 and R4C5 means they are the same. R4C6 is a cat, so R4C5 is a cat.
  2. R4C5 and R4C6 are both cats, so R4C4 must be a dog (no three in a row).
  3. R4C2 and R4C4 are both dogs with one square between them, so R4C3 must be a cat.
  4. R3C5 and R4C5 are both cats, so R2C5 must be a dog (no three in a row).
  5. The × clue between R2C5 and R1C5 means they are different. R2C5 is a dog, so R1C5 is a cat.
  6. The = clue between R2C5 and R2C6 means they are the same. R2C5 is a dog, so R2C6 is a dog.
  7. R2C5 and R2C6 are both dogs, so R2C4 must be a cat (no three in a row).
  8. R3C5 and R4C5 are both cats, so R5C5 must be a dog (no three in a row).
  9. R5C5 and R5C6 are both dogs, so R5C4 must be a cat (no three in a row).
  10. Row 4 already has its 3 cats, so R4C1 must be dogs.
  11. Column 5 already has its 3 cats, so R6C5 must be dogs.
  12. R6C3 and R6C5 are both dogs with one square between them, so R6C4 must be a cat.
  13. Column 4 already has its 3 cats, so R1C4 and R3C4 must be dogs.
  14. R3C3 and R3C4 are both dogs, so R3C2 must be a cat (no three in a row).
  15. The × clue between R3C2 and R2C2 means they are different. R3C2 is a cat, so R2C2 is a dog.
  16. The × clue between R3C2 and R3C1 means they are different. R3C2 is a cat, so R3C1 is a dog.
  17. R3C1 and R4C1 are both dogs, so R2C1 must be a cat (no three in a row).
  18. The × clue between R2C1 and R1C1 means they are different. R2C1 is a cat, so R1C1 is a dog.
  19. The = clue between R1C1 and R1C2 means they are the same. R1C1 is a dog, so R1C2 is a dog.
  20. R1C1 and R1C2 are both dogs, so R1C3 must be a cat (no three in a row).
  21. R3C1 and R4C1 are both dogs, so R5C1 must be a cat (no three in a row).
  22. Row 1 already has its 3 dogs, so R1C6 must be cats.
  23. Row 2 already has its 3 dogs, so R2C3 must be cats.
  24. Row 3 already has its 3 dogs, so R3C6 must be cats.
  25. Column 1 already has its 3 dogs, so R6C1 must be cats.
  26. Column 2 already has its 3 dogs, so R5C2 must be cats.
  27. R5C1 and R5C2 are both cats, so R5C3 must be a dog (no three in a row).
  28. Column 2 already has its 3 dogs, so R6C2 must be cats.
  29. Row 6 already has its 3 cats, so R6C6 must be dogs.

About this puzzle

This 6×6 grid starts with 6 filled squares and 7 = / × clues. It can be solved in 29 steps using pairs, gaps, counts and clues.

Count as you go. Once a row or column has all of one animal, every remaining empty square in it must be the other.

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

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