Cats & Dogs #45: 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

Use pure logic to place every cat and dog. Each row and column holds 3 of each animal, three in a row is never allowed, and the clues between squares settle the rest.

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

About this puzzle

This 6×6 grid starts with 6 filled squares and 5 = / × 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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