Cats & Dogs #56: 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. The = clue between R4C2 and R3C2 means they are the same. R4C2 is a cat, so R3C2 is a cat.
  2. The = clue between R3C2 and R3C1 means they are the same. R3C2 is a cat, so R3C1 is a cat.
  3. R3C1 and R3C2 are both cats, so R3C3 must be a dog (no three in a row).
  4. R3C3 and R3C4 are both dogs, so R3C5 must be a cat (no three in a row).
  5. R3C2 and R4C2 are both cats, so R2C2 must be a dog (no three in a row).
  6. R3C2 and R4C2 are both cats, so R5C2 must be a dog (no three in a row).
  7. The × clue between R5C2 and R5C3 means they are different. R5C2 is a dog, so R5C3 is a cat.
  8. The = clue between R5C3 and R4C3 means they are the same. R5C3 is a cat, so R4C3 is a cat.
  9. R4C2 and R4C3 are both cats, so R4C1 must be a dog (no three in a row).
  10. R4C2 and R4C3 are both cats, so R4C4 must be a dog (no three in a row).
  11. R4C3 and R5C3 are both cats, so R6C3 must be a dog (no three in a row).
  12. R3C4 and R4C4 are both dogs, so R2C4 must be a cat (no three in a row).
  13. R2C4 and R2C6 are both cats with one square between them, so R2C5 must be a dog.
  14. R3C4 and R4C4 are both dogs, so R5C4 must be a cat (no three in a row).
  15. R5C3 and R5C4 are both cats, so R5C5 must be a dog (no three in a row).
  16. Row 3 already has its 3 cats, so R3C6 must be dogs.
  17. The × clue between R3C6 and R4C6 means they are different. R3C6 is a dog, so R4C6 is a cat.
  18. Row 4 already has its 3 cats, so R4C5 must be dogs.
  19. R4C5 and R5C5 are both dogs, so R6C5 must be a cat (no three in a row).
  20. The = clue between R6C5 and R6C4 means they are the same. R6C5 is a cat, so R6C4 is a cat.
  21. R6C4 and R6C5 are both cats, so R6C6 must be a dog (no three in a row).
  22. Column 4 already has its 3 cats, so R1C4 must be dogs.
  23. Column 5 already has its 3 dogs, so R1C5 must be cats.
  24. The × clue between R1C5 and R1C6 means they are different. R1C5 is a cat, so R1C6 is a dog.
  25. Column 6 already has its 3 dogs, so R5C6 must be cats.
  26. Row 5 already has its 3 cats, so R5C1 must be dogs.
  27. R4C1 and R5C1 are both dogs, so R6C1 must be a cat (no three in a row).
  28. Row 6 already has its 3 cats, so R6C2 must be dogs.
  29. Column 2 already has its 3 dogs, so R1C2 must be cats.
  30. The × clue between R1C2 and R1C1 means they are different. R1C2 is a cat, so R1C1 is a dog.
  31. Row 1 already has its 3 dogs, so R1C3 must be cats.
  32. Column 1 already has its 3 dogs, so R2C1 must be cats.
  33. Row 2 already has its 3 cats, so R2C3 must be dogs.

About this puzzle

This 6×6 grid starts with 3 filled squares and 8 = / × clues. It can be solved in 33 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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