Cats & Dogs #231: 10x10 Grid Puzzle (Hard)

hard

Tap a square: 🐱 cat → 🐶 dog → clear

0 / 100 · 0:00
🐱 5 cats and 🐶 5 dogs in every row and column = same   × different

Fill the 10x10 grid with cats and dogs so that every row and every column has exactly 5 of each, and never more than two of the same animal side by side.

  • Exactly 5 cats and 5 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 R6C1 and R5C1 means they are the same. R6C1 is a dog, so R5C1 is a dog.
  2. The × clue between R8C3 and R9C3 means they are different. R8C3 is a cat, so R9C3 is a dog.
  3. R5C1 and R6C1 are both dogs, so R4C1 must be a cat (no three in a row).
  4. The = clue between R4C1 and R4C2 means they are the same. R4C1 is a cat, so R4C2 is a cat.
  5. R4C1 and R4C2 are both cats, so R4C3 must be a dog (no three in a row).
  6. R5C1 and R6C1 are both dogs, so R7C1 must be a cat (no three in a row).
  7. R8C6 and R9C6 are both dogs, so R7C6 must be a cat (no three in a row).
  8. R6C6 and R7C6 are both cats, so R5C6 must be a dog (no three in a row).
  9. R8C6 and R9C6 are both dogs, so R10C6 must be a cat (no three in a row).
  10. Imagine R1C3 were a cat: following the rules from there soon forces a contradiction, so R1C3 must be a dog.
  11. The = clue between R1C3 and R1C4 means they are the same. R1C3 is a dog, so R1C4 is a dog.
  12. R1C3 and R1C4 are both dogs, so R1C5 must be a cat (no three in a row).
  13. Imagine R4C10 were a dog: following the rules from there soon forces a contradiction, so R4C10 must be a cat.
  14. The = clue between R4C10 and R5C10 means they are the same. R4C10 is a cat, so R5C10 is a cat.
  15. R4C10 and R5C10 are both cats, so R3C10 must be a dog (no three in a row).
  16. R3C9 and R3C10 are both dogs, so R3C8 must be a cat (no three in a row).
  17. R4C10 and R5C10 are both cats, so R6C10 must be a dog (no three in a row).
  18. The = clue between R6C10 and R7C10 means they are the same. R6C10 is a dog, so R7C10 is a dog.
  19. Imagine R3C6 were a dog: following the rules from there soon forces a contradiction, so R3C6 must be a cat.
  20. R3C6 and R3C8 are both cats with one square between them, so R3C7 must be a dog.
  21. Imagine R2C5 were a dog: following the rules from there soon forces a contradiction, so R2C5 must be a cat.
  22. The × clue between R2C5 and R2C6 means they are different. R2C5 is a cat, so R2C6 is a dog.
  23. The × clue between R2C5 and R3C5 means they are different. R2C5 is a cat, so R3C5 is a dog.
  24. Imagine R1C6 were a dog: following the rules from there soon forces a contradiction, so R1C6 must be a cat.
  25. R1C5 and R1C6 are both cats, so R1C7 must be a dog (no three in a row).
  26. R1C7 and R1C8 are both dogs, so R1C9 must be a cat (no three in a row).
  27. R1C7 and R3C7 are both dogs with one square between them, so R2C7 must be a cat.
  28. Row 1 already has its 5 cats, so R1C1 must be dogs.
  29. Column 6 already has its 5 cats, so R4C6 must be dogs.
  30. The × clue between R4C6 and R4C5 means they are different. R4C6 is a dog, so R4C5 is a cat.
  31. The × clue between R4C6 and R4C7 means they are different. R4C6 is a dog, so R4C7 is a cat.
  32. Row 4 already has its 5 cats, so R4C4, R4C8 and R4C9 must be dogs.
  33. R3C9 and R4C9 are both dogs, so R2C9 must be a cat (no three in a row).
  34. R2C7 and R2C9 are both cats with one square between them, so R2C8 must be a dog.
  35. R3C9 and R4C9 are both dogs, so R5C9 must be a cat (no three in a row).
  36. R5C9 and R5C10 are both cats, so R5C8 must be a dog (no three in a row).
  37. R5C6 and R5C8 are both dogs with one square between them, so R5C7 must be a cat.
  38. R4C7 and R5C7 are both cats, so R6C7 must be a dog (no three in a row).
  39. R4C8 and R5C8 are both dogs, so R6C8 must be a cat (no three in a row).
  40. Imagine R2C1 were a cat: following the rules from there soon forces a contradiction, so R2C1 must be a dog.
  41. R1C1 and R2C1 are both dogs, so R3C1 must be a cat (no three in a row).
  42. Imagine R3C4 were a dog: following the rules from there soon forces a contradiction, so R3C4 must be a cat.
  43. Imagine R5C3 were a dog: following the rules from there soon forces a contradiction, so R5C3 must be a cat.
  44. The × clue between R5C3 and R5C4 means they are different. R5C3 is a cat, so R5C4 is a dog.
  45. R5C4 and R5C6 are both dogs with one square between them, so R5C5 must be a cat.
  46. R4C4 and R5C4 are both dogs, so R6C4 must be a cat (no three in a row).
  47. R6C4 and R6C6 are both cats with one square between them, so R6C5 must be a dog.
  48. Row 5 already has its 5 cats, so R5C2 must be dogs.
  49. Imagine R6C2 were a dog: following the rules from there soon forces a contradiction, so R6C2 must be a cat.
  50. The = clue between R6C2 and R7C2 means they are the same. R6C2 is a cat, so R7C2 is a cat.
  51. R6C2 and R6C4 are both cats with one square between them, so R6C3 must be a dog.
  52. R7C1 and R7C2 are both cats, so R7C3 must be a dog (no three in a row).
  53. R6C2 and R7C2 are both cats, so R8C2 must be a dog (no three in a row).
  54. Row 6 already has its 5 dogs, so R6C9 must be cats.
  55. R5C9 and R6C9 are both cats, so R7C9 must be a dog (no three in a row).
  56. R7C9 and R7C10 are both dogs, so R7C8 must be a cat (no three in a row).
  57. R7C6 and R7C8 are both cats with one square between them, so R7C7 must be a dog.
  58. R6C7 and R7C7 are both dogs, so R8C7 must be a cat (no three in a row).
  59. R6C8 and R7C8 are both cats, so R8C8 must be a dog (no three in a row).
  60. Column 3 already has its 5 dogs, so R2C3 must be cats.
  61. R2C3 and R2C5 are both cats with one square between them, so R2C4 must be a dog.
  62. Column 3 already has its 5 dogs, so R3C3 must be cats.
  63. R3C1 and R3C3 are both cats with one square between them, so R3C2 must be a dog.
  64. Column 3 already has its 5 dogs, so R10C3 must be cats.
  65. Column 8 already has its 5 dogs, so R9C8 and R10C8 must be cats.
  66. R10C6 and R10C8 are both cats with one square between them, so R10C7 must be a dog.
  67. Column 7 already has its 5 dogs, so R9C7 must be cats.
  68. R9C7 and R9C8 are both cats, so R9C9 must be a dog (no three in a row).
  69. R7C9 and R9C9 are both dogs with one square between them, so R8C9 must be a cat.
  70. Column 9 already has its 5 cats, so R10C9 must be dogs.
  71. Imagine R2C2 were a cat: following the rules from there soon forces a contradiction, so R2C2 must be a dog.
  72. Row 2 already has its 5 dogs, so R2C10 must be cats.
  73. Column 10 already has its 5 cats, so R9C10 and R10C10 must be dogs.
  74. Imagine R7C4 were a dog: following the rules from there soon forces a contradiction, so R7C4 must be a cat.
  75. R7C4 and R7C6 are both cats with one square between them, so R7C5 must be a dog.
  76. R6C4 and R7C4 are both cats, so R8C4 must be a dog (no three in a row).
  77. R8C4 and R8C6 are both dogs with one square between them, so R8C5 must be a cat.
  78. Row 8 already has its 5 cats, so R8C1 must be dogs.
  79. Column 1 already has its 5 dogs, so R9C1 and R10C1 must be cats.
  80. R10C1 and R10C3 are both cats with one square between them, so R10C2 must be a dog.
  81. R8C2 and R10C2 are both dogs with one square between them, so R9C2 must be a cat.
  82. Column 4 already has its 5 dogs, so R9C4 must be cats.
  83. Row 9 already has its 5 cats, so R9C5 must be dogs.
  84. Column 4 already has its 5 dogs, so R10C4 must be cats.
  85. R10C3 and R10C4 are both cats, so R10C5 must be a dog (no three in a row).

About this puzzle

This 10×10 grid starts with 10 filled squares and 12 = / × clues. It can be solved in 85 steps using a "what if" trial of one square on top of the basic rules.

Watch for a gap: if the squares on either side of an empty square match, the empty one must be different.

Stuck? Open the step-by-step solution below -- each step names the squares involved, so you can use it as a hint and finish the puzzle yourself.

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