Cats & Dogs #236: 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. R6C5 and R7C5 are both dogs, so R5C5 must be a cat (no three in a row).
  2. The = clue between R5C5 and R5C6 means they are the same. R5C5 is a cat, so R5C6 is a cat.
  3. R5C5 and R5C6 are both cats, so R5C4 must be a dog (no three in a row).
  4. R5C5 and R5C6 are both cats, so R5C7 must be a dog (no three in a row).
  5. R6C5 and R7C5 are both dogs, so R8C5 must be a cat (no three in a row).
  6. Imagine R1C1 were a dog: following the rules from there soon forces a contradiction, so R1C1 must be a cat.
  7. The = clue between R1C1 and R2C1 means they are the same. R1C1 is a cat, so R2C1 is a cat.
  8. R1C1 and R2C1 are both cats, so R3C1 must be a dog (no three in a row).
  9. The = clue between R3C1 and R4C1 means they are the same. R3C1 is a dog, so R4C1 is a dog.
  10. Imagine R4C4 were a dog: following the rules from there soon forces a contradiction, so R4C4 must be a cat.
  11. Imagine R4C6 were a cat: following the rules from there soon forces a contradiction, so R4C6 must be a dog.
  12. Imagine R5C8 were a dog: following the rules from there soon forces a contradiction, so R5C8 must be a cat.
  13. Imagine R5C9 were a cat: following the rules from there soon forces a contradiction, so R5C9 must be a dog.
  14. Imagine R5C10 were a cat: following the rules from there soon forces a contradiction, so R5C10 must be a dog.
  15. Imagine R6C3 were a dog: following the rules from there soon forces a contradiction, so R6C3 must be a cat.
  16. Imagine R5C2 were a dog: following the rules from there soon forces a contradiction, so R5C2 must be a cat.
  17. R5C1 and R5C2 are both cats, so R5C3 must be a dog (no three in a row).
  18. Imagine R6C4 were a cat: following the rules from there soon forces a contradiction, so R6C4 must be a dog.
  19. The × clue between R6C4 and R7C4 means they are different. R6C4 is a dog, so R7C4 is a cat.
  20. The = clue between R7C4 and R7C3 means they are the same. R7C4 is a cat, so R7C3 is a cat.
  21. R6C4 and R6C5 are both dogs, so R6C6 must be a cat (no three in a row).
  22. R7C3 and R7C4 are both cats, so R7C2 must be a dog (no three in a row).
  23. R6C3 and R7C3 are both cats, so R8C3 must be a dog (no three in a row).
  24. R5C6 and R6C6 are both cats, so R7C6 must be a dog (no three in a row).
  25. R7C5 and R7C6 are both dogs, so R7C7 must be a cat (no three in a row).
  26. Imagine R8C1 were a cat: following the rules from there soon forces a contradiction, so R8C1 must be a dog.
  27. The × clue between R8C1 and R8C2 means they are different. R8C1 is a dog, so R8C2 is a cat.
  28. Imagine R9C3 were a dog: following the rules from there soon forces a contradiction, so R9C3 must be a cat.
  29. The = clue between R9C3 and R10C3 means they are the same. R9C3 is a cat, so R10C3 is a cat.
  30. Imagine R1C3 were a cat: following the rules from there soon forces a contradiction, so R1C3 must be a dog.
  31. Imagine R2C2 were a dog: following the rules from there soon forces a contradiction, so R2C2 must be a cat.
  32. R2C1 and R2C2 are both cats, so R2C3 must be a dog (no three in a row).
  33. R2C3 and R2C4 are both dogs, so R2C5 must be a cat (no three in a row).
  34. R1C3 and R2C3 are both dogs, so R3C3 must be a cat (no three in a row).
  35. Column 3 already has its 5 cats, so R4C3 must be dogs.
  36. R4C1 and R4C3 are both dogs with one square between them, so R4C2 must be a cat.
  37. R2C2 and R4C2 are both cats with one square between them, so R3C2 must be a dog.
  38. R4C2 and R5C2 are both cats, so R6C2 must be a dog (no three in a row).
  39. Imagine R7C9 were a dog: following the rules from there soon forces a contradiction, so R7C9 must be a cat.
  40. Imagine R8C8 were a dog: following the rules from there soon forces a contradiction, so R8C8 must be a cat.
  41. Imagine R9C5 were a cat: following the rules from there soon forces a contradiction, so R9C5 must be a dog.
  42. The × clue between R9C5 and R9C6 means they are different. R9C5 is a dog, so R9C6 is a cat.
  43. The = clue between R9C5 and R10C5 means they are the same. R9C5 is a dog, so R10C5 is a dog.
  44. Imagine R1C5 were a dog: following the rules from there soon forces a contradiction, so R1C5 must be a cat.
  45. R1C5 and R2C5 are both cats, so R3C5 must be a dog (no three in a row).
  46. Column 5 already has its 5 dogs, so R4C5 must be cats.
  47. Imagine R3C10 were a dog: following the rules from there soon forces a contradiction, so R3C10 must be a cat.
  48. Imagine R4C10 were a cat: following the rules from there soon forces a contradiction, so R4C10 must be a dog.
  49. R4C10 and R5C10 are both dogs, so R6C10 must be a cat (no three in a row).
  50. Imagine R6C8 were a cat: following the rules from there soon forces a contradiction, so R6C8 must be a dog.
  51. The = clue between R6C8 and R6C9 means they are the same. R6C8 is a dog, so R6C9 is a dog.
  52. R6C8 and R6C9 are both dogs, so R6C7 must be a cat (no three in a row).
  53. R6C7 and R7C7 are both cats, so R8C7 must be a dog (no three in a row).
  54. Row 6 already has its 5 dogs, so R6C1 must be cats.
  55. R5C1 and R6C1 are both cats, so R7C1 must be a dog (no three in a row).
  56. R7C1 and R8C1 are both dogs, so R9C1 must be a cat (no three in a row).
  57. R9C1 and R9C3 are both cats with one square between them, so R9C2 must be a dog.
  58. Row 7 already has its 5 dogs, so R7C10 must be cats.
  59. R6C10 and R7C10 are both cats, so R8C10 must be a dog (no three in a row).
  60. Column 1 already has its 5 cats, so R10C1 must be dogs.
  61. Imagine R8C9 were a dog: following the rules from there soon forces a contradiction, so R8C9 must be a cat.
  62. R7C9 and R8C9 are both cats, so R9C9 must be a dog (no three in a row).
  63. Imagine R9C4 were a cat: following the rules from there soon forces a contradiction, so R9C4 must be a dog.
  64. Imagine R9C7 were a dog: following the rules from there soon forces a contradiction, so R9C7 must be a cat.
  65. The = clue between R9C7 and R10C7 means they are the same. R9C7 is a cat, so R10C7 is a cat.
  66. R9C6 and R9C7 are both cats, so R9C8 must be a dog (no three in a row).
  67. R9C8 and R9C9 are both dogs, so R9C10 must be a cat (no three in a row).
  68. Imagine R1C7 were a cat: following the rules from there soon forces a contradiction, so R1C7 must be a dog.
  69. The = clue between R1C7 and R1C8 means they are the same. R1C7 is a dog, so R1C8 is a dog.
  70. R1C7 and R1C8 are both dogs, so R1C6 must be a cat (no three in a row).
  71. R1C5 and R1C6 are both cats, so R1C4 must be a dog (no three in a row).
  72. R1C3 and R1C4 are both dogs, so R1C2 must be a cat (no three in a row).
  73. R1C7 and R1C8 are both dogs, so R1C9 must be a cat (no three in a row).
  74. R1C4 and R2C4 are both dogs, so R3C4 must be a cat (no three in a row).
  75. Row 1 already has its 5 cats, so R1C10 must be dogs.
  76. Column 2 already has its 5 cats, so R10C2 must be dogs.
  77. Column 4 already has its 5 dogs, so R8C4 must be cats.
  78. R8C4 and R8C5 are both cats, so R8C6 must be a dog (no three in a row).
  79. Column 4 already has its 5 dogs, so R10C4 must be cats.
  80. Imagine R2C7 were a cat: following the rules from there soon forces a contradiction, so R2C7 must be a dog.
  81. R1C7 and R2C7 are both dogs, so R3C7 must be a cat (no three in a row).
  82. Column 7 already has its 5 cats, so R4C7 must be dogs.
  83. R4C6 and R4C7 are both dogs, so R4C8 must be a cat (no three in a row).
  84. R4C8 and R5C8 are both cats, so R3C8 must be a dog (no three in a row).
  85. R1C8 and R3C8 are both dogs with one square between them, so R2C8 must be a cat.
  86. The × clue between R2C8 and R2C9 means they are different. R2C8 is a cat, so R2C9 is a dog.
  87. Column 8 already has its 5 dogs, so R10C8 must be cats.
  88. R10C7 and R10C8 are both cats, so R10C6 must be a dog (no three in a row).
  89. R10C7 and R10C8 are both cats, so R10C9 must be a dog (no three in a row).
  90. Row 10 already has its 5 dogs, so R10C10 must be cats.
  91. Column 9 already has its 5 dogs, so R3C9 must be cats.
  92. Row 3 already has its 5 cats, so R3C6 must be dogs.
  93. R3C6 and R4C6 are both dogs, so R2C6 must be a cat (no three in a row).
  94. Row 2 already has its 5 cats, so R2C10 must be dogs.

About this puzzle

This 10×10 grid starts with 6 filled squares and 13 = / × clues. It can be solved in 94 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.

When every square is filled, press Check Answer. The grid is verified against the stored solution and any broken rule is named.

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