Cats & Dogs #265: 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 R9C7 and R8C7 means they are different. R9C7 is a cat, so R8C7 is a dog.
  2. R8C7 and R8C9 are both dogs with one square between them, so R8C8 must be a cat.
  3. Imagine R1C2 were a dog: following the rules from there soon forces a contradiction, so R1C2 must be a cat.
  4. Imagine R1C3 were a cat: following the rules from there soon forces a contradiction, so R1C3 must be a dog.
  5. R1C3 and R1C4 are both dogs, so R1C5 must be a cat (no three in a row).
  6. Imagine R2C3 were a dog: following the rules from there soon forces a contradiction, so R2C3 must be a cat.
  7. The = clue between R2C3 and R2C4 means they are the same. R2C3 is a cat, so R2C4 is a cat.
  8. The = clue between R2C4 and R3C4 means they are the same. R2C4 is a cat, so R3C4 is a cat.
  9. R2C3 and R2C4 are both cats, so R2C2 must be a dog (no three in a row).
  10. R2C3 and R2C4 are both cats, so R2C5 must be a dog (no three in a row).
  11. R3C3 and R3C4 are both cats, so R3C2 must be a dog (no three in a row).
  12. R3C3 and R3C4 are both cats, so R3C5 must be a dog (no three in a row).
  13. R2C2 and R3C2 are both dogs, so R4C2 must be a cat (no three in a row).
  14. R2C3 and R3C3 are both cats, so R4C3 must be a dog (no three in a row).
  15. R2C4 and R3C4 are both cats, so R4C4 must be a dog (no three in a row).
  16. R4C3 and R4C4 are both dogs, so R4C5 must be a cat (no three in a row).
  17. Imagine R2C7 were a dog: following the rules from there soon forces a contradiction, so R2C7 must be a cat.
  18. The = clue between R2C7 and R2C8 means they are the same. R2C7 is a cat, so R2C8 is a cat.
  19. R2C7 and R2C8 are both cats, so R2C6 must be a dog (no three in a row).
  20. Imagine R6C1 were a dog: following the rules from there soon forces a contradiction, so R6C1 must be a cat.
  21. The = clue between R6C1 and R7C1 means they are the same. R6C1 is a cat, so R7C1 is a cat.
  22. R6C1 and R7C1 are both cats, so R8C1 must be a dog (no three in a row).
  23. Imagine R9C1 were a dog: following the rules from there soon forces a contradiction, so R9C1 must be a cat.
  24. The = clue between R9C1 and R10C1 means they are the same. R9C1 is a cat, so R10C1 is a cat.
  25. R10C1 and R10C3 are both cats with one square between them, so R10C2 must be a dog.
  26. Imagine R1C1 were a cat: following the rules from there soon forces a contradiction, so R1C1 must be a dog.
  27. Imagine R2C1 were a cat: following the rules from there soon forces a contradiction, so R2C1 must be a dog.
  28. R1C1 and R2C1 are both dogs, so R3C1 must be a cat (no three in a row).
  29. Row 2 already has its 5 dogs, so R2C10 must be cats.
  30. Column 1 already has its 5 cats, so R4C1 must be dogs.
  31. Imagine R9C8 were a cat: following the rules from there soon forces a contradiction, so R9C8 must be a dog.
  32. Imagine R9C9 were a dog: following the rules from there soon forces a contradiction, so R9C9 must be a cat.
  33. The × clue between R9C9 and R10C9 means they are different. R9C9 is a cat, so R10C9 is a dog.
  34. The = clue between R10C9 and R10C8 means they are the same. R10C9 is a dog, so R10C8 is a dog.
  35. R10C8 and R10C9 are both dogs, so R10C7 must be a cat (no three in a row).
  36. R10C8 and R10C9 are both dogs, so R10C10 must be a cat (no three in a row).
  37. The = clue between R10C10 and R9C10 means they are the same. R10C10 is a cat, so R9C10 is a cat.
  38. R9C10 and R10C10 are both cats, so R8C10 must be a dog (no three in a row).
  39. Imagine R8C2 were a dog: following the rules from there soon forces a contradiction, so R8C2 must be a cat.
  40. Imagine R6C2 were a cat: following the rules from there soon forces a contradiction, so R6C2 must be a dog.
  41. Imagine R5C2 were a dog: following the rules from there soon forces a contradiction, so R5C2 must be a cat.
  42. Imagine R7C2 were a dog: following the rules from there soon forces a contradiction, so R7C2 must be a cat.
  43. R7C1 and R7C2 are both cats, so R7C3 must be a dog (no three in a row).
  44. R7C2 and R8C2 are both cats, so R9C2 must be a dog (no three in a row).
  45. Imagine R8C3 were a dog: following the rules from there soon forces a contradiction, so R8C3 must be a cat.
  46. R8C2 and R8C3 are both cats, so R8C4 must be a dog (no three in a row).
  47. R8C3 and R10C3 are both cats with one square between them, so R9C3 must be a dog.
  48. R9C2 and R9C3 are both dogs, so R9C4 must be a cat (no three in a row).
  49. Row 8 already has its 5 dogs, so R8C5 and R8C6 must be cats.
  50. Row 9 already has its 5 cats, so R9C5 and R9C6 must be dogs.
  51. Imagine R5C7 were a dog: following the rules from there soon forces a contradiction, so R5C7 must be a cat.
  52. The = clue between R5C7 and R5C8 means they are the same. R5C7 is a cat, so R5C8 is a cat.
  53. R5C7 and R5C8 are both cats, so R5C6 must be a dog (no three in a row).
  54. The × clue between R5C6 and R6C6 means they are different. R5C6 is a dog, so R6C6 is a cat.
  55. The = clue between R6C6 and R6C7 means they are the same. R6C6 is a cat, so R6C7 is a cat.
  56. R5C7 and R5C8 are both cats, so R5C9 must be a dog (no three in a row).
  57. The × clue between R5C9 and R6C9 means they are different. R5C9 is a dog, so R6C9 is a cat.
  58. R6C6 and R6C7 are both cats, so R6C5 must be a dog (no three in a row).
  59. R6C6 and R6C7 are both cats, so R6C8 must be a dog (no three in a row).
  60. R6C6 and R8C6 are both cats with one square between them, so R7C6 must be a dog.
  61. R5C7 and R6C7 are both cats, so R4C7 must be a dog (no three in a row).
  62. R5C7 and R6C7 are both cats, so R7C7 must be a dog (no three in a row).
  63. R7C6 and R7C7 are both dogs, so R7C5 must be a cat (no three in a row).
  64. R7C6 and R7C7 are both dogs, so R7C8 must be a cat (no three in a row).
  65. Column 7 already has its 5 cats, so R1C7 and R3C7 must be dogs.
  66. R3C5 and R3C7 are both dogs with one square between them, so R3C6 must be a cat.
  67. Imagine R1C6 were a dog: following the rules from there soon forces a contradiction, so R1C6 must be a cat.
  68. Imagine R1C9 were a dog: following the rules from there soon forces a contradiction, so R1C9 must be a cat.
  69. Imagine R3C8 were a cat: following the rules from there soon forces a contradiction, so R3C8 must be a dog.
  70. R3C7 and R3C8 are both dogs, so R3C9 must be a cat (no three in a row).
  71. Row 3 already has its 5 cats, so R3C10 must be dogs.
  72. Imagine R4C6 were a dog: following the rules from there soon forces a contradiction, so R4C6 must be a cat.
  73. Column 6 already has its 5 cats, so R10C6 must be dogs.
  74. Imagine R4C9 were a dog: following the rules from there soon forces a contradiction, so R4C9 must be a cat.
  75. Column 9 already has its 5 cats, so R7C9 must be dogs.
  76. Imagine R1C8 were a dog: following the rules from there soon forces a contradiction, so R1C8 must be a cat.
  77. R1C8 and R1C9 are both cats, so R1C10 must be a dog (no three in a row).
  78. Column 8 already has its 5 cats, so R4C8 must be dogs.
  79. Row 4 already has its 5 dogs, so R4C10 must be cats.
  80. Imagine R5C3 were a dog: following the rules from there soon forces a contradiction, so R5C3 must be a cat.
  81. R5C2 and R5C3 are both cats, so R5C4 must be a dog (no three in a row).
  82. R5C4 and R5C6 are both dogs with one square between them, so R5C5 must be a cat.
  83. R4C4 and R5C4 are both dogs, so R6C4 must be a cat (no three in a row).
  84. Row 5 already has its 5 cats, so R5C10 must be dogs.
  85. Row 6 already has its 5 cats, so R6C3 and R6C10 must be dogs.
  86. R5C10 and R6C10 are both dogs, so R7C10 must be a cat (no three in a row).
  87. Row 7 already has its 5 cats, so R7C4 must be dogs.
  88. Column 4 already has its 5 dogs, so R10C4 must be cats.
  89. 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 7 filled squares and 13 = / × clues. It can be solved in 89 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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