Cats & Dogs #203: 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 R2C2 and R1C2 means they are the same. R2C2 is a cat, so R1C2 is a cat.
  2. The = clue between R5C9 and R5C10 means they are the same. R5C9 is a dog, so R5C10 is a dog.
  3. The × clue between R5C10 and R4C10 means they are different. R5C10 is a dog, so R4C10 is a cat.
  4. The = clue between R8C6 and R8C5 means they are the same. R8C6 is a cat, so R8C5 is a cat.
  5. R2C1 and R2C2 are both cats, so R2C3 must be a dog (no three in a row).
  6. R5C7 and R5C9 are both dogs with one square between them, so R5C8 must be a cat.
  7. R8C5 and R8C6 are both cats, so R8C4 must be a dog (no three in a row).
  8. R8C5 and R8C6 are both cats, so R8C7 must be a dog (no three in a row).
  9. The × clue between R8C7 and R9C7 means they are different. R8C7 is a dog, so R9C7 is a cat.
  10. R1C2 and R2C2 are both cats, so R3C2 must be a dog (no three in a row).
  11. R4C9 and R5C9 are both dogs, so R3C9 must be a cat (no three in a row).
  12. R3C9 and R3C10 are both cats, so R3C8 must be a dog (no three in a row).
  13. The × clue between R3C8 and R3C7 means they are different. R3C8 is a dog, so R3C7 is a cat.
  14. R4C9 and R5C9 are both dogs, so R6C9 must be a cat (no three in a row).
  15. R3C10 and R4C10 are both cats, so R2C10 must be a dog (no three in a row).
  16. The = clue between R2C10 and R2C9 means they are the same. R2C10 is a dog, so R2C9 is a dog.
  17. R2C9 and R2C10 are both dogs, so R2C8 must be a cat (no three in a row).
  18. Imagine R2C7 were a cat: following the rules from there soon forces a contradiction, so R2C7 must be a dog.
  19. Imagine R4C7 were a dog: following the rules from there soon forces a contradiction, so R4C7 must be a cat.
  20. Imagine R6C2 were a cat: following the rules from there soon forces a contradiction, so R6C2 must be a dog.
  21. Imagine R6C7 were a cat: following the rules from there soon forces a contradiction, so R6C7 must be a dog.
  22. The = clue between R6C7 and R6C8 means they are the same. R6C7 is a dog, so R6C8 is a dog.
  23. R6C7 and R6C8 are both dogs, so R6C6 must be a cat (no three in a row).
  24. R6C6 and R8C6 are both cats with one square between them, so R7C6 must be a dog.
  25. R5C7 and R6C7 are both dogs, so R7C7 must be a cat (no three in a row).
  26. Imagine R1C7 were a cat: following the rules from there soon forces a contradiction, so R1C7 must be a dog.
  27. R1C7 and R1C9 are both dogs with one square between them, so R1C8 must be a cat.
  28. Column 7 already has its 5 dogs, so R10C7 must be cats.
  29. The × clue between R10C7 and R10C8 means they are different. R10C7 is a cat, so R10C8 is a dog.
  30. Imagine R7C8 were a cat: following the rules from there soon forces a contradiction, so R7C8 must be a dog.
  31. R6C8 and R7C8 are both dogs, so R8C8 must be a cat (no three in a row).
  32. Imagine R4C6 were a cat: following the rules from there soon forces a contradiction, so R4C6 must be a dog.
  33. Imagine R4C8 were a dog: following the rules from there soon forces a contradiction, so R4C8 must be a cat.
  34. Column 8 already has its 5 cats, so R9C8 must be dogs.
  35. Imagine R7C9 were a dog: following the rules from there soon forces a contradiction, so R7C9 must be a cat.
  36. R6C9 and R7C9 are both cats, so R8C9 must be a dog (no three in a row).
  37. Column 9 already has its 5 dogs, so R9C9 must be cats.
  38. The = clue between R9C9 and R9C10 means they are the same. R9C9 is a cat, so R9C10 is a cat.
  39. R9C10 and R10C10 are both cats, so R8C10 must be a dog (no three in a row).
  40. Column 9 already has its 5 dogs, so R10C9 must be cats.
  41. Imagine R1C10 were a cat: following the rules from there soon forces a contradiction, so R1C10 must be a dog.
  42. Imagine R1C3 were a cat: following the rules from there soon forces a contradiction, so R1C3 must be a dog.
  43. R1C3 and R2C3 are both dogs, so R3C3 must be a cat (no three in a row).
  44. Imagine R1C1 were a dog: following the rules from there soon forces a contradiction, so R1C1 must be a cat.
  45. R1C1 and R2C1 are both cats, so R3C1 must be a dog (no three in a row).
  46. The × clue between R3C1 and R4C1 means they are different. R3C1 is a dog, so R4C1 is a cat.
  47. Imagine R1C4 were a dog: following the rules from there soon forces a contradiction, so R1C4 must be a cat.
  48. Imagine R2C4 were a cat: following the rules from there soon forces a contradiction, so R2C4 must be a dog.
  49. R2C3 and R2C4 are both dogs, so R2C5 must be a cat (no three in a row).
  50. Row 2 already has its 5 dogs, so R2C6 must be cats.
  51. Imagine R3C4 were a dog: following the rules from there soon forces a contradiction, so R3C4 must be a cat.
  52. The = clue between R3C4 and R4C4 means they are the same. R3C4 is a cat, so R4C4 is a cat.
  53. R3C3 and R3C4 are both cats, so R3C5 must be a dog (no three in a row).
  54. R3C4 and R4C4 are both cats, so R5C4 must be a dog (no three in a row).
  55. Row 3 already has its 5 cats, so R3C6 must be dogs.
  56. R3C6 and R4C6 are both dogs, so R5C6 must be a cat (no three in a row).
  57. Row 4 already has its 5 cats, so R4C2 must be dogs.
  58. R3C2 and R4C2 are both dogs, so R5C2 must be a cat (no three in a row).
  59. Row 4 already has its 5 cats, so R4C3 and R4C5 must be dogs.
  60. R3C5 and R4C5 are both dogs, so R5C5 must be a cat (no three in a row).
  61. The × clue between R5C5 and R6C5 means they are different. R5C5 is a cat, so R6C5 is a dog.
  62. Imagine R6C10 were a dog: following the rules from there soon forces a contradiction, so R6C10 must be a cat.
  63. Column 10 already has its 5 cats, so R7C10 must be dogs.
  64. Imagine R7C2 were a dog: following the rules from there soon forces a contradiction, so R7C2 must be a cat.
  65. The × clue between R7C2 and R7C3 means they are different. R7C2 is a cat, so R7C3 is a dog.
  66. The × clue between R7C3 and R7C4 means they are different. R7C3 is a dog, so R7C4 is a cat.
  67. Imagine R5C1 were a cat: following the rules from there soon forces a contradiction, so R5C1 must be a dog.
  68. Row 5 already has its 5 dogs, so R5C3 must be cats.
  69. Imagine R6C1 were a dog: following the rules from there soon forces a contradiction, so R6C1 must be a cat.
  70. Row 6 already has its 5 cats, so R6C4 must be dogs.
  71. Imagine R7C1 were a cat: following the rules from there soon forces a contradiction, so R7C1 must be a dog.
  72. Row 7 already has its 5 dogs, so R7C5 must be cats.
  73. R7C5 and R8C5 are both cats, so R9C5 must be a dog (no three in a row).
  74. The = clue between R9C5 and R10C5 means they are the same. R9C5 is a dog, so R10C5 is a dog.
  75. Column 5 already has its 5 dogs, so R1C5 must be cats.
  76. The × clue between R1C5 and R1C6 means they are different. R1C5 is a cat, so R1C6 is a dog.
  77. Imagine R8C1 were a dog: following the rules from there soon forces a contradiction, so R8C1 must be a cat.
  78. Column 1 already has its 5 cats, so R9C1 and R10C1 must be dogs.
  79. Imagine R8C2 were a cat: following the rules from there soon forces a contradiction, so R8C2 must be a dog.
  80. R8C2 and R8C4 are both dogs with one square between them, so R8C3 must be a cat.
  81. R8C3 and R10C3 are both cats with one square between them, so R9C3 must be a dog.
  82. R9C1 and R9C3 are both dogs with one square between them, so R9C2 must be a cat.
  83. The × clue between R9C2 and R10C2 means they are different. R9C2 is a cat, so R10C2 is a dog.
  84. R9C3 and R9C5 are both dogs with one square between them, so R9C4 must be a cat.
  85. Row 9 already has its 5 cats, so R9C6 must be dogs.
  86. Column 4 already has its 5 cats, so R10C4 must be dogs.
  87. R10C4 and R10C5 are both dogs, so R10C6 must be a cat (no three in a row).

About this puzzle

This 10×10 grid starts with 11 filled squares and 18 = / × clues. It can be solved in 87 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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