Cats & Dogs #270: 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 R7C5 and R7C4 means they are the same. R7C5 is a cat, so R7C4 is a cat.
  2. R7C4 and R7C5 are both cats, so R7C3 must be a dog (no three in a row).
  3. R7C4 and R7C5 are both cats, so R7C6 must be a dog (no three in a row).
  4. R3C3 and R4C3 are both dogs, so R2C3 must be a cat (no three in a row).
  5. The × clue between R2C3 and R1C3 means they are different. R2C3 is a cat, so R1C3 is a dog.
  6. R3C3 and R4C3 are both dogs, so R5C3 must be a cat (no three in a row).
  7. The × clue between R5C3 and R5C4 means they are different. R5C3 is a cat, so R5C4 is a dog.
  8. Imagine R2C1 were a cat: following the rules from there soon forces a contradiction, so R2C1 must be a dog.
  9. The = clue between R2C1 and R2C2 means they are the same. R2C1 is a dog, so R2C2 is a dog.
  10. Imagine R6C3 were a dog: following the rules from there soon forces a contradiction, so R6C3 must be a cat.
  11. Imagine R7C9 were a cat: following the rules from there soon forces a contradiction, so R7C9 must be a dog.
  12. Imagine R8C10 were a cat: following the rules from there soon forces a contradiction, so R8C10 must be a dog.
  13. The = clue between R8C10 and R9C10 means they are the same. R8C10 is a dog, so R9C10 is a dog.
  14. R8C10 and R9C10 are both dogs, so R10C10 must be a cat (no three in a row).
  15. Imagine R9C6 were a cat: following the rules from there soon forces a contradiction, so R9C6 must be a dog.
  16. The = clue between R9C6 and R10C6 means they are the same. R9C6 is a dog, so R10C6 is a dog.
  17. R10C4 and R10C6 are both dogs with one square between them, so R10C5 must be a cat.
  18. Imagine R3C4 were a dog: following the rules from there soon forces a contradiction, so R3C4 must be a cat.
  19. Imagine R2C4 were a cat: following the rules from there soon forces a contradiction, so R2C4 must be a dog.
  20. Imagine R1C7 were a cat: following the rules from there soon forces a contradiction, so R1C7 must be a dog.
  21. The = clue between R1C7 and R1C8 means they are the same. R1C7 is a dog, so R1C8 is a dog.
  22. The × clue between R1C7 and R2C7 means they are different. R1C7 is a dog, so R2C7 is a cat.
  23. R1C7 and R1C8 are both dogs, so R1C6 must be a cat (no three in a row).
  24. R1C7 and R1C8 are both dogs, so R1C9 must be a cat (no three in a row).
  25. The = clue between R1C9 and R2C9 means they are the same. R1C9 is a cat, so R2C9 is a cat.
  26. R2C7 and R2C9 are both cats with one square between them, so R2C8 must be a dog.
  27. R1C8 and R2C8 are both dogs, so R3C8 must be a cat (no three in a row).
  28. The × clue between R3C8 and R4C8 means they are different. R3C8 is a cat, so R4C8 is a dog.
  29. The = clue between R4C8 and R5C8 means they are the same. R4C8 is a dog, so R5C8 is a dog.
  30. R4C8 and R5C8 are both dogs, so R6C8 must be a cat (no three in a row).
  31. R1C9 and R2C9 are both cats, so R3C9 must be a dog (no three in a row).
  32. Imagine R2C10 were a dog: following the rules from there soon forces a contradiction, so R2C10 must be a cat.
  33. The = clue between R2C10 and R3C10 means they are the same. R2C10 is a cat, so R3C10 is a cat.
  34. R2C10 and R3C10 are both cats, so R1C10 must be a dog (no three in a row).
  35. R2C10 and R3C10 are both cats, so R4C10 must be a dog (no three in a row).
  36. The × clue between R4C10 and R4C9 means they are different. R4C10 is a dog, so R4C9 is a cat.
  37. Imagine R1C1 were a dog: following the rules from there soon forces a contradiction, so R1C1 must be a cat.
  38. Imagine R1C2 were a dog: following the rules from there soon forces a contradiction, so R1C2 must be a cat.
  39. Imagine R3C1 were a cat: following the rules from there soon forces a contradiction, so R3C1 must be a dog.
  40. R2C1 and R3C1 are both dogs, so R4C1 must be a cat (no three in a row).
  41. Imagine R3C7 were a cat: following the rules from there soon forces a contradiction, so R3C7 must be a dog.
  42. Imagine R7C7 were a cat: following the rules from there soon forces a contradiction, so R7C7 must be a dog.
  43. The = clue between R7C7 and R8C7 means they are the same. R7C7 is a dog, so R8C7 is a dog.
  44. R7C6 and R7C7 are both dogs, so R7C8 must be a cat (no three in a row).
  45. R7C7 and R8C7 are both dogs, so R6C7 must be a cat (no three in a row).
  46. R6C7 and R6C8 are both cats, so R6C6 must be a dog (no three in a row).
  47. The × clue between R6C6 and R5C6 means they are different. R6C6 is a dog, so R5C6 is a cat.
  48. R6C7 and R6C8 are both cats, so R6C9 must be a dog (no three in a row).
  49. R7C7 and R8C7 are both dogs, so R9C7 must be a cat (no three in a row).
  50. R6C8 and R7C8 are both cats, so R8C8 must be a dog (no three in a row).
  51. R8C7 and R8C8 are both dogs, so R8C9 must be a cat (no three in a row).
  52. R6C9 and R7C9 are both dogs, so R5C9 must be a cat (no three in a row).
  53. Column 8 already has its 5 dogs, so R9C8 must be cats.
  54. R9C7 and R9C8 are both cats, so R9C9 must be a dog (no three in a row).
  55. Column 8 already has its 5 dogs, so R10C8 must be cats.
  56. R10C8 and R10C10 are both cats with one square between them, so R10C9 must be a dog.
  57. Imagine R2C5 were a cat: following the rules from there soon forces a contradiction, so R2C5 must be a dog.
  58. R2C4 and R2C5 are both dogs, so R2C6 must be a cat (no three in a row).
  59. R1C6 and R2C6 are both cats, so R3C6 must be a dog (no three in a row).
  60. R3C6 and R3C7 are both dogs, so R3C5 must be a cat (no three in a row).
  61. The = clue between R3C5 and R4C5 means they are the same. R3C5 is a cat, so R4C5 is a cat.
  62. R3C5 and R4C5 are both cats, so R5C5 must be a dog (no three in a row).
  63. Column 6 already has its 5 dogs, so R4C6 must be cats.
  64. R4C5 and R4C6 are both cats, so R4C4 must be a dog (no three in a row).
  65. R4C3 and R4C4 are both dogs, so R4C2 must be a cat (no three in a row).
  66. R4C5 and R4C6 are both cats, so R4C7 must be a dog (no three in a row).
  67. R3C2 and R4C2 are both cats, so R5C2 must be a dog (no three in a row).
  68. R4C4 and R5C4 are both dogs, so R6C4 must be a cat (no three in a row).
  69. R6C3 and R6C4 are both cats, so R6C2 must be a dog (no three in a row).
  70. R6C3 and R6C4 are both cats, so R6C5 must be a dog (no three in a row).
  71. R5C2 and R6C2 are both dogs, so R7C2 must be a cat (no three in a row).
  72. R6C4 and R7C4 are both cats, so R8C4 must be a dog (no three in a row).
  73. The × clue between R8C4 and R8C3 means they are different. R8C4 is a dog, so R8C3 is a cat.
  74. R8C3 and R10C3 are both cats with one square between them, so R9C3 must be a dog.
  75. R8C4 and R10C4 are both dogs with one square between them, so R9C4 must be a cat.
  76. R3C7 and R4C7 are both dogs, so R5C7 must be a cat (no three in a row).
  77. Row 6 already has its 5 dogs, so R6C10 must be cats.
  78. R6C10 and R7C10 are both cats, so R5C10 must be a dog (no three in a row).
  79. Row 5 already has its 5 dogs, so R5C1 must be cats.
  80. Row 7 already has its 5 cats, so R7C1 must be dogs.
  81. R6C1 and R7C1 are both dogs, so R8C1 must be a cat (no three in a row).
  82. R8C1 and R8C3 are both cats with one square between them, so R8C2 must be a dog.
  83. Row 8 already has its 5 dogs, so R8C5 must be cats.
  84. R7C5 and R8C5 are both cats, so R9C5 must be a dog (no three in a row).
  85. Row 9 already has its 5 dogs, so R9C1 must be cats.
  86. R8C1 and R9C1 are both cats, so R10C1 must be a dog (no three in a row).
  87. Row 9 already has its 5 dogs, so R9C2 must be cats.
  88. Column 2 already has its 5 cats, so R10C2 must be dogs.
  89. Row 10 already has its 5 dogs, so R10C7 must be cats.
  90. Column 4 already has its 5 dogs, so R1C4 must be cats.
  91. R1C4 and R1C6 are both cats with one square between them, so R1C5 must be a dog.

About this puzzle

This 10×10 grid starts with 9 filled squares and 17 = / × clues. It can be solved in 91 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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