Cats & Dogs #243: 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

Can you finish the grid? Cats and dogs must balance in every line, no animal may appear three times in a row, and = / × signs tell you whether two neighbors match.

  • 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 R2C3 and R2C4 means they are different. R2C3 is a dog, so R2C4 is a cat.
  2. The × clue between R9C3 and R8C3 means they are different. R9C3 is a dog, so R8C3 is a cat.
  3. R2C4 and R2C5 are both cats, so R2C6 must be a dog (no three in a row).
  4. R1C3 and R2C3 are both dogs, so R3C3 must be a cat (no three in a row).
  5. The × clue between R3C3 and R3C4 means they are different. R3C3 is a cat, so R3C4 is a dog.
  6. R3C1 and R3C3 are both cats with one square between them, so R3C2 must be a dog.
  7. Imagine R1C8 were a cat: following the rules from there soon forces a contradiction, so R1C8 must be a dog.
  8. Imagine R2C7 were a dog: following the rules from there soon forces a contradiction, so R2C7 must be a cat.
  9. The = clue between R2C7 and R2C8 means they are the same. R2C7 is a cat, so R2C8 is a cat.
  10. R2C7 and R2C8 are both cats, so R2C9 must be a dog (no three in a row).
  11. R2C8 and R3C8 are both cats, so R4C8 must be a dog (no three in a row).
  12. The = clue between R4C8 and R4C7 means they are the same. R4C8 is a dog, so R4C7 is a dog.
  13. R4C7 and R4C8 are both dogs, so R4C6 must be a cat (no three in a row).
  14. R4C7 and R4C8 are both dogs, so R4C9 must be a cat (no three in a row).
  15. Imagine R1C4 were a dog: following the rules from there soon forces a contradiction, so R1C4 must be a cat.
  16. Imagine R1C5 were a cat: following the rules from there soon forces a contradiction, so R1C5 must be a dog.
  17. Imagine R1C6 were a dog: following the rules from there soon forces a contradiction, so R1C6 must be a cat.
  18. Imagine R2C10 were a cat: following the rules from there soon forces a contradiction, so R2C10 must be a dog.
  19. Imagine R3C5 were a dog: following the rules from there soon forces a contradiction, so R3C5 must be a cat.
  20. R2C5 and R3C5 are both cats, so R4C5 must be a dog (no three in a row).
  21. Imagine R3C6 were a cat: following the rules from there soon forces a contradiction, so R3C6 must be a dog.
  22. Imagine R4C4 were a dog: following the rules from there soon forces a contradiction, so R4C4 must be a cat.
  23. The = clue between R4C4 and R5C4 means they are the same. R4C4 is a cat, so R5C4 is a cat.
  24. R4C4 and R5C4 are both cats, so R6C4 must be a dog (no three in a row).
  25. Imagine R6C5 were a dog: following the rules from there soon forces a contradiction, so R6C5 must be a cat.
  26. Imagine R6C6 were a cat: following the rules from there soon forces a contradiction, so R6C6 must be a dog.
  27. Imagine R7C4 were a cat: following the rules from there soon forces a contradiction, so R7C4 must be a dog.
  28. R6C4 and R7C4 are both dogs, so R8C4 must be a cat (no three in a row).
  29. R8C3 and R8C4 are both cats, so R8C2 must be a dog (no three in a row).
  30. R8C3 and R8C4 are both cats, so R8C5 must be a dog (no three in a row).
  31. The × clue between R8C5 and R8C6 means they are different. R8C5 is a dog, so R8C6 is a cat.
  32. R8C5 and R10C5 are both dogs with one square between them, so R9C5 must be a cat.
  33. R7C6 and R8C6 are both cats, so R9C6 must be a dog (no three in a row).
  34. Column 4 already has its 5 cats, so R9C4 must be dogs.
  35. R9C3 and R9C4 are both dogs, so R9C2 must be a cat (no three in a row).
  36. Column 4 already has its 5 cats, so R10C4 must be dogs.
  37. R10C4 and R10C5 are both dogs, so R10C3 must be a cat (no three in a row).
  38. R10C2 and R10C3 are both cats, so R10C1 must be a dog (no three in a row).
  39. R10C4 and R10C5 are both dogs, so R10C6 must be a cat (no three in a row).
  40. R10C6 and R10C7 are both cats, so R10C8 must be a dog (no three in a row).
  41. R10C8 and R10C9 are both dogs, so R10C10 must be a cat (no three in a row).
  42. Column 6 already has its 5 cats, so R5C6 must be dogs.
  43. The = clue between R5C6 and R5C7 means they are the same. R5C6 is a dog, so R5C7 is a dog.
  44. R5C6 and R5C7 are both dogs, so R5C5 must be a cat (no three in a row).
  45. R5C4 and R5C5 are both cats, so R5C3 must be a dog (no three in a row).
  46. R5C6 and R5C7 are both dogs, so R5C8 must be a cat (no three in a row).
  47. R5C5 and R6C5 are both cats, so R7C5 must be a dog (no three in a row).
  48. R7C4 and R7C5 are both dogs, so R7C3 must be a cat (no three in a row).
  49. R7C3 and R8C3 are both cats, so R6C3 must be a dog (no three in a row).
  50. R6C3 and R6C4 are both dogs, so R6C2 must be a cat (no three in a row).
  51. R5C3 and R6C3 are both dogs, so R4C3 must be a cat (no three in a row).
  52. R4C3 and R4C4 are both cats, so R4C2 must be a dog (no three in a row).
  53. R3C2 and R4C2 are both dogs, so R2C2 must be a cat (no three in a row).
  54. R3C2 and R4C2 are both dogs, so R5C2 must be a cat (no three in a row).
  55. R5C2 and R6C2 are both cats, so R7C2 must be a dog (no three in a row).
  56. R4C7 and R5C7 are both dogs, so R3C7 must be a cat (no three in a row).
  57. R3C7 and R3C8 are both cats, so R3C9 must be a dog (no three in a row).
  58. R2C7 and R3C7 are both cats, so R1C7 must be a dog (no three in a row).
  59. R1C7 and R1C8 are both dogs, so R1C9 must be a cat (no three in a row).
  60. R4C7 and R5C7 are both dogs, so R6C7 must be a cat (no three in a row).
  61. Row 2 already has its 5 cats, so R2C1 must be dogs.
  62. Row 3 already has its 5 cats, so R3C10 must be dogs.
  63. R2C10 and R3C10 are both dogs, so R1C10 must be a cat (no three in a row).
  64. R2C10 and R3C10 are both dogs, so R4C10 must be a cat (no three in a row).
  65. Row 4 already has its 5 cats, so R4C1 must be dogs.
  66. Column 2 already has its 5 cats, so R1C2 must be dogs.
  67. R1C2 and R1C3 are both dogs, so R1C1 must be a cat (no three in a row).
  68. Imagine R9C7 were a cat: following the rules from there soon forces a contradiction, so R9C7 must be a dog.
  69. R9C6 and R9C7 are both dogs, so R9C8 must be a cat (no three in a row).
  70. Imagine R7C1 were a cat: following the rules from there soon forces a contradiction, so R7C1 must be a dog.
  71. The = clue between R7C1 and R8C1 means they are the same. R7C1 is a dog, so R8C1 is a dog.
  72. R7C1 and R8C1 are both dogs, so R6C1 must be a cat (no three in a row).
  73. R7C1 and R8C1 are both dogs, so R9C1 must be a cat (no three in a row).
  74. Column 1 already has its 5 dogs, so R5C1 must be cats.
  75. Row 5 already has its 5 cats, so R5C9 and R5C10 must be dogs.
  76. Imagine R6C8 were a cat: following the rules from there soon forces a contradiction, so R6C8 must be a dog.
  77. Imagine R6C9 were a dog: following the rules from there soon forces a contradiction, so R6C9 must be a cat.
  78. Row 6 already has its 5 cats, so R6C10 must be dogs.
  79. R5C10 and R6C10 are both dogs, so R7C10 must be a cat (no three in a row).
  80. Imagine R7C7 were a dog: following the rules from there soon forces a contradiction, so R7C7 must be a cat.
  81. The × clue between R7C7 and R8C7 means they are different. R7C7 is a cat, so R8C7 is a dog.
  82. R7C6 and R7C7 are both cats, so R7C8 must be a dog (no three in a row).
  83. R6C8 and R7C8 are both dogs, so R8C8 must be a cat (no three in a row).
  84. Row 7 already has its 5 dogs, so R7C9 must be cats.
  85. R6C9 and R7C9 are both cats, so R8C9 must be a dog (no three in a row).
  86. R8C9 and R10C9 are both dogs with one square between them, so R9C9 must be a cat.
  87. R9C8 and R9C9 are both cats, so R9C10 must be a dog (no three in a row).
  88. Row 8 already has its 5 dogs, so R8C10 must be cats.

About this puzzle

This 10×10 grid starts with 11 filled squares and 10 = / × clues. It can be solved in 88 steps using a "what if" trial of one square on top of the basic rules.

Start with the clues and the squares already filled in. An = or × next to a known animal gives you its neighbor immediately.

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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