Cats & Dogs #208: 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 R7C6 and R7C5 means they are different. R7C6 is a cat, so R7C5 is a dog.
  2. The = clue between R9C10 and R10C10 means they are the same. R9C10 is a cat, so R10C10 is a cat.
  3. R7C5 and R8C5 are both dogs, so R6C5 must be a cat (no three in a row).
  4. R7C5 and R8C5 are both dogs, so R9C5 must be a cat (no three in a row).
  5. R5C8 and R6C8 are both dogs, so R4C8 must be a cat (no three in a row).
  6. R4C8 and R4C10 are both cats with one square between them, so R4C9 must be a dog.
  7. R5C8 and R6C8 are both dogs, so R7C8 must be a cat (no three in a row).
  8. R7C6 and R7C8 are both cats with one square between them, so R7C7 must be a dog.
  9. R9C10 and R10C10 are both cats, so R8C10 must be a dog (no three in a row).
  10. Imagine R4C7 were a cat: following the rules from there soon forces a contradiction, so R4C7 must be a dog.
  11. Imagine R5C9 were a dog: following the rules from there soon forces a contradiction, so R5C9 must be a cat.
  12. Imagine R5C10 were a cat: following the rules from there soon forces a contradiction, so R5C10 must be a dog.
  13. The × clue between R5C10 and R6C10 means they are different. R5C10 is a dog, so R6C10 is a cat.
  14. Imagine R6C6 were a cat: following the rules from there soon forces a contradiction, so R6C6 must be a dog.
  15. R6C6 and R6C8 are both dogs with one square between them, so R6C7 must be a cat.
  16. Imagine R7C3 were a dog: following the rules from there soon forces a contradiction, so R7C3 must be a cat.
  17. The = clue between R7C3 and R7C4 means they are the same. R7C3 is a cat, so R7C4 is a cat.
  18. R7C3 and R7C4 are both cats, so R7C2 must be a dog (no three in a row).
  19. Imagine R6C3 were a cat: following the rules from there soon forces a contradiction, so R6C3 must be a dog.
  20. Imagine R7C10 were a cat: following the rules from there soon forces a contradiction, so R7C10 must be a dog.
  21. Imagine R6C9 were a cat: following the rules from there soon forces a contradiction, so R6C9 must be a dog.
  22. Imagine R8C6 were a dog: following the rules from there soon forces a contradiction, so R8C6 must be a cat.
  23. R7C6 and R8C6 are both cats, so R9C6 must be a dog (no three in a row).
  24. Imagine R8C8 were a cat: following the rules from there soon forces a contradiction, so R8C8 must be a dog.
  25. The = clue between R8C8 and R9C8 means they are the same. R8C8 is a dog, so R9C8 is a dog.
  26. R8C8 and R8C10 are both dogs with one square between them, so R8C9 must be a cat.
  27. R9C6 and R9C8 are both dogs with one square between them, so R9C7 must be a cat.
  28. R8C8 and R9C8 are both dogs, so R10C8 must be a cat (no three in a row).
  29. R10C8 and R10C10 are both cats with one square between them, so R10C9 must be a dog.
  30. Imagine R1C7 were a cat: following the rules from there soon forces a contradiction, so R1C7 must be a dog.
  31. Imagine R1C8 were a dog: following the rules from there soon forces a contradiction, so R1C8 must be a cat.
  32. Imagine R1C9 were a dog: following the rules from there soon forces a contradiction, so R1C9 must be a cat.
  33. The = clue between R1C9 and R2C9 means they are the same. R1C9 is a cat, so R2C9 is a cat.
  34. R1C8 and R1C9 are both cats, so R1C10 must be a dog (no three in a row).
  35. R2C7 and R2C9 are both cats with one square between them, so R2C8 must be a dog.
  36. R1C9 and R2C9 are both cats, so R3C9 must be a dog (no three in a row).
  37. Column 8 already has its 5 dogs, so R3C8 must be cats.
  38. Imagine R5C4 were a cat: following the rules from there soon forces a contradiction, so R5C4 must be a dog.
  39. Imagine R5C6 were a dog: following the rules from there soon forces a contradiction, so R5C6 must be a cat.
  40. Imagine R6C1 were a cat: following the rules from there soon forces a contradiction, so R6C1 must be a dog.
  41. The = clue between R6C1 and R7C1 means they are the same. R6C1 is a dog, so R7C1 is a dog.
  42. R6C1 and R6C3 are both dogs with one square between them, so R6C2 must be a cat.
  43. R6C1 and R7C1 are both dogs, so R5C1 must be a cat (no three in a row).
  44. The × clue between R5C1 and R4C1 means they are different. R5C1 is a cat, so R4C1 is a dog.
  45. R6C1 and R7C1 are both dogs, so R8C1 must be a cat (no three in a row).
  46. R8C1 and R9C1 are both cats, so R10C1 must be a dog (no three in a row).
  47. Row 6 already has its 5 dogs, so R6C4 must be cats.
  48. R6C4 and R7C4 are both cats, so R8C4 must be a dog (no three in a row).
  49. R8C4 and R8C5 are both dogs, so R8C3 must be a cat (no three in a row).
  50. R8C1 and R8C3 are both cats with one square between them, so R8C2 must be a dog.
  51. R7C2 and R8C2 are both dogs, so R9C2 must be a cat (no three in a row).
  52. R9C1 and R9C2 are both cats, so R9C3 must be a dog (no three in a row).
  53. Row 7 already has its 5 dogs, so R7C9 must be cats.
  54. R7C9 and R8C9 are both cats, so R9C9 must be a dog (no three in a row).
  55. Row 8 already has its 5 dogs, so R8C7 must be cats.
  56. R8C7 and R9C7 are both cats, so R10C7 must be a dog (no three in a row).
  57. The × clue between R10C7 and R10C6 means they are different. R10C7 is a dog, so R10C6 is a cat.
  58. Row 9 already has its 5 cats, so R9C4 must be dogs.
  59. The × clue between R9C4 and R10C4 means they are different. R9C4 is a dog, so R10C4 is a cat.
  60. R10C4 and R10C6 are both cats with one square between them, so R10C5 must be a dog.
  61. Column 4 already has its 5 cats, so R2C4 and R3C4 must be dogs.
  62. R3C4 and R3C6 are both dogs with one square between them, so R3C5 must be a cat.
  63. The = clue between R3C5 and R4C5 means they are the same. R3C5 is a cat, so R4C5 is a cat.
  64. R4C4 and R4C5 are both cats, so R4C3 must be a dog (no three in a row).
  65. R4C1 and R4C3 are both dogs with one square between them, so R4C2 must be a cat.
  66. R4C4 and R4C5 are both cats, so R4C6 must be a dog (no three in a row).
  67. R4C2 and R6C2 are both cats with one square between them, so R5C2 must be a dog.
  68. R5C2 and R5C4 are both dogs with one square between them, so R5C3 must be a cat.
  69. R3C5 and R4C5 are both cats, so R2C5 must be a dog (no three in a row).
  70. R2C4 and R2C5 are both dogs, so R2C3 must be a cat (no three in a row).
  71. R2C4 and R2C5 are both dogs, so R2C6 must be a cat (no three in a row).
  72. R3C5 and R4C5 are both cats, so R5C5 must be a dog (no three in a row).
  73. Row 5 already has its 5 dogs, so R5C7 must be cats.
  74. Column 5 already has its 5 dogs, so R1C5 must be cats.
  75. R1C4 and R1C5 are both cats, so R1C3 must be a dog (no three in a row).
  76. R1C4 and R1C5 are both cats, so R1C6 must be a dog (no three in a row).
  77. Column 7 already has its 5 cats, so R3C7 must be dogs.
  78. Imagine R2C2 were a cat: following the rules from there soon forces a contradiction, so R2C2 must be a dog.
  79. Imagine R2C1 were a dog: following the rules from there soon forces a contradiction, so R2C1 must be a cat.
  80. Row 2 already has its 5 cats, so R2C10 must be dogs.
  81. R1C10 and R2C10 are both dogs, so R3C10 must be a cat (no three in a row).
  82. Imagine R3C2 were a dog: following the rules from there soon forces a contradiction, so R3C2 must be a cat.
  83. The = clue between R3C2 and R3C3 means they are the same. R3C2 is a cat, so R3C3 is a cat.
  84. R3C2 and R3C3 are both cats, so R3C1 must be a dog (no three in a row).
  85. Column 1 already has its 5 dogs, so R1C1 must be cats.
  86. Row 1 already has its 5 cats, so R1C2 must be dogs.
  87. Column 2 already has its 5 dogs, so R10C2 must be cats.
  88. R10C2 and R10C4 are both cats with one square between them, so R10C3 must be a dog.

About this puzzle

This 10×10 grid starts with 11 filled squares and 12 = / × 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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