Cats & Dogs #271: 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 R2C2 and R1C2 means they are the same. R2C2 is a dog, so R1C2 is a dog.
  2. The × clue between R2C2 and R2C3 means they are different. R2C2 is a dog, so R2C3 is a cat.
  3. The × clue between R2C3 and R1C3 means they are different. R2C3 is a cat, so R1C3 is a dog.
  4. The × clue between R3C4 and R4C4 means they are different. R3C4 is a dog, so R4C4 is a cat.
  5. R1C2 and R1C3 are both dogs, so R1C1 must be a cat (no three in a row).
  6. R1C2 and R1C3 are both dogs, so R1C4 must be a cat (no three in a row).
  7. R4C3 and R4C4 are both cats, so R4C2 must be a dog (no three in a row).
  8. R4C3 and R4C4 are both cats, so R4C5 must be a dog (no three in a row).
  9. R1C1 and R2C1 are both cats, so R3C1 must be a dog (no three in a row).
  10. R1C2 and R2C2 are both dogs, so R3C2 must be a cat (no three in a row).
  11. R2C3 and R4C3 are both cats with one square between them, so R3C3 must be a dog.
  12. R3C3 and R3C4 are both dogs, so R3C5 must be a cat (no three in a row).
  13. The × clue between R3C5 and R3C6 means they are different. R3C5 is a cat, so R3C6 is a dog.
  14. Imagine R1C10 were a cat: following the rules from there soon forces a contradiction, so R1C10 must be a dog.
  15. The = clue between R1C10 and R2C10 means they are the same. R1C10 is a dog, so R2C10 is a dog.
  16. R1C10 and R2C10 are both dogs, so R3C10 must be a cat (no three in a row).
  17. R3C10 and R5C10 are both cats with one square between them, so R4C10 must be a dog.
  18. The = clue between R4C10 and R4C9 means they are the same. R4C10 is a dog, so R4C9 is a dog.
  19. R4C9 and R4C10 are both dogs, so R4C8 must be a cat (no three in a row).
  20. Imagine R2C8 were a cat: following the rules from there soon forces a contradiction, so R2C8 must be a dog.
  21. R2C8 and R2C10 are both dogs with one square between them, so R2C9 must be a cat.
  22. Imagine R3C7 were a dog: following the rules from there soon forces a contradiction, so R3C7 must be a cat.
  23. The = clue between R3C7 and R3C8 means they are the same. R3C7 is a cat, so R3C8 is a cat.
  24. R3C7 and R3C8 are both cats, so R3C9 must be a dog (no three in a row).
  25. R3C8 and R4C8 are both cats, so R5C8 must be a dog (no three in a row).
  26. R3C9 and R4C9 are both dogs, so R5C9 must be a cat (no three in a row).
  27. Imagine R4C1 were a dog: following the rules from there soon forces a contradiction, so R4C1 must be a cat.
  28. Imagine R5C1 were a cat: following the rules from there soon forces a contradiction, so R5C1 must be a dog.
  29. R5C1 and R7C1 are both dogs with one square between them, so R6C1 must be a cat.
  30. Column 1 already has its 5 cats, so R8C1 and R10C1 must be dogs.
  31. Imagine R5C2 were a dog: following the rules from there soon forces a contradiction, so R5C2 must be a cat.
  32. Imagine R6C5 were a dog: following the rules from there soon forces a contradiction, so R6C5 must be a cat.
  33. The = clue between R6C5 and R7C5 means they are the same. R6C5 is a cat, so R7C5 is a cat.
  34. R6C5 and R7C5 are both cats, so R5C5 must be a dog (no three in a row).
  35. Imagine R6C6 were a cat: following the rules from there soon forces a contradiction, so R6C6 must be a dog.
  36. The = clue between R6C6 and R6C7 means they are the same. R6C6 is a dog, so R6C7 is a dog.
  37. R6C6 and R6C7 are both dogs, so R6C8 must be a cat (no three in a row).
  38. Imagine R6C9 were a cat: following the rules from there soon forces a contradiction, so R6C9 must be a dog.
  39. The = clue between R6C9 and R7C9 means they are the same. R6C9 is a dog, so R7C9 is a dog.
  40. R6C9 and R7C9 are both dogs, so R8C9 must be a cat (no three in a row).
  41. Imagine R1C9 were a dog: following the rules from there soon forces a contradiction, so R1C9 must be a cat.
  42. Imagine R7C4 were a cat: following the rules from there soon forces a contradiction, so R7C4 must be a dog.
  43. Imagine R6C3 were a cat: following the rules from there soon forces a contradiction, so R6C3 must be a dog.
  44. The × clue between R6C3 and R7C3 means they are different. R6C3 is a dog, so R7C3 is a cat.
  45. Imagine R5C3 were a dog: following the rules from there soon forces a contradiction, so R5C3 must be a cat.
  46. R5C2 and R5C3 are both cats, so R5C4 must be a dog (no three in a row).
  47. R5C4 and R5C5 are both dogs, so R5C6 must be a cat (no three in a row).
  48. R5C4 and R7C4 are both dogs with one square between them, so R6C4 must be a cat.
  49. Row 5 already has its 5 cats, so R5C7 must be dogs.
  50. R5C7 and R6C7 are both dogs, so R4C7 must be a cat (no three in a row).
  51. R4C7 and R4C8 are both cats, so R4C6 must be a dog (no three in a row).
  52. R3C6 and R4C6 are both dogs, so R2C6 must be a cat (no three in a row).
  53. The × clue between R2C6 and R2C5 means they are different. R2C6 is a cat, so R2C5 is a dog.
  54. R3C7 and R4C7 are both cats, so R2C7 must be a dog (no three in a row).
  55. R5C7 and R6C7 are both dogs, so R7C7 must be a cat (no three in a row).
  56. R7C5 and R7C7 are both cats with one square between them, so R7C6 must be a dog.
  57. R6C6 and R7C6 are both dogs, so R8C6 must be a cat (no three in a row).
  58. Row 2 already has its 5 dogs, so R2C4 must be cats.
  59. Column 3 already has its 5 cats, so R8C3 must be dogs.
  60. R8C1 and R8C3 are both dogs with one square between them, so R8C2 must be a cat.
  61. R8C3 and R8C5 are both dogs with one square between them, so R8C4 must be a cat.
  62. Column 3 already has its 5 cats, so R9C3 must be dogs.
  63. Column 4 already has its 5 cats, so R9C4 must be dogs.
  64. R9C3 and R9C4 are both dogs, so R9C2 must be a cat (no three in a row).
  65. R9C3 and R9C4 are both dogs, so R9C5 must be a cat (no three in a row).
  66. R8C2 and R9C2 are both cats, so R7C2 must be a dog (no three in a row).
  67. R8C2 and R9C2 are both cats, so R10C2 must be a dog (no three in a row).
  68. Row 7 already has its 5 dogs, so R7C8 must be cats.
  69. R6C8 and R7C8 are both cats, so R8C8 must be a dog (no three in a row).
  70. The × clue between R8C8 and R8C7 means they are different. R8C8 is a dog, so R8C7 is a cat.
  71. R7C7 and R8C7 are both cats, so R9C7 must be a dog (no three in a row).
  72. Row 7 already has its 5 dogs, so R7C10 must be cats.
  73. R5C10 and R7C10 are both cats with one square between them, so R6C10 must be a dog.
  74. Row 6 already has its 5 dogs, so R6C2 must be cats.
  75. Row 8 already has its 5 cats, so R8C10 must be dogs.
  76. Column 4 already has its 5 cats, so R10C4 must be dogs.
  77. Column 10 already has its 5 dogs, so R9C10 and R10C10 must be cats.
  78. Imagine R1C5 were a cat: following the rules from there soon forces a contradiction, so R1C5 must be a dog.
  79. Column 5 already has its 5 dogs, so R10C5 must be cats.
  80. Imagine R1C6 were a dog: following the rules from there soon forces a contradiction, so R1C6 must be a cat.
  81. Imagine R1C7 were a dog: following the rules from there soon forces a contradiction, so R1C7 must be a cat.
  82. R1C6 and R1C7 are both cats, so R1C8 must be a dog (no three in a row).
  83. Column 7 already has its 5 cats, so R10C7 must be dogs.
  84. Imagine R9C6 were a cat: following the rules from there soon forces a contradiction, so R9C6 must be a dog.
  85. R9C6 and R9C7 are both dogs, so R9C8 must be a cat (no three in a row).
  86. R9C8 and R9C10 are both cats with one square between them, so R9C9 must be a dog.
  87. Column 6 already has its 5 dogs, so R10C6 must be cats.
  88. Column 8 already has its 5 cats, so R10C8 must be dogs.
  89. R10C7 and R10C8 are both dogs, so R10C9 must be a cat (no three in a row).

About this puzzle

This 10×10 grid starts with 9 filled squares and 14 = / × clues. It can be solved in 89 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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