Cats & Dogs #248: 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 R6C3 and R6C2 means they are the same. R6C3 is a dog, so R6C2 is a dog.
  2. R6C2 and R6C3 are both dogs, so R6C1 must be a cat (no three in a row).
  3. R6C2 and R6C3 are both dogs, so R6C4 must be a cat (no three in a row).
  4. The = clue between R6C4 and R6C5 means they are the same. R6C4 is a cat, so R6C5 is a cat.
  5. R6C4 and R6C5 are both cats, so R6C6 must be a dog (no three in a row).
  6. R6C6 and R6C7 are both dogs, so R6C8 must be a cat (no three in a row).
  7. R6C3 and R7C3 are both dogs, so R5C3 must be a cat (no three in a row).
  8. The = clue between R5C3 and R5C4 means they are the same. R5C3 is a cat, so R5C4 is a cat.
  9. R5C3 and R5C4 are both cats, so R5C2 must be a dog (no three in a row).
  10. R5C3 and R5C4 are both cats, so R5C5 must be a dog (no three in a row).
  11. R5C2 and R6C2 are both dogs, so R4C2 must be a cat (no three in a row).
  12. R5C2 and R6C2 are both dogs, so R7C2 must be a cat (no three in a row).
  13. R6C3 and R7C3 are both dogs, so R8C3 must be a cat (no three in a row).
  14. R5C4 and R6C4 are both cats, so R4C4 must be a dog (no three in a row).
  15. R5C4 and R6C4 are both cats, so R7C4 must be a dog (no three in a row).
  16. R7C3 and R7C4 are both dogs, so R7C5 must be a cat (no three in a row).
  17. R6C5 and R7C5 are both cats, so R8C5 must be a dog (no three in a row).
  18. The × clue between R8C5 and R8C4 means they are different. R8C5 is a dog, so R8C4 is a cat.
  19. R8C3 and R8C4 are both cats, so R8C2 must be a dog (no three in a row).
  20. Imagine R1C5 were a cat: following the rules from there soon forces a contradiction, so R1C5 must be a dog.
  21. The = clue between R1C5 and R2C5 means they are the same. R1C5 is a dog, so R2C5 is a dog.
  22. The × clue between R2C5 and R2C6 means they are different. R2C5 is a dog, so R2C6 is a cat.
  23. R1C5 and R2C5 are both dogs, so R3C5 must be a cat (no three in a row).
  24. Imagine R9C3 were a cat: following the rules from there soon forces a contradiction, so R9C3 must be a dog.
  25. The = clue between R9C3 and R10C3 means they are the same. R9C3 is a dog, so R10C3 is a dog.
  26. Imagine R1C3 were a dog: following the rules from there soon forces a contradiction, so R1C3 must be a cat.
  27. Imagine R1C6 were a dog: following the rules from there soon forces a contradiction, so R1C6 must be a cat.
  28. R1C6 and R2C6 are both cats, so R3C6 must be a dog (no three in a row).
  29. Imagine R1C7 were a cat: following the rules from there soon forces a contradiction, so R1C7 must be a dog.
  30. The = clue between R1C7 and R2C7 means they are the same. R1C7 is a dog, so R2C7 is a dog.
  31. The × clue between R2C7 and R2C8 means they are different. R2C7 is a dog, so R2C8 is a cat.
  32. R1C7 and R2C7 are both dogs, so R3C7 must be a cat (no three in a row).
  33. The = clue between R3C7 and R3C8 means they are the same. R3C7 is a cat, so R3C8 is a cat.
  34. R3C7 and R3C8 are both cats, so R3C9 must be a dog (no three in a row).
  35. R2C8 and R3C8 are both cats, so R1C8 must be a dog (no three in a row).
  36. R1C7 and R1C8 are both dogs, so R1C9 must be a cat (no three in a row).
  37. R2C8 and R3C8 are both cats, so R4C8 must be a dog (no three in a row).
  38. Imagine R2C3 were a dog: following the rules from there soon forces a contradiction, so R2C3 must be a cat.
  39. R1C3 and R2C3 are both cats, so R3C3 must be a dog (no three in a row).
  40. Column 3 already has its 5 dogs, so R4C3 must be cats.
  41. R4C2 and R4C3 are both cats, so R4C1 must be a dog (no three in a row).
  42. The × clue between R4C1 and R5C1 means they are different. R4C1 is a dog, so R5C1 is a cat.
  43. R5C1 and R6C1 are both cats, so R7C1 must be a dog (no three in a row).
  44. Imagine R5C6 were a dog: following the rules from there soon forces a contradiction, so R5C6 must be a cat.
  45. Imagine R4C7 were a dog: following the rules from there soon forces a contradiction, so R4C7 must be a cat.
  46. R3C7 and R4C7 are both cats, so R5C7 must be a dog (no three in a row).
  47. R5C7 and R6C7 are both dogs, so R7C7 must be a cat (no three in a row).
  48. R7C5 and R7C7 are both cats with one square between them, so R7C6 must be a dog.
  49. R6C6 and R7C6 are both dogs, so R8C6 must be a cat (no three in a row).
  50. Row 7 already has its 5 dogs, so R7C8 must be cats.
  51. R6C8 and R7C8 are both cats, so R5C8 must be a dog (no three in a row).
  52. R5C7 and R5C8 are both dogs, so R5C9 must be a cat (no three in a row).
  53. R6C8 and R7C8 are both cats, so R8C8 must be a dog (no three in a row).
  54. Row 5 already has its 5 cats, so R5C10 must be dogs.
  55. Row 7 already has its 5 dogs, so R7C10 must be cats.
  56. Imagine R1C2 were a cat: following the rules from there soon forces a contradiction, so R1C2 must be a dog.
  57. Imagine R1C1 were a dog: following the rules from there soon forces a contradiction, so R1C1 must be a cat.
  58. Imagine R1C4 were a dog: following the rules from there soon forces a contradiction, so R1C4 must be a cat.
  59. Row 1 already has its 5 cats, so R1C10 must be dogs.
  60. The = clue between R1C10 and R2C10 means they are the same. R1C10 is a dog, so R2C10 is a dog.
  61. R1C10 and R2C10 are both dogs, so R3C10 must be a cat (no three in a row).
  62. Imagine R2C1 were a dog: following the rules from there soon forces a contradiction, so R2C1 must be a cat.
  63. R2C1 and R2C3 are both cats with one square between them, so R2C2 must be a dog.
  64. R1C1 and R2C1 are both cats, so R3C1 must be a dog (no three in a row).
  65. R3C1 and R3C3 are both dogs with one square between them, so R3C2 must be a cat.
  66. Row 3 already has its 5 cats, so R3C4 must be dogs.
  67. R3C4 and R4C4 are both dogs, so R2C4 must be a cat (no three in a row).
  68. Row 2 already has its 5 cats, so R2C9 must be dogs.
  69. R2C9 and R3C9 are both dogs, so R4C9 must be a cat (no three in a row).
  70. R4C9 and R5C9 are both cats, so R6C9 must be a dog (no three in a row).
  71. R6C9 and R7C9 are both dogs, so R8C9 must be a cat (no three in a row).
  72. R8C9 and R9C9 are both cats, so R10C9 must be a dog (no three in a row).
  73. Row 6 already has its 5 dogs, so R6C10 must be cats.
  74. R6C10 and R7C10 are both cats, so R8C10 must be a dog (no three in a row).
  75. Column 2 already has its 5 dogs, so R9C2 and R10C2 must be cats.
  76. Column 4 already has its 5 cats, so R9C4 must be dogs.
  77. R9C3 and R9C4 are both dogs, so R9C5 must be a cat (no three in a row).
  78. Column 4 already has its 5 cats, so R10C4 must be dogs.
  79. R10C3 and R10C4 are both dogs, so R10C5 must be a cat (no three in a row).
  80. Column 5 already has its 5 cats, so R4C5 must be dogs.
  81. R4C4 and R4C5 are both dogs, so R4C6 must be a cat (no three in a row).
  82. Row 4 already has its 5 cats, so R4C10 must be dogs.
  83. Column 6 already has its 5 cats, so R9C6 and R10C6 must be dogs.
  84. Column 10 already has its 5 dogs, so R9C10 must be cats.
  85. R9C9 and R9C10 are both cats, so R9C8 must be a dog (no three in a row).
  86. R9C6 and R9C8 are both dogs with one square between them, so R9C7 must be a cat.
  87. R7C7 and R9C7 are both cats with one square between them, so R8C7 must be a dog.
  88. R8C8 and R9C8 are both dogs, so R10C8 must be a cat (no three in a row).
  89. Row 8 already has its 5 dogs, so R8C1 must be cats.
  90. Row 9 already has its 5 cats, so R9C1 must be dogs.
  91. Column 1 already has its 5 cats, so R10C1 must be dogs.
  92. Row 10 already has its 5 dogs, so R10C7 and R10C10 must be cats.

About this puzzle

This 10×10 grid starts with 5 filled squares and 12 = / × clues. It can be solved in 92 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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