Cats & Dogs #277: 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 R6C8 and R6C9 means they are different. R6C8 is a cat, so R6C9 is a dog.
  2. The = clue between R6C9 and R7C9 means they are the same. R6C9 is a dog, so R7C9 is a dog.
  3. R3C3 and R3C4 are both dogs, so R3C2 must be a cat (no three in a row).
  4. The × clue between R3C2 and R2C2 means they are different. R3C2 is a cat, so R2C2 is a dog.
  5. R3C3 and R3C4 are both dogs, so R3C5 must be a cat (no three in a row).
  6. R3C2 and R5C2 are both cats with one square between them, so R4C2 must be a dog.
  7. R6C9 and R7C9 are both dogs, so R5C9 must be a cat (no three in a row).
  8. R6C9 and R7C9 are both dogs, so R8C9 must be a cat (no three in a row).
  9. The × clue between R8C9 and R8C8 means they are different. R8C9 is a cat, so R8C8 is a dog.
  10. Imagine R3C1 were a dog: following the rules from there soon forces a contradiction, so R3C1 must be a cat.
  11. The = clue between R3C1 and R4C1 means they are the same. R3C1 is a cat, so R4C1 is a cat.
  12. R3C1 and R4C1 are both cats, so R2C1 must be a dog (no three in a row).
  13. R2C1 and R2C2 are both dogs, so R2C3 must be a cat (no three in a row).
  14. Imagine R8C6 were a dog: following the rules from there soon forces a contradiction, so R8C6 must be a cat.
  15. The = clue between R8C6 and R8C7 means they are the same. R8C6 is a cat, so R8C7 is a cat.
  16. R8C6 and R8C7 are both cats, so R8C5 must be a dog (no three in a row).
  17. Imagine R6C5 were a dog: following the rules from there soon forces a contradiction, so R6C5 must be a cat.
  18. The = clue between R6C5 and R7C5 means they are the same. R6C5 is a cat, so R7C5 is a cat.
  19. R6C5 and R7C5 are both cats, so R5C5 must be a dog (no three in a row).
  20. The × clue between R5C5 and R4C5 means they are different. R5C5 is a dog, so R4C5 is a cat.
  21. R4C5 and R4C6 are both cats, so R4C4 must be a dog (no three in a row).
  22. R4C2 and R4C4 are both dogs with one square between them, so R4C3 must be a cat.
  23. R4C5 and R4C6 are both cats, so R4C7 must be a dog (no three in a row).
  24. R3C4 and R4C4 are both dogs, so R2C4 must be a cat (no three in a row).
  25. R2C3 and R2C4 are both cats, so R2C5 must be a dog (no three in a row).
  26. R3C4 and R4C4 are both dogs, so R5C4 must be a cat (no three in a row).
  27. R5C2 and R5C4 are both cats with one square between them, so R5C3 must be a dog.
  28. The × clue between R5C3 and R6C3 means they are different. R5C3 is a dog, so R6C3 is a cat.
  29. R6C3 and R6C5 are both cats with one square between them, so R6C4 must be a dog.
  30. Imagine R1C3 were a dog: following the rules from there soon forces a contradiction, so R1C3 must be a cat.
  31. The = clue between R1C3 and R1C4 means they are the same. R1C3 is a cat, so R1C4 is a cat.
  32. R1C3 and R1C4 are both cats, so R1C2 must be a dog (no three in a row).
  33. R1C3 and R1C4 are both cats, so R1C5 must be a dog (no three in a row).
  34. Imagine R4C10 were a cat: following the rules from there soon forces a contradiction, so R4C10 must be a dog.
  35. Imagine R5C8 were a cat: following the rules from there soon forces a contradiction, so R5C8 must be a dog.
  36. Imagine R6C1 were a cat: following the rules from there soon forces a contradiction, so R6C1 must be a dog.
  37. The = clue between R6C1 and R6C2 means they are the same. R6C1 is a dog, so R6C2 is a dog.
  38. R5C1 and R6C1 are both dogs, so R7C1 must be a cat (no three in a row).
  39. Column 2 already has its 5 dogs, so R7C2 must be cats.
  40. R7C1 and R7C2 are both cats, so R7C3 must be a dog (no three in a row).
  41. Column 2 already has its 5 dogs, so R8C2 and R10C2 must be cats.
  42. Imagine R6C10 were a dog: following the rules from there soon forces a contradiction, so R6C10 must be a cat.
  43. Imagine R7C8 were a dog: following the rules from there soon forces a contradiction, so R7C8 must be a cat.
  44. Imagine R8C1 were a cat: following the rules from there soon forces a contradiction, so R8C1 must be a dog.
  45. Imagine R8C10 were a cat: following the rules from there soon forces a contradiction, so R8C10 must be a dog.
  46. Imagine R9C1 were a dog: following the rules from there soon forces a contradiction, so R9C1 must be a cat.
  47. The = clue between R9C1 and R10C1 means they are the same. R9C1 is a cat, so R10C1 is a cat.
  48. R10C1 and R10C2 are both cats, so R10C3 must be a dog (no three in a row).
  49. Column 1 already has its 5 cats, so R1C1 must be dogs.
  50. Imagine R10C6 were a cat: following the rules from there soon forces a contradiction, so R10C6 must be a dog.
  51. The = clue between R10C6 and R10C7 means they are the same. R10C6 is a dog, so R10C7 is a dog.
  52. R10C6 and R10C7 are both dogs, so R10C5 must be a cat (no three in a row).
  53. R10C6 and R10C7 are both dogs, so R10C8 must be a cat (no three in a row).
  54. Column 5 already has its 5 cats, so R9C5 must be dogs.
  55. The × clue between R9C5 and R9C6 means they are different. R9C5 is a dog, so R9C6 is a cat.
  56. R8C6 and R9C6 are both cats, so R7C6 must be a dog (no three in a row).
  57. Imagine R1C6 were a cat: following the rules from there soon forces a contradiction, so R1C6 must be a dog.
  58. The = clue between R1C6 and R2C6 means they are the same. R1C6 is a dog, so R2C6 is a dog.
  59. R1C5 and R1C6 are both dogs, so R1C7 must be a cat (no three in a row).
  60. R2C5 and R2C6 are both dogs, so R2C7 must be a cat (no three in a row).
  61. R1C6 and R2C6 are both dogs, so R3C6 must be a cat (no three in a row).
  62. R3C5 and R3C6 are both cats, so R3C7 must be a dog (no three in a row).
  63. R3C6 and R4C6 are both cats, so R5C6 must be a dog (no three in a row).
  64. R5C5 and R5C6 are both dogs, so R5C7 must be a cat (no three in a row).
  65. R5C6 and R7C6 are both dogs with one square between them, so R6C6 must be a cat.
  66. R6C5 and R6C6 are both cats, so R6C7 must be a dog (no three in a row).
  67. Row 5 already has its 5 dogs, so R5C10 must be cats.
  68. R5C10 and R6C10 are both cats, so R7C10 must be a dog (no three in a row).
  69. R7C10 and R8C10 are both dogs, so R9C10 must be a cat (no three in a row).
  70. Imagine R1C10 were a dog: following the rules from there soon forces a contradiction, so R1C10 must be a cat.
  71. Imagine R2C10 were a dog: following the rules from there soon forces a contradiction, so R2C10 must be a cat.
  72. R1C10 and R2C10 are both cats, so R3C10 must be a dog (no three in a row).
  73. Column 10 already has its 5 cats, so R10C10 must be dogs.
  74. Row 10 already has its 5 dogs, so R10C4 must be cats.
  75. Imagine R7C4 were a cat: following the rules from there soon forces a contradiction, so R7C4 must be a dog.
  76. R6C4 and R7C4 are both dogs, so R8C4 must be a cat (no three in a row).
  77. R8C2 and R8C4 are both cats with one square between them, so R8C3 must be a dog.
  78. R7C3 and R8C3 are both dogs, so R9C3 must be a cat (no three in a row).
  79. R8C4 and R10C4 are both cats with one square between them, so R9C4 must be a dog.
  80. Row 7 already has its 5 dogs, so R7C7 must be cats.
  81. R7C7 and R8C7 are both cats, so R9C7 must be a dog (no three in a row).
  82. The × clue between R9C7 and R9C8 means they are different. R9C7 is a dog, so R9C8 is a cat.
  83. R9C8 and R9C10 are both cats with one square between them, so R9C9 must be a dog.
  84. Imagine R1C8 were a cat: following the rules from there soon forces a contradiction, so R1C8 must be a dog.
  85. Row 1 already has its 5 dogs, so R1C9 must be cats.
  86. Imagine R2C8 were a cat: following the rules from there soon forces a contradiction, so R2C8 must be a dog.
  87. R1C8 and R2C8 are both dogs, so R3C8 must be a cat (no three in a row).
  88. Row 2 already has its 5 dogs, so R2C9 must be cats.
  89. R1C9 and R2C9 are both cats, so R3C9 must be a dog (no three in a row).
  90. Column 8 already has its 5 cats, so R4C8 must be dogs.
  91. R4C7 and R4C8 are both dogs, so R4C9 must be a cat (no three in a row).

About this puzzle

This 10×10 grid starts with 8 filled squares and 16 = / × clues. It can be solved in 91 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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