Cats & Dogs #211: 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 R5C7 and R5C6 means they are different. R5C7 is a cat, so R5C6 is a dog.
  2. The × clue between R5C6 and R6C6 means they are different. R5C6 is a dog, so R6C6 is a cat.
  3. R10C2 and R10C4 are both dogs with one square between them, so R10C3 must be a cat.
  4. R9C3 and R10C3 are both cats, so R8C3 must be a dog (no three in a row).
  5. R6C6 and R7C6 are both cats, so R8C6 must be a dog (no three in a row).
  6. Imagine R3C3 were a dog: following the rules from there soon forces a contradiction, so R3C3 must be a cat.
  7. Imagine R4C4 were a dog: following the rules from there soon forces a contradiction, so R4C4 must be a cat.
  8. Imagine R3C4 were a cat: following the rules from there soon forces a contradiction, so R3C4 must be a dog.
  9. Imagine R4C5 were a cat: following the rules from there soon forces a contradiction, so R4C5 must be a dog.
  10. The = clue between R4C5 and R5C5 means they are the same. R4C5 is a dog, so R5C5 is a dog.
  11. R5C5 and R5C6 are both dogs, so R5C4 must be a cat (no three in a row).
  12. The × clue between R5C4 and R5C3 means they are different. R5C4 is a cat, so R5C3 is a dog.
  13. R4C3 and R5C3 are both dogs, so R6C3 must be a cat (no three in a row).
  14. R4C4 and R5C4 are both cats, so R6C4 must be a dog (no three in a row).
  15. R4C5 and R5C5 are both dogs, so R3C5 must be a cat (no three in a row).
  16. R4C5 and R5C5 are both dogs, so R6C5 must be a cat (no three in a row).
  17. The × clue between R6C5 and R7C5 means they are different. R6C5 is a cat, so R7C5 is a dog.
  18. R6C5 and R6C6 are both cats, so R6C7 must be a dog (no three in a row).
  19. The = clue between R6C7 and R6C8 means they are the same. R6C7 is a dog, so R6C8 is a dog.
  20. The × clue between R6C7 and R7C7 means they are different. R6C7 is a dog, so R7C7 is a cat.
  21. R6C7 and R6C8 are both dogs, so R6C9 must be a cat (no three in a row).
  22. R7C6 and R7C7 are both cats, so R7C8 must be a dog (no three in a row).
  23. The × clue between R7C8 and R7C9 means they are different. R7C8 is a dog, so R7C9 is a cat.
  24. R6C8 and R7C8 are both dogs, so R5C8 must be a cat (no three in a row).
  25. R5C7 and R5C8 are both cats, so R5C9 must be a dog (no three in a row).
  26. R6C8 and R7C8 are both dogs, so R8C8 must be a cat (no three in a row).
  27. R6C9 and R7C9 are both cats, so R8C9 must be a dog (no three in a row).
  28. Imagine R8C2 were a dog: following the rules from there soon forces a contradiction, so R8C2 must be a cat.
  29. Imagine R8C4 were a dog: following the rules from there soon forces a contradiction, so R8C4 must be a cat.
  30. The = clue between R8C4 and R9C4 means they are the same. R8C4 is a cat, so R9C4 is a cat.
  31. R9C3 and R9C4 are both cats, so R9C2 must be a dog (no three in a row).
  32. R9C3 and R9C4 are both cats, so R9C5 must be a dog (no three in a row).
  33. R8C4 and R9C4 are both cats, so R7C4 must be a dog (no three in a row).
  34. R7C4 and R7C5 are both dogs, so R7C3 must be a cat (no three in a row).
  35. R7C5 and R9C5 are both dogs with one square between them, so R8C5 must be a cat.
  36. Column 3 already has its 5 cats, so R1C3 and R2C3 must be dogs.
  37. Imagine R9C8 were a cat: following the rules from there soon forces a contradiction, so R9C8 must be a dog.
  38. Imagine R9C9 were a dog: following the rules from there soon forces a contradiction, so R9C9 must be a cat.
  39. The = clue between R9C9 and R10C9 means they are the same. R9C9 is a cat, so R10C9 is a cat.
  40. Imagine R1C7 were a dog: following the rules from there soon forces a contradiction, so R1C7 must be a cat.
  41. The = clue between R1C7 and R1C8 means they are the same. R1C7 is a cat, so R1C8 is a cat.
  42. R1C7 and R1C8 are both cats, so R1C6 must be a dog (no three in a row).
  43. R1C7 and R1C8 are both cats, so R1C9 must be a dog (no three in a row).
  44. Imagine R2C9 were a cat: following the rules from there soon forces a contradiction, so R2C9 must be a dog.
  45. R1C9 and R2C9 are both dogs, so R3C9 must be a cat (no three in a row).
  46. Column 9 already has its 5 cats, so R4C9 must be dogs.
  47. Imagine R3C7 were a cat: following the rules from there soon forces a contradiction, so R3C7 must be a dog.
  48. Imagine R3C6 were a dog: following the rules from there soon forces a contradiction, so R3C6 must be a cat.
  49. Imagine R3C8 were a cat: following the rules from there soon forces a contradiction, so R3C8 must be a dog.
  50. Imagine R2C8 were a dog: following the rules from there soon forces a contradiction, so R2C8 must be a cat.
  51. Imagine R4C7 were a dog: following the rules from there soon forces a contradiction, so R4C7 must be a cat.
  52. Imagine R2C7 were a cat: following the rules from there soon forces a contradiction, so R2C7 must be a dog.
  53. Imagine R4C6 were a cat: following the rules from there soon forces a contradiction, so R4C6 must be a dog.
  54. Imagine R4C8 were a dog: following the rules from there soon forces a contradiction, so R4C8 must be a cat.
  55. Column 8 already has its 5 cats, so R10C8 must be dogs.
  56. The = clue between R10C8 and R10C7 means they are the same. R10C8 is a dog, so R10C7 is a dog.
  57. R10C7 and R10C8 are both dogs, so R10C6 must be a cat (no three in a row).
  58. Column 6 already has its 5 cats, so R2C6 must be dogs.
  59. R2C6 and R2C7 are both dogs, so R2C5 must be a cat (no three in a row).
  60. R2C5 and R3C5 are both cats, so R1C5 must be a dog (no three in a row).
  61. R1C3 and R1C5 are both dogs with one square between them, so R1C4 must be a cat.
  62. Column 4 already has its 5 cats, so R2C4 must be dogs.
  63. R2C3 and R2C4 are both dogs, so R2C2 must be a cat (no three in a row).
  64. Row 2 already has its 5 dogs, so R2C1 and R2C10 must be cats.
  65. Column 5 already has its 5 dogs, so R10C5 must be cats.
  66. Imagine R6C1 were a dog: following the rules from there soon forces a contradiction, so R6C1 must be a cat.
  67. The = clue between R6C1 and R7C1 means they are the same. R6C1 is a cat, so R7C1 is a cat.
  68. R6C1 and R6C3 are both cats with one square between them, so R6C2 must be a dog.
  69. R7C1 and R7C3 are both cats with one square between them, so R7C2 must be a dog.
  70. R6C1 and R7C1 are both cats, so R5C1 must be a dog (no three in a row).
  71. R5C1 and R5C3 are both dogs with one square between them, so R5C2 must be a cat.
  72. R6C1 and R7C1 are both cats, so R8C1 must be a dog (no three in a row).
  73. Row 5 already has its 5 dogs, so R5C10 must be cats.
  74. Row 6 already has its 5 cats, so R6C10 must be dogs.
  75. Row 7 already has its 5 cats, so R7C10 must be dogs.
  76. R6C10 and R7C10 are both dogs, so R8C10 must be a cat (no three in a row).
  77. Row 8 already has its 5 cats, so R8C7 must be dogs.
  78. R8C7 and R10C7 are both dogs with one square between them, so R9C7 must be a cat.
  79. Row 9 already has its 5 cats, so R9C1 must be dogs.
  80. R8C1 and R9C1 are both dogs, so R10C1 must be a cat (no three in a row).
  81. Row 9 already has its 5 cats, so R9C10 must be dogs.
  82. The = clue between R9C10 and R10C10 means they are the same. R9C10 is a dog, so R10C10 is a dog.
  83. Imagine R1C1 were a cat: following the rules from there soon forces a contradiction, so R1C1 must be a dog.
  84. R1C1 and R1C3 are both dogs with one square between them, so R1C2 must be a cat.
  85. R1C2 and R2C2 are both cats, so R3C2 must be a dog (no three in a row).
  86. Row 1 already has its 5 dogs, so R1C10 must be cats.
  87. R1C10 and R2C10 are both cats, so R3C10 must be a dog (no three in a row).
  88. Row 3 already has its 5 dogs, so R3C1 must be cats.
  89. R2C1 and R3C1 are both cats, so R4C1 must be a dog (no three in a row).
  90. R4C1 and R4C3 are both dogs with one square between them, so R4C2 must be a cat.
  91. Row 4 already has its 5 dogs, so R4C10 must be cats.

About this puzzle

This 10×10 grid starts with 7 filled squares and 14 = / × 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.

Stuck? Open the step-by-step solution below -- each step names the squares involved, so you can use it as a hint and finish the puzzle yourself.

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