Cats & Dogs #235: 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 R7C2 and R7C3 means they are the same. R7C2 is a cat, so R7C3 is a cat.
  2. R7C2 and R7C3 are both cats, so R7C1 must be a dog (no three in a row).
  3. R7C2 and R7C3 are both cats, so R7C4 must be a dog (no three in a row).
  4. The = clue between R7C4 and R6C4 means they are the same. R7C4 is a dog, so R6C4 is a dog.
  5. R6C4 and R7C4 are both dogs, so R5C4 must be a cat (no three in a row).
  6. R6C4 and R7C4 are both dogs, so R8C4 must be a cat (no three in a row).
  7. Imagine R3C8 were a cat: following the rules from there soon forces a contradiction, so R3C8 must be a dog.
  8. The = clue between R3C8 and R4C8 means they are the same. R3C8 is a dog, so R4C8 is a dog.
  9. R3C8 and R4C8 are both dogs, so R5C8 must be a cat (no three in a row).
  10. Imagine R4C6 were a cat: following the rules from there soon forces a contradiction, so R4C6 must be a dog.
  11. The = clue between R4C6 and R5C6 means they are the same. R4C6 is a dog, so R5C6 is a dog.
  12. R4C6 and R4C8 are both dogs with one square between them, so R4C7 must be a cat.
  13. R4C6 and R5C6 are both dogs, so R3C6 must be a cat (no three in a row).
  14. R4C6 and R5C6 are both dogs, so R6C6 must be a cat (no three in a row).
  15. The = clue between R6C6 and R6C5 means they are the same. R6C6 is a cat, so R6C5 is a cat.
  16. R6C5 and R6C6 are both cats, so R6C7 must be a dog (no three in a row).
  17. Imagine R4C10 were a dog: following the rules from there soon forces a contradiction, so R4C10 must be a cat.
  18. Imagine R5C2 were a cat: following the rules from there soon forces a contradiction, so R5C2 must be a dog.
  19. Imagine R5C1 were a dog: following the rules from there soon forces a contradiction, so R5C1 must be a cat.
  20. Imagine R5C3 were a cat: following the rules from there soon forces a contradiction, so R5C3 must be a dog.
  21. The = clue between R5C3 and R6C3 means they are the same. R5C3 is a dog, so R6C3 is a dog.
  22. R6C3 and R6C4 are both dogs, so R6C2 must be a cat (no three in a row).
  23. R6C2 and R7C2 are both cats, so R8C2 must be a dog (no three in a row).
  24. R5C3 and R6C3 are both dogs, so R4C3 must be a cat (no three in a row).
  25. Imagine R2C2 were a dog: following the rules from there soon forces a contradiction, so R2C2 must be a cat.
  26. The = clue between R2C2 and R3C2 means they are the same. R2C2 is a cat, so R3C2 is a cat.
  27. R2C2 and R3C2 are both cats, so R1C2 must be a dog (no three in a row).
  28. R2C2 and R3C2 are both cats, so R4C2 must be a dog (no three in a row).
  29. The = clue between R4C2 and R4C1 means they are the same. R4C2 is a dog, so R4C1 is a dog.
  30. Imagine R2C7 were a cat: following the rules from there soon forces a contradiction, so R2C7 must be a dog.
  31. Imagine R1C7 were a dog: following the rules from there soon forces a contradiction, so R1C7 must be a cat.
  32. Imagine R2C10 were a cat: following the rules from there soon forces a contradiction, so R2C10 must be a dog.
  33. Imagine R3C4 were a cat: following the rules from there soon forces a contradiction, so R3C4 must be a dog.
  34. Imagine R2C1 were a dog: following the rules from there soon forces a contradiction, so R2C1 must be a cat.
  35. R2C1 and R2C2 are both cats, so R2C3 must be a dog (no three in a row).
  36. Imagine R3C1 were a cat: following the rules from there soon forces a contradiction, so R3C1 must be a dog.
  37. Imagine R3C3 were a dog: following the rules from there soon forces a contradiction, so R3C3 must be a cat.
  38. Imagine R3C5 were a cat: following the rules from there soon forces a contradiction, so R3C5 must be a dog.
  39. Imagine R2C5 were a dog: following the rules from there soon forces a contradiction, so R2C5 must be a cat.
  40. Imagine R3C7 were a dog: following the rules from there soon forces a contradiction, so R3C7 must be a cat.
  41. R3C7 and R4C7 are both cats, so R5C7 must be a dog (no three in a row).
  42. R5C6 and R5C7 are both dogs, so R5C5 must be a cat (no three in a row).
  43. R5C5 and R6C5 are both cats, so R4C5 must be a dog (no three in a row).
  44. R4C5 and R4C6 are both dogs, so R4C4 must be a cat (no three in a row).
  45. R5C5 and R6C5 are both cats, so R7C5 must be a dog (no three in a row).
  46. R7C4 and R7C5 are both dogs, so R7C6 must be a cat (no three in a row).
  47. R6C6 and R7C6 are both cats, so R8C6 must be a dog (no three in a row).
  48. R5C7 and R6C7 are both dogs, so R7C7 must be a cat (no three in a row).
  49. R7C6 and R7C7 are both cats, so R7C8 must be a dog (no three in a row).
  50. The × clue between R7C8 and R8C8 means they are different. R7C8 is a dog, so R8C8 is a cat.
  51. The × clue between R8C8 and R9C8 means they are different. R8C8 is a cat, so R9C8 is a dog.
  52. R8C7 and R8C8 are both cats, so R8C9 must be a dog (no three in a row).
  53. R7C7 and R8C7 are both cats, so R9C7 must be a dog (no three in a row).
  54. R9C7 and R9C8 are both dogs, so R9C6 must be a cat (no three in a row).
  55. R9C7 and R9C8 are both dogs, so R9C9 must be a cat (no three in a row).
  56. Row 4 already has its 5 dogs, so R4C9 must be cats.
  57. The × clue between R4C9 and R3C9 means they are different. R4C9 is a cat, so R3C9 is a dog.
  58. R3C8 and R3C9 are both dogs, so R3C10 must be a cat (no three in a row).
  59. R3C10 and R4C10 are both cats, so R5C10 must be a dog (no three in a row).
  60. Row 5 already has its 5 dogs, so R5C9 must be cats.
  61. R4C9 and R5C9 are both cats, so R6C9 must be a dog (no three in a row).
  62. R6C7 and R6C9 are both dogs with one square between them, so R6C8 must be a cat.
  63. R6C9 and R8C9 are both dogs with one square between them, so R7C9 must be a cat.
  64. Row 7 already has its 5 cats, so R7C10 must be dogs.
  65. R5C10 and R7C10 are both dogs with one square between them, so R6C10 must be a cat.
  66. Row 6 already has its 5 cats, so R6C1 must be dogs.
  67. R6C1 and R7C1 are both dogs, so R8C1 must be a cat (no three in a row).
  68. R8C1 and R9C1 are both cats, so R10C1 must be a dog (no three in a row).
  69. Column 1 already has its 5 dogs, so R1C1 must be cats.
  70. Imagine R1C8 were a cat: following the rules from there soon forces a contradiction, so R1C8 must be a dog.
  71. Column 8 already has its 5 dogs, so R10C8 must be cats.
  72. Imagine R8C3 were a cat: following the rules from there soon forces a contradiction, so R8C3 must be a dog.
  73. Imagine R9C4 were a cat: following the rules from there soon forces a contradiction, so R9C4 must be a dog.
  74. The × clue between R9C4 and R9C5 means they are different. R9C4 is a dog, so R9C5 is a cat.
  75. The = clue between R9C4 and R10C4 means they are the same. R9C4 is a dog, so R10C4 is a dog.
  76. Column 4 already has its 5 dogs, so R1C4 and R2C4 must be cats.
  77. R2C4 and R2C5 are both cats, so R2C6 must be a dog (no three in a row).
  78. Row 2 already has its 5 cats, so R2C9 must be dogs.
  79. R2C9 and R3C9 are both dogs, so R1C9 must be a cat (no three in a row).
  80. Column 9 already has its 5 cats, so R10C9 must be dogs.
  81. Imagine R1C5 were a cat: following the rules from there soon forces a contradiction, so R1C5 must be a dog.
  82. Imagine R1C6 were a cat: following the rules from there soon forces a contradiction, so R1C6 must be a dog.
  83. Column 6 already has its 5 dogs, so R10C6 must be cats.
  84. Imagine R8C5 were a cat: following the rules from there soon forces a contradiction, so R8C5 must be a dog.
  85. Row 8 already has its 5 dogs, so R8C10 must be cats.
  86. Column 5 already has its 5 dogs, so R10C5 must be cats.
  87. Imagine R9C2 were a cat: following the rules from there soon forces a contradiction, so R9C2 must be a dog.
  88. R9C2 and R9C4 are both dogs with one square between them, so R9C3 must be a cat.
  89. R8C2 and R9C2 are both dogs, so R10C2 must be a cat (no three in a row).
  90. Row 9 already has its 5 cats, so R9C10 must be dogs.
  91. The = clue between R9C10 and R10C10 means they are the same. R9C10 is a dog, so R10C10 is a dog.
  92. Row 10 already has its 5 dogs, so R10C3 must be cats.
  93. Column 3 already has its 5 cats, so R1C3 must be dogs.
  94. Row 1 already has its 5 dogs, so R1C10 must be cats.

About this puzzle

This 10×10 grid starts with 5 filled squares and 14 = / × clues. It can be solved in 94 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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