Cats & Dogs #202: 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 R2C9 and R2C10 means they are the same. R2C9 is a dog, so R2C10 is a dog.
  2. The = clue between R2C9 and R3C9 means they are the same. R2C9 is a dog, so R3C9 is a dog.
  3. The = clue between R6C7 and R6C6 means they are the same. R6C7 is a cat, so R6C6 is a cat.
  4. The × clue between R6C7 and R7C7 means they are different. R6C7 is a cat, so R7C7 is a dog.
  5. The = clue between R7C3 and R7C4 means they are the same. R7C3 is a cat, so R7C4 is a cat.
  6. R2C9 and R2C10 are both dogs, so R2C8 must be a cat (no three in a row).
  7. R6C6 and R6C7 are both cats, so R6C5 must be a dog (no three in a row).
  8. R6C6 and R6C7 are both cats, so R6C8 must be a dog (no three in a row).
  9. R6C8 and R6C9 are both dogs, so R6C10 must be a cat (no three in a row).
  10. R7C3 and R7C4 are both cats, so R7C2 must be a dog (no three in a row).
  11. R7C3 and R7C4 are both cats, so R7C5 must be a dog (no three in a row).
  12. R7C5 and R7C7 are both dogs with one square between them, so R7C6 must be a cat.
  13. R9C6 and R9C7 are both dogs, so R9C5 must be a cat (no three in a row).
  14. R9C6 and R9C7 are both dogs, so R9C8 must be a cat (no three in a row).
  15. R6C3 and R7C3 are both cats, so R5C3 must be a dog (no three in a row).
  16. The × clue between R5C3 and R4C3 means they are different. R5C3 is a dog, so R4C3 is a cat.
  17. R4C2 and R4C3 are both cats, so R4C1 must be a dog (no three in a row).
  18. R4C2 and R4C3 are both cats, so R4C4 must be a dog (no three in a row).
  19. R6C3 and R7C3 are both cats, so R8C3 must be a dog (no three in a row).
  20. R8C1 and R8C3 are both dogs with one square between them, so R8C2 must be a cat.
  21. R8C3 and R9C3 are both dogs, so R10C3 must be a cat (no three in a row).
  22. R6C5 and R7C5 are both dogs, so R5C5 must be a cat (no three in a row).
  23. R6C5 and R7C5 are both dogs, so R8C5 must be a cat (no three in a row).
  24. R8C5 and R9C5 are both cats, so R10C5 must be a dog (no three in a row).
  25. The × clue between R10C5 and R10C4 means they are different. R10C5 is a dog, so R10C4 is a cat.
  26. R10C3 and R10C4 are both cats, so R10C2 must be a dog (no three in a row).
  27. R6C6 and R7C6 are both cats, so R5C6 must be a dog (no three in a row).
  28. R6C6 and R7C6 are both cats, so R8C6 must be a dog (no three in a row).
  29. R8C6 and R9C6 are both dogs, so R10C6 must be a cat (no three in a row).
  30. R7C7 and R9C7 are both dogs with one square between them, so R8C7 must be a cat.
  31. R2C9 and R3C9 are both dogs, so R1C9 must be a cat (no three in a row).
  32. R2C9 and R3C9 are both dogs, so R4C9 must be a cat (no three in a row).
  33. The × clue between R4C9 and R5C9 means they are different. R4C9 is a cat, so R5C9 is a dog.
  34. R5C9 and R6C9 are both dogs, so R7C9 must be a cat (no three in a row).
  35. Imagine R3C5 were a cat: following the rules from there soon forces a contradiction, so R3C5 must be a dog.
  36. The = clue between R3C5 and R3C6 means they are the same. R3C5 is a dog, so R3C6 is a dog.
  37. R3C5 and R3C6 are both dogs, so R3C4 must be a cat (no three in a row).
  38. R3C5 and R3C6 are both dogs, so R3C7 must be a cat (no three in a row).
  39. R3C6 and R5C6 are both dogs with one square between them, so R4C6 must be a cat.
  40. Imagine R1C5 were a dog: following the rules from there soon forces a contradiction, so R1C5 must be a cat.
  41. Imagine R2C5 were a dog: following the rules from there soon forces a contradiction, so R2C5 must be a cat.
  42. Column 5 already has its 5 cats, so R4C5 must be dogs.
  43. Imagine R2C7 were a cat: following the rules from there soon forces a contradiction, so R2C7 must be a dog.
  44. Imagine R3C8 were a cat: following the rules from there soon forces a contradiction, so R3C8 must be a dog.
  45. The = clue between R3C8 and R4C8 means they are the same. R3C8 is a dog, so R4C8 is a dog.
  46. The × clue between R4C8 and R4C7 means they are different. R4C8 is a dog, so R4C7 is a cat.
  47. R3C8 and R3C9 are both dogs, so R3C10 must be a cat (no three in a row).
  48. R3C7 and R4C7 are both cats, so R5C7 must be a dog (no three in a row).
  49. R5C6 and R5C7 are both dogs, so R5C8 must be a cat (no three in a row).
  50. Row 4 already has its 5 cats, so R4C10 must be dogs.
  51. Imagine R1C3 were a cat: following the rules from there soon forces a contradiction, so R1C3 must be a dog.
  52. Imagine R2C3 were a cat: following the rules from there soon forces a contradiction, so R2C3 must be a dog.
  53. R1C3 and R2C3 are both dogs, so R3C3 must be a cat (no three in a row).
  54. R3C3 and R3C4 are both cats, so R3C2 must be a dog (no three in a row).
  55. Row 3 already has its 5 dogs, so R3C1 must be cats.
  56. Imagine R1C1 were a cat: following the rules from there soon forces a contradiction, so R1C1 must be a dog.
  57. R1C1 and R1C3 are both dogs with one square between them, so R1C2 must be a cat.
  58. Imagine R2C1 were a dog: following the rules from there soon forces a contradiction, so R2C1 must be a cat.
  59. Imagine R2C2 were a dog: following the rules from there soon forces a contradiction, so R2C2 must be a cat.
  60. Imagine R5C2 were a dog: following the rules from there soon forces a contradiction, so R5C2 must be a cat.
  61. R4C2 and R5C2 are both cats, so R6C2 must be a dog (no three in a row).
  62. Column 2 already has its 5 cats, so R9C2 must be dogs.
  63. R9C2 and R9C3 are both dogs, so R9C1 must be a cat (no three in a row).
  64. R9C2 and R9C3 are both dogs, so R9C4 must be a cat (no three in a row).
  65. R7C4 and R9C4 are both cats with one square between them, so R8C4 must be a dog.
  66. Imagine R1C4 were a cat: following the rules from there soon forces a contradiction, so R1C4 must be a dog.
  67. Imagine R1C6 were a cat: following the rules from there soon forces a contradiction, so R1C6 must be a dog.
  68. R1C6 and R3C6 are both dogs with one square between them, so R2C6 must be a cat.
  69. R2C5 and R2C6 are both cats, so R2C4 must be a dog (no three in a row).
  70. Imagine R1C7 were a dog: following the rules from there soon forces a contradiction, so R1C7 must be a cat.
  71. R1C7 and R1C9 are both cats with one square between them, so R1C8 must be a dog.
  72. Row 1 already has its 5 dogs, so R1C10 must be cats.
  73. Column 7 already has its 5 cats, so R10C7 must be dogs.
  74. Imagine R5C4 were a dog: following the rules from there soon forces a contradiction, so R5C4 must be a cat.
  75. R5C4 and R7C4 are both cats with one square between them, so R6C4 must be a dog.
  76. Row 6 already has its 5 dogs, so R6C1 must be cats.
  77. Imagine R7C1 were a cat: following the rules from there soon forces a contradiction, so R7C1 must be a dog.
  78. Imagine R5C1 were a dog: following the rules from there soon forces a contradiction, so R5C1 must be a cat.
  79. Row 5 already has its 5 cats, so R5C10 must be dogs.
  80. Column 1 already has its 5 cats, so R10C1 must be dogs.
  81. Imagine R7C8 were a dog: following the rules from there soon forces a contradiction, so R7C8 must be a cat.
  82. R7C8 and R7C9 are both cats, so R7C10 must be a dog (no three in a row).
  83. R7C8 and R9C8 are both cats with one square between them, so R8C8 must be a dog.
  84. Row 8 already has its 5 dogs, so R8C9 must be cats.
  85. R7C9 and R8C9 are both cats, so R9C9 must be a dog (no three in a row).
  86. Row 8 already has its 5 dogs, so R8C10 must be cats.
  87. Row 9 already has its 5 dogs, so R9C10 must be cats.
  88. R8C10 and R9C10 are both cats, so R10C10 must be a dog (no three in a row).
  89. Row 10 already has its 5 dogs, so R10C8 and R10C9 must be cats.

About this puzzle

This 10×10 grid starts with 10 filled squares and 11 = / × 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.

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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