Cats & Dogs #220: 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 R2C3 and R2C4 means they are the same. R2C3 is a dog, so R2C4 is a dog.
  2. The = clue between R4C8 and R5C8 means they are the same. R4C8 is a cat, so R5C8 is a cat.
  3. The × clue between R7C10 and R7C9 means they are different. R7C10 is a cat, so R7C9 is a dog.
  4. R2C3 and R2C4 are both dogs, so R2C2 must be a cat (no three in a row).
  5. The = clue between R2C2 and R2C1 means they are the same. R2C2 is a cat, so R2C1 is a cat.
  6. R2C3 and R2C4 are both dogs, so R2C5 must be a cat (no three in a row).
  7. The = clue between R2C5 and R2C6 means they are the same. R2C5 is a cat, so R2C6 is a cat.
  8. R2C5 and R2C6 are both cats, so R2C7 must be a dog (no three in a row).
  9. R2C6 and R3C6 are both cats, so R1C6 must be a dog (no three in a row).
  10. R2C6 and R3C6 are both cats, so R4C6 must be a dog (no three in a row).
  11. R4C8 and R5C8 are both cats, so R3C8 must be a dog (no three in a row).
  12. R4C8 and R5C8 are both cats, so R6C8 must be a dog (no three in a row).
  13. Imagine R1C5 were a dog: following the rules from there soon forces a contradiction, so R1C5 must be a cat.
  14. R1C5 and R2C5 are both cats, so R3C5 must be a dog (no three in a row).
  15. Imagine R1C7 were a cat: following the rules from there soon forces a contradiction, so R1C7 must be a dog.
  16. The × clue between R1C7 and R1C8 means they are different. R1C7 is a dog, so R1C8 is a cat.
  17. The = clue between R1C8 and R2C8 means they are the same. R1C8 is a cat, so R2C8 is a cat.
  18. R1C7 and R2C7 are both dogs, so R3C7 must be a cat (no three in a row).
  19. Row 2 already has its 5 cats, so R2C9 and R2C10 must be dogs.
  20. Imagine R1C1 were a dog: following the rules from there soon forces a contradiction, so R1C1 must be a cat.
  21. The = clue between R1C1 and R1C2 means they are the same. R1C1 is a cat, so R1C2 is a cat.
  22. R1C1 and R1C2 are both cats, so R1C3 must be a dog (no three in a row).
  23. R1C1 and R2C1 are both cats, so R3C1 must be a dog (no three in a row).
  24. R1C2 and R2C2 are both cats, so R3C2 must be a dog (no three in a row).
  25. R3C1 and R3C2 are both dogs, so R3C3 must be a cat (no three in a row).
  26. Imagine R1C9 were a cat: following the rules from there soon forces a contradiction, so R1C9 must be a dog.
  27. R1C9 and R2C9 are both dogs, so R3C9 must be a cat (no three in a row).
  28. The = clue between R3C9 and R3C10 means they are the same. R3C9 is a cat, so R3C10 is a cat.
  29. Row 3 already has its 5 cats, so R3C4 must be dogs.
  30. R2C4 and R3C4 are both dogs, so R1C4 must be a cat (no three in a row).
  31. R2C4 and R3C4 are both dogs, so R4C4 must be a cat (no three in a row).
  32. The = clue between R4C4 and R4C3 means they are the same. R4C4 is a cat, so R4C3 is a cat.
  33. R4C3 and R4C4 are both cats, so R4C2 must be a dog (no three in a row).
  34. R4C3 and R4C4 are both cats, so R4C5 must be a dog (no three in a row).
  35. R4C5 and R4C6 are both dogs, so R4C7 must be a cat (no three in a row).
  36. R4C7 and R4C8 are both cats, so R4C9 must be a dog (no three in a row).
  37. R3C2 and R4C2 are both dogs, so R5C2 must be a cat (no three in a row).
  38. R3C3 and R4C3 are both cats, so R5C3 must be a dog (no three in a row).
  39. R3C5 and R4C5 are both dogs, so R5C5 must be a cat (no three in a row).
  40. R3C7 and R4C7 are both cats, so R5C7 must be a dog (no three in a row).
  41. Row 1 already has its 5 cats, so R1C10 must be dogs.
  42. Imagine R5C9 were a dog: following the rules from there soon forces a contradiction, so R5C9 must be a cat.
  43. R5C8 and R5C9 are both cats, so R5C10 must be a dog (no three in a row).
  44. Imagine R5C4 were a cat: following the rules from there soon forces a contradiction, so R5C4 must be a dog.
  45. Imagine R6C6 were a dog: following the rules from there soon forces a contradiction, so R6C6 must be a cat.
  46. Imagine R6C7 were a cat: following the rules from there soon forces a contradiction, so R6C7 must be a dog.
  47. The × clue between R6C7 and R7C7 means they are different. R6C7 is a dog, so R7C7 is a cat.
  48. R6C7 and R6C8 are both dogs, so R6C9 must be a cat (no three in a row).
  49. Column 7 already has its 5 dogs, so R9C7 must be cats.
  50. R9C7 and R9C9 are both cats with one square between them, so R9C8 must be a dog.
  51. Column 7 already has its 5 dogs, so R10C7 must be cats.
  52. Imagine R7C8 were a cat: following the rules from there soon forces a contradiction, so R7C8 must be a dog.
  53. R6C8 and R7C8 are both dogs, so R8C8 must be a cat (no three in a row).
  54. Column 8 already has its 5 cats, so R10C8 must be dogs.
  55. Imagine R6C3 were a dog: following the rules from there soon forces a contradiction, so R6C3 must be a cat.
  56. The = clue between R6C3 and R6C4 means they are the same. R6C3 is a cat, so R6C4 is a cat.
  57. R6C3 and R6C4 are both cats, so R6C2 must be a dog (no three in a row).
  58. R6C3 and R6C4 are both cats, so R6C5 must be a dog (no three in a row).
  59. Imagine R5C1 were a dog: following the rules from there soon forces a contradiction, so R5C1 must be a cat.
  60. Row 5 already has its 5 cats, so R5C6 must be dogs.
  61. Imagine R4C1 were a cat: following the rules from there soon forces a contradiction, so R4C1 must be a dog.
  62. Row 4 already has its 5 dogs, so R4C10 must be cats.
  63. Imagine R6C1 were a cat: following the rules from there soon forces a contradiction, so R6C1 must be a dog.
  64. Row 6 already has its 5 dogs, so R6C10 must be cats.
  65. R6C10 and R7C10 are both cats, so R8C10 must be a dog (no three in a row).
  66. Imagine R7C1 were a cat: following the rules from there soon forces a contradiction, so R7C1 must be a dog.
  67. The = clue between R7C1 and R7C2 means they are the same. R7C1 is a dog, so R7C2 is a dog.
  68. R7C1 and R7C2 are both dogs, so R7C3 must be a cat (no three in a row).
  69. R6C1 and R7C1 are both dogs, so R8C1 must be a cat (no three in a row).
  70. The × clue between R8C1 and R9C1 means they are different. R8C1 is a cat, so R9C1 is a dog.
  71. R6C2 and R7C2 are both dogs, so R8C2 must be a cat (no three in a row).
  72. R8C1 and R8C2 are both cats, so R8C3 must be a dog (no three in a row).
  73. Imagine R7C4 were a dog: following the rules from there soon forces a contradiction, so R7C4 must be a cat.
  74. R7C3 and R7C4 are both cats, so R7C5 must be a dog (no three in a row).
  75. R6C4 and R7C4 are both cats, so R8C4 must be a dog (no three in a row).
  76. R8C3 and R8C4 are both dogs, so R8C5 must be a cat (no three in a row).
  77. Row 7 already has its 5 dogs, so R7C6 must be cats.
  78. R6C6 and R7C6 are both cats, so R8C6 must be a dog (no three in a row).
  79. Row 8 already has its 5 dogs, so R8C9 must be cats.
  80. R8C9 and R9C9 are both cats, so R10C9 must be a dog (no three in a row).
  81. R10C8 and R10C9 are both dogs, so R10C10 must be a cat (no three in a row).
  82. Column 10 already has its 5 cats, so R9C10 must be dogs.
  83. Imagine R9C3 were a dog: following the rules from there soon forces a contradiction, so R9C3 must be a cat.
  84. The = clue between R9C3 and R9C4 means they are the same. R9C3 is a cat, so R9C4 is a cat.
  85. R9C3 and R9C4 are both cats, so R9C2 must be a dog (no three in a row).
  86. R9C3 and R9C4 are both cats, so R9C5 must be a dog (no three in a row).
  87. The × clue between R9C5 and R10C5 means they are different. R9C5 is a dog, so R10C5 is a cat.
  88. R10C5 and R10C7 are both cats with one square between them, so R10C6 must be a dog.
  89. R8C6 and R10C6 are both dogs with one square between them, so R9C6 must be a cat.
  90. Column 2 already has its 5 dogs, so R10C2 must be cats.
  91. R10C1 and R10C2 are both cats, so R10C3 must be a dog (no three in a row).
  92. Row 10 already has its 5 cats, so R10C4 must be dogs.

About this puzzle

This 10×10 grid starts with 7 filled squares and 16 = / × 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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