Cats & Dogs #291: 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 R6C1 and R5C1 means they are the same. R6C1 is a dog, so R5C1 is a dog.
  2. The = clue between R6C1 and R6C2 means they are the same. R6C1 is a dog, so R6C2 is a dog.
  3. R5C1 and R5C2 are both dogs, so R5C3 must be a cat (no three in a row).
  4. R6C1 and R6C2 are both dogs, so R6C3 must be a cat (no three in a row).
  5. R5C1 and R6C1 are both dogs, so R4C1 must be a cat (no three in a row).
  6. R5C1 and R6C1 are both dogs, so R7C1 must be a cat (no three in a row).
  7. R5C2 and R6C2 are both dogs, so R4C2 must be a cat (no three in a row).
  8. R4C1 and R4C2 are both cats, so R4C3 must be a dog (no three in a row).
  9. R5C2 and R6C2 are both dogs, so R7C2 must be a cat (no three in a row).
  10. R7C1 and R7C2 are both cats, so R7C3 must be a dog (no three in a row).
  11. Imagine R5C7 were a dog: following the rules from there soon forces a contradiction, so R5C7 must be a cat.
  12. Imagine R7C4 were a dog: following the rules from there soon forces a contradiction, so R7C4 must be a cat.
  13. The = clue between R7C4 and R7C5 means they are the same. R7C4 is a cat, so R7C5 is a cat.
  14. R7C4 and R7C5 are both cats, so R7C6 must be a dog (no three in a row).
  15. R5C6 and R7C6 are both dogs with one square between them, so R6C6 must be a cat.
  16. Imagine R2C7 were a dog: following the rules from there soon forces a contradiction, so R2C7 must be a cat.
  17. The = clue between R2C7 and R3C7 means they are the same. R2C7 is a cat, so R3C7 is a cat.
  18. R2C7 and R3C7 are both cats, so R1C7 must be a dog (no three in a row).
  19. R2C7 and R3C7 are both cats, so R4C7 must be a dog (no three in a row).
  20. Imagine R6C5 were a cat: following the rules from there soon forces a contradiction, so R6C5 must be a dog.
  21. Imagine R6C7 were a dog: following the rules from there soon forces a contradiction, so R6C7 must be a cat.
  22. The × clue between R6C7 and R7C7 means they are different. R6C7 is a cat, so R7C7 is a dog.
  23. R6C6 and R6C7 are both cats, so R6C8 must be a dog (no three in a row).
  24. R7C6 and R7C7 are both dogs, so R7C8 must be a cat (no three in a row).
  25. Row 7 already has its 5 cats, so R7C9 and R7C10 must be dogs.
  26. Imagine R8C2 were a cat: following the rules from there soon forces a contradiction, so R8C2 must be a dog.
  27. The = clue between R8C2 and R8C3 means they are the same. R8C2 is a dog, so R8C3 is a dog.
  28. The = clue between R8C2 and R9C2 means they are the same. R8C2 is a dog, so R9C2 is a dog.
  29. R8C2 and R8C3 are both dogs, so R8C1 must be a cat (no three in a row).
  30. R8C2 and R8C3 are both dogs, so R8C4 must be a cat (no three in a row).
  31. R7C1 and R8C1 are both cats, so R9C1 must be a dog (no three in a row).
  32. R9C1 and R9C2 are both dogs, so R9C3 must be a cat (no three in a row).
  33. R8C2 and R9C2 are both dogs, so R10C2 must be a cat (no three in a row).
  34. R10C1 and R10C2 are both cats, so R10C3 must be a dog (no three in a row).
  35. R7C4 and R8C4 are both cats, so R6C4 must be a dog (no three in a row).
  36. The × clue between R6C4 and R5C4 means they are different. R6C4 is a dog, so R5C4 is a cat.
  37. R5C3 and R5C4 are both cats, so R5C5 must be a dog (no three in a row).
  38. R7C4 and R8C4 are both cats, so R9C4 must be a dog (no three in a row).
  39. R5C5 and R6C5 are both dogs, so R4C5 must be a cat (no three in a row).
  40. Row 6 already has its 5 dogs, so R6C9 and R6C10 must be cats.
  41. Imagine R1C1 were a dog: following the rules from there soon forces a contradiction, so R1C1 must be a cat.
  42. The = clue between R1C1 and R1C2 means they are the same. R1C1 is a cat, so R1C2 is a cat.
  43. The = clue between R1C2 and R2C2 means they are the same. R1C2 is a cat, so R2C2 is a cat.
  44. R1C1 and R1C2 are both cats, so R1C3 must be a dog (no three in a row).
  45. R1C2 and R2C2 are both cats, so R3C2 must be a dog (no three in a row).
  46. Column 1 already has its 5 cats, so R2C1 and R3C1 must be dogs.
  47. R3C1 and R3C2 are both dogs, so R3C3 must be a cat (no three in a row).
  48. Column 3 already has its 5 dogs, so R2C3 must be cats.
  49. R2C2 and R2C3 are both cats, so R2C4 must be a dog (no three in a row).
  50. Imagine R1C4 were a dog: following the rules from there soon forces a contradiction, so R1C4 must be a cat.
  51. Imagine R2C5 were a cat: following the rules from there soon forces a contradiction, so R2C5 must be a dog.
  52. R2C4 and R2C5 are both dogs, so R2C6 must be a cat (no three in a row).
  53. The = clue between R2C6 and R3C6 means they are the same. R2C6 is a cat, so R3C6 is a cat.
  54. The × clue between R3C6 and R3C5 means they are different. R3C6 is a cat, so R3C5 is a dog.
  55. R2C6 and R2C7 are both cats, so R2C8 must be a dog (no three in a row).
  56. R3C6 and R3C7 are both cats, so R3C8 must be a dog (no three in a row).
  57. R2C5 and R3C5 are both dogs, so R1C5 must be a cat (no three in a row).
  58. R1C4 and R1C5 are both cats, so R1C6 must be a dog (no three in a row).
  59. R1C6 and R1C7 are both dogs, so R1C8 must be a cat (no three in a row).
  60. R2C6 and R3C6 are both cats, so R4C6 must be a dog (no three in a row).
  61. R4C6 and R4C7 are both dogs, so R4C8 must be a cat (no three in a row).
  62. The × clue between R4C8 and R4C9 means they are different. R4C8 is a cat, so R4C9 is a dog.
  63. Row 1 already has its 5 cats, so R1C9 and R1C10 must be dogs.
  64. Imagine R3C4 were a cat: following the rules from there soon forces a contradiction, so R3C4 must be a dog.
  65. R2C4 and R3C4 are both dogs, so R4C4 must be a cat (no three in a row).
  66. Row 3 already has its 5 dogs, so R3C9 and R3C10 must be cats.
  67. Row 4 already has its 5 cats, so R4C10 must be dogs.
  68. Column 4 already has its 5 cats, so R10C4 must be dogs.
  69. R10C3 and R10C4 are both dogs, so R10C5 must be a cat (no three in a row).
  70. Imagine R5C10 were a dog: following the rules from there soon forces a contradiction, so R5C10 must be a cat.
  71. Imagine R8C5 were a dog: following the rules from there soon forces a contradiction, so R8C5 must be a cat.
  72. R8C4 and R8C5 are both cats, so R8C6 must be a dog (no three in a row).
  73. R7C5 and R8C5 are both cats, so R9C5 must be a dog (no three in a row).
  74. The × clue between R9C5 and R9C6 means they are different. R9C5 is a dog, so R9C6 is a cat.
  75. The = clue between R9C6 and R10C6 means they are the same. R9C6 is a cat, so R10C6 is a cat.
  76. R10C5 and R10C6 are both cats, so R10C7 must be a dog (no three in a row).
  77. Imagine R8C7 were a cat: following the rules from there soon forces a contradiction, so R8C7 must be a dog.
  78. R8C6 and R8C7 are both dogs, so R8C8 must be a cat (no three in a row).
  79. R7C7 and R8C7 are both dogs, so R9C7 must be a cat (no three in a row).
  80. R9C6 and R9C7 are both cats, so R9C8 must be a dog (no three in a row).
  81. The = clue between R9C8 and R10C8 means they are the same. R9C8 is a dog, so R10C8 is a dog.
  82. R10C7 and R10C8 are both dogs, so R10C9 must be a cat (no three in a row).
  83. Row 9 already has its 5 dogs, so R9C9 must be cats.
  84. R9C9 and R10C9 are both cats, so R8C9 must be a dog (no three in a row).
  85. Row 8 already has its 5 dogs, so R8C10 must be cats.
  86. Row 9 already has its 5 dogs, so R9C10 must be cats.
  87. R8C10 and R9C10 are both cats, so R10C10 must be a dog (no three in a row).
  88. Column 8 already has its 5 dogs, so R5C8 must be cats.
  89. R5C7 and R5C8 are both cats, so R5C9 must be a dog (no three in a row).
  90. Column 9 already has its 5 dogs, so R2C9 must be cats.
  91. Row 2 already has its 5 cats, so R2C10 must be dogs.

About this puzzle

This 10×10 grid starts with 4 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.

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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