Cats & Dogs #252: 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 R1C8 and R2C8 means they are the same. R1C8 is a cat, so R2C8 is a cat.
  2. The × clue between R10C2 and R9C2 means they are different. R10C2 is a cat, so R9C2 is a dog.
  3. R1C8 and R2C8 are both cats, so R3C8 must be a dog (no three in a row).
  4. The = clue between R3C8 and R3C7 means they are the same. R3C8 is a dog, so R3C7 is a dog.
  5. R3C7 and R3C8 are both dogs, so R3C6 must be a cat (no three in a row).
  6. R3C7 and R3C8 are both dogs, so R3C9 must be a cat (no three in a row).
  7. The = clue between R3C9 and R4C9 means they are the same. R3C9 is a cat, so R4C9 is a cat.
  8. R3C9 and R4C9 are both cats, so R2C9 must be a dog (no three in a row).
  9. The = clue between R2C9 and R1C9 means they are the same. R2C9 is a dog, so R1C9 is a dog.
  10. R3C9 and R4C9 are both cats, so R5C9 must be a dog (no three in a row).
  11. Imagine R1C1 were a cat: following the rules from there soon forces a contradiction, so R1C1 must be a dog.
  12. The = clue between R1C1 and R1C2 means they are the same. R1C1 is a dog, so R1C2 is a dog.
  13. The = clue between R1C2 and R2C2 means they are the same. R1C2 is a dog, so R2C2 is a dog.
  14. R1C1 and R1C2 are both dogs, so R1C3 must be a cat (no three in a row).
  15. R1C2 and R2C2 are both dogs, so R3C2 must be a cat (no three in a row).
  16. Imagine R2C1 were a dog: following the rules from there soon forces a contradiction, so R2C1 must be a cat.
  17. Imagine R2C3 were a cat: following the rules from there soon forces a contradiction, so R2C3 must be a dog.
  18. The = clue between R2C3 and R3C3 means they are the same. R2C3 is a dog, so R3C3 is a dog.
  19. R2C3 and R3C3 are both dogs, so R4C3 must be a cat (no three in a row).
  20. Imagine R4C4 were a cat: following the rules from there soon forces a contradiction, so R4C4 must be a dog.
  21. The = clue between R4C4 and R4C5 means they are the same. R4C4 is a dog, so R4C5 is a dog.
  22. R4C4 and R4C5 are both dogs, so R4C6 must be a cat (no three in a row).
  23. R3C6 and R4C6 are both cats, so R2C6 must be a dog (no three in a row).
  24. R3C6 and R4C6 are both cats, so R5C6 must be a dog (no three in a row).
  25. Imagine R7C5 were a cat: following the rules from there soon forces a contradiction, so R7C5 must be a dog.
  26. The = clue between R7C5 and R8C5 means they are the same. R7C5 is a dog, so R8C5 is a dog.
  27. R7C5 and R8C5 are both dogs, so R6C5 must be a cat (no three in a row).
  28. R6C4 and R6C5 are both cats, so R6C3 must be a dog (no three in a row).
  29. R6C4 and R6C5 are both cats, so R6C6 must be a dog (no three in a row).
  30. R5C6 and R6C6 are both dogs, so R7C6 must be a cat (no three in a row).
  31. Imagine R7C7 were a cat: following the rules from there soon forces a contradiction, so R7C7 must be a dog.
  32. The = clue between R7C7 and R7C8 means they are the same. R7C7 is a dog, so R7C8 is a dog.
  33. R7C7 and R7C8 are both dogs, so R7C9 must be a cat (no three in a row).
  34. The × clue between R7C9 and R6C9 means they are different. R7C9 is a cat, so R6C9 is a dog.
  35. Imagine R5C5 were a dog: following the rules from there soon forces a contradiction, so R5C5 must be a cat.
  36. Imagine R6C10 were a dog: following the rules from there soon forces a contradiction, so R6C10 must be a cat.
  37. R6C10 and R8C10 are both cats with one square between them, so R7C10 must be a dog.
  38. Imagine R1C4 were a cat: following the rules from there soon forces a contradiction, so R1C4 must be a dog.
  39. Imagine R1C5 were a dog: following the rules from there soon forces a contradiction, so R1C5 must be a cat.
  40. Imagine R1C10 were a dog: following the rules from there soon forces a contradiction, so R1C10 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. R1C5 and R2C5 are both cats, so R3C5 must be a dog (no three in a row).
  43. R3C3 and R3C5 are both dogs with one square between them, so R3C4 must be a cat.
  44. Column 5 already has its 5 cats, so R10C5 must be dogs.
  45. Imagine R5C4 were a cat: following the rules from there soon forces a contradiction, so R5C4 must be a dog.
  46. Imagine R4C10 were a cat: following the rules from there soon forces a contradiction, so R4C10 must be a dog.
  47. Imagine R4C2 were a dog: following the rules from there soon forces a contradiction, so R4C2 must be a cat.
  48. R3C2 and R4C2 are both cats, so R5C2 must be a dog (no three in a row).
  49. R5C2 and R5C4 are both dogs with one square between them, so R5C3 must be a cat.
  50. Imagine R5C1 were a dog: following the rules from there soon forces a contradiction, so R5C1 must be a cat.
  51. The × clue between R5C1 and R6C1 means they are different. R5C1 is a cat, so R6C1 is a dog.
  52. R6C1 and R6C3 are both dogs with one square between them, so R6C2 must be a cat.
  53. Imagine R5C10 were a dog: following the rules from there soon forces a contradiction, so R5C10 must be a cat.
  54. Imagine R7C1 were a dog: following the rules from there soon forces a contradiction, so R7C1 must be a cat.
  55. Imagine R7C2 were a dog: following the rules from there soon forces a contradiction, so R7C2 must be a cat.
  56. R7C1 and R7C2 are both cats, so R7C3 must be a dog (no three in a row).
  57. R7C3 and R7C5 are both dogs with one square between them, so R7C4 must be a cat.
  58. R6C2 and R7C2 are both cats, so R8C2 must be a dog (no three in a row).
  59. R6C3 and R7C3 are both dogs, so R8C3 must be a cat (no three in a row).
  60. R6C4 and R7C4 are both cats, so R8C4 must be a dog (no three in a row).
  61. R8C4 and R8C5 are both dogs, so R8C6 must be a cat (no three in a row).
  62. R7C6 and R8C6 are both cats, so R9C6 must be a dog (no three in a row).
  63. Imagine R2C7 were a dog: following the rules from there soon forces a contradiction, so R2C7 must be a cat.
  64. Row 2 already has its 5 cats, so R2C10 must be dogs.
  65. R2C10 and R4C10 are both dogs with one square between them, so R3C10 must be a cat.
  66. Row 3 already has its 5 cats, so R3C1 must be dogs.
  67. Column 10 already has its 5 cats, so R9C10 and R10C10 must be dogs.
  68. Imagine R4C7 were a cat: following the rules from there soon forces a contradiction, so R4C7 must be a dog.
  69. R3C7 and R4C7 are both dogs, so R5C7 must be a cat (no three in a row).
  70. The × clue between R5C7 and R5C8 means they are different. R5C7 is a cat, so R5C8 is a dog.
  71. R3C8 and R5C8 are both dogs with one square between them, so R4C8 must be a cat.
  72. R5C8 and R7C8 are both dogs with one square between them, so R6C8 must be a cat.
  73. The × clue between R6C8 and R6C7 means they are different. R6C8 is a cat, so R6C7 is a dog.
  74. R6C7 and R7C7 are both dogs, so R8C7 must be a cat (no three in a row).
  75. R8C6 and R8C7 are both cats, so R8C8 must be a dog (no three in a row).
  76. R7C8 and R8C8 are both dogs, so R9C8 must be a cat (no three in a row).
  77. Column 8 already has its 5 cats, so R10C8 must be dogs.
  78. R10C8 and R10C10 are both dogs with one square between them, so R10C9 must be a cat.
  79. Imagine R1C6 were a cat: following the rules from there soon forces a contradiction, so R1C6 must be a dog.
  80. Row 1 already has its 5 dogs, so R1C7 must be cats.
  81. Column 6 already has its 5 dogs, so R10C6 must be cats.
  82. Imagine R8C1 were a cat: following the rules from there soon forces a contradiction, so R8C1 must be a dog.
  83. Row 8 already has its 5 dogs, so R8C9 must be cats.
  84. R7C9 and R8C9 are both cats, so R9C9 must be a dog (no three in a row).
  85. Column 1 already has its 5 dogs, so R9C1 and R10C1 must be cats.
  86. R10C1 and R10C2 are both cats, so R10C3 must be a dog (no three in a row).
  87. R10C3 and R10C5 are both dogs with one square between them, so R10C4 must be a cat.
  88. Row 10 already has its 5 cats, so R10C7 must be dogs.
  89. Column 3 already has its 5 dogs, so R9C3 must be cats.
  90. R9C3 and R9C5 are both cats with one square between them, so R9C4 must be a dog.
  91. Row 9 already has its 5 dogs, so R9C7 must be cats.

About this puzzle

This 10×10 grid starts with 7 filled squares and 15 = / × 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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