Cats & Dogs #268: 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 R1C5 and R1C4 means they are different. R1C5 is a cat, so R1C4 is a dog.
  2. The = clue between R9C7 and R8C7 means they are the same. R9C7 is a cat, so R8C7 is a cat.
  3. The × clue between R10C1 and R10C2 means they are different. R10C1 is a dog, so R10C2 is a cat.
  4. R8C5 and R8C7 are both cats with one square between them, so R8C6 must be a dog.
  5. R9C1 and R10C1 are both dogs, so R8C1 must be a cat (no three in a row).
  6. R8C7 and R9C7 are both cats, so R7C7 must be a dog (no three in a row).
  7. R8C7 and R9C7 are both cats, so R10C7 must be a dog (no three in a row).
  8. Imagine R2C1 were a dog: following the rules from there soon forces a contradiction, so R2C1 must be a cat.
  9. Imagine R3C1 were a dog: following the rules from there soon forces a contradiction, so R3C1 must be a cat.
  10. R3C1 and R3C2 are both cats, so R3C3 must be a dog (no three in a row).
  11. Imagine R5C1 were a dog: following the rules from there soon forces a contradiction, so R5C1 must be a cat.
  12. Imagine R7C6 were a dog: following the rules from there soon forces a contradiction, so R7C6 must be a cat.
  13. Imagine R8C3 were a cat: following the rules from there soon forces a contradiction, so R8C3 must be a dog.
  14. The = clue between R8C3 and R8C4 means they are the same. R8C3 is a dog, so R8C4 is a dog.
  15. R8C3 and R8C4 are both dogs, so R8C2 must be a cat (no three in a row).
  16. R8C2 and R10C2 are both cats with one square between them, so R9C2 must be a dog.
  17. R9C1 and R9C2 are both dogs, so R9C3 must be a cat (no three in a row).
  18. Imagine R3C4 were a dog: following the rules from there soon forces a contradiction, so R3C4 must be a cat.
  19. Imagine R3C5 were a cat: following the rules from there soon forces a contradiction, so R3C5 must be a dog.
  20. The = clue between R3C5 and R4C5 means they are the same. R3C5 is a dog, so R4C5 is a dog.
  21. The = clue between R4C5 and R4C4 means they are the same. R4C5 is a dog, so R4C4 is a dog.
  22. R4C4 and R4C5 are both dogs, so R4C3 must be a cat (no three in a row).
  23. R4C4 and R4C5 are both dogs, so R4C6 must be a cat (no three in a row).
  24. R3C5 and R4C5 are both dogs, so R2C5 must be a cat (no three in a row).
  25. R3C5 and R4C5 are both dogs, so R5C5 must be a cat (no three in a row).
  26. Imagine R5C3 were a cat: following the rules from there soon forces a contradiction, so R5C3 must be a dog.
  27. The = clue between R5C3 and R5C4 means they are the same. R5C3 is a dog, so R5C4 is a dog.
  28. R5C3 and R5C4 are both dogs, so R5C2 must be a cat (no three in a row).
  29. R3C2 and R5C2 are both cats with one square between them, so R4C2 must be a dog.
  30. R4C4 and R5C4 are both dogs, so R6C4 must be a cat (no three in a row).
  31. Imagine R1C2 were a cat: following the rules from there soon forces a contradiction, so R1C2 must be a dog.
  32. The × clue between R1C2 and R1C3 means they are different. R1C2 is a dog, so R1C3 is a cat.
  33. The × clue between R1C3 and R2C3 means they are different. R1C3 is a cat, so R2C3 is a dog.
  34. Imagine R2C4 were a dog: following the rules from there soon forces a contradiction, so R2C4 must be a cat.
  35. R2C4 and R2C5 are both cats, so R2C6 must be a dog (no three in a row).
  36. Imagine R4C7 were a dog: following the rules from there soon forces a contradiction, so R4C7 must be a cat.
  37. R4C6 and R4C7 are both cats, so R4C8 must be a dog (no three in a row).
  38. Row 4 already has its 5 dogs, so R4C9 and R4C10 must be cats.
  39. Imagine R2C8 were a dog: following the rules from there soon forces a contradiction, so R2C8 must be a cat.
  40. Imagine R3C8 were a cat: following the rules from there soon forces a contradiction, so R3C8 must be a dog.
  41. R3C8 and R4C8 are both dogs, so R5C8 must be a cat (no three in a row).
  42. Imagine R6C1 were a dog: following the rules from there soon forces a contradiction, so R6C1 must be a cat.
  43. The × clue between R6C1 and R6C2 means they are different. R6C1 is a cat, so R6C2 is a dog.
  44. R5C1 and R6C1 are both cats, so R7C1 must be a dog (no three in a row).
  45. Imagine R8C10 were a cat: following the rules from there soon forces a contradiction, so R8C10 must be a dog.
  46. Imagine R9C6 were a cat: following the rules from there soon forces a contradiction, so R9C6 must be a dog.
  47. R8C6 and R9C6 are both dogs, so R10C6 must be a cat (no three in a row).
  48. Imagine R9C8 were a dog: following the rules from there soon forces a contradiction, so R9C8 must be a cat.
  49. The = clue between R9C8 and R10C8 means they are the same. R9C8 is a cat, so R10C8 is a cat.
  50. R9C7 and R9C8 are both cats, so R9C9 must be a dog (no three in a row).
  51. R9C8 and R10C8 are both cats, so R8C8 must be a dog (no three in a row).
  52. The × clue between R8C8 and R7C8 means they are different. R8C8 is a dog, so R7C8 is a cat.
  53. R7C8 and R7C10 are both cats with one square between them, so R7C9 must be a dog.
  54. R8C8 and R8C10 are both dogs with one square between them, so R8C9 must be a cat.
  55. R5C8 and R7C8 are both cats with one square between them, so R6C8 must be a dog.
  56. The × clue between R6C8 and R6C7 means they are different. R6C8 is a dog, so R6C7 is a cat.
  57. R4C7 and R6C7 are both cats with one square between them, so R5C7 must be a dog.
  58. Column 8 already has its 5 cats, so R1C8 must be dogs.
  59. The × clue between R1C8 and R1C7 means they are different. R1C8 is a dog, so R1C7 is a cat.
  60. R1C5 and R1C7 are both cats with one square between them, so R1C6 must be a dog.
  61. R1C6 and R2C6 are both dogs, so R3C6 must be a cat (no three in a row).
  62. R3C6 and R4C6 are both cats, so R5C6 must be a dog (no three in a row).
  63. Row 1 already has its 5 dogs, so R1C9 and R1C10 must be cats.
  64. Column 6 already has its 5 dogs, so R6C6 must be cats.
  65. R6C4 and R6C6 are both cats with one square between them, so R6C5 must be a dog.
  66. Column 7 already has its 5 cats, so R2C7 and R3C7 must be dogs.
  67. R3C7 and R3C8 are both dogs, so R3C9 must be a cat (no three in a row).
  68. The × clue between R3C9 and R3C10 means they are different. R3C9 is a cat, so R3C10 is a dog.
  69. R1C9 and R3C9 are both cats with one square between them, so R2C9 must be a dog.
  70. R3C9 and R4C9 are both cats, so R5C9 must be a dog (no three in a row).
  71. R5C9 and R7C9 are both dogs with one square between them, so R6C9 must be a cat.
  72. Row 5 already has its 5 dogs, so R5C10 must be cats.
  73. R4C10 and R5C10 are both cats, so R6C10 must be a dog (no three in a row).
  74. Row 6 already has its 5 cats, so R6C3 must be dogs.
  75. R5C3 and R6C3 are both dogs, so R7C3 must be a cat (no three in a row).
  76. Column 3 already has its 5 dogs, so R10C3 must be cats.
  77. R10C2 and R10C3 are both cats, so R10C4 must be a dog (no three in a row).
  78. R8C4 and R10C4 are both dogs with one square between them, so R9C4 must be a cat.
  79. R9C3 and R9C4 are both cats, so R9C5 must be a dog (no three in a row).
  80. Row 9 already has its 5 dogs, so R9C10 must be cats.
  81. Column 4 already has its 5 dogs, so R7C4 must be cats.
  82. R7C3 and R7C4 are both cats, so R7C2 must be a dog (no three in a row).
  83. R7C3 and R7C4 are both cats, so R7C5 must be a dog (no three in a row).
  84. Column 2 already has its 5 dogs, so R2C2 must be cats.
  85. Row 2 already has its 5 cats, so R2C10 must be dogs.
  86. Column 5 already has its 5 dogs, so R10C5 must be cats.
  87. Row 10 already has its 5 cats, so R10C9 and R10C10 must be dogs.

About this puzzle

This 10×10 grid starts with 9 filled squares and 15 = / × clues. It can be solved in 87 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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