Cats & Dogs #286: 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 R5C7 and R6C7 means they are different. R5C7 is a dog, so R6C7 is a cat.
  2. The × clue between R5C9 and R5C8 means they are different. R5C9 is a cat, so R5C8 is a dog.
  3. The × clue between R5C9 and R5C10 means they are different. R5C9 is a cat, so R5C10 is a dog.
  4. The × clue between R6C7 and R7C7 means they are different. R6C7 is a cat, so R7C7 is a dog.
  5. The × clue between R8C5 and R8C4 means they are different. R8C5 is a dog, so R8C4 is a cat.
  6. The × clue between R8C4 and R8C3 means they are different. R8C4 is a cat, so R8C3 is a dog.
  7. The × clue between R8C5 and R8C6 means they are different. R8C5 is a dog, so R8C6 is a cat.
  8. The × clue between R8C6 and R8C7 means they are different. R8C6 is a cat, so R8C7 is a dog.
  9. R2C5 and R2C6 are both dogs, so R2C4 must be a cat (no three in a row).
  10. R2C5 and R2C6 are both dogs, so R2C7 must be a cat (no three in a row).
  11. R5C7 and R5C8 are both dogs, so R5C6 must be a cat (no three in a row).
  12. R10C7 and R10C8 are both dogs, so R10C6 must be a cat (no three in a row).
  13. R10C7 and R10C8 are both dogs, so R10C9 must be a cat (no three in a row).
  14. R2C4 and R4C4 are both cats with one square between them, so R3C4 must be a dog.
  15. R8C6 and R10C6 are both cats with one square between them, so R9C6 must be a dog.
  16. R7C7 and R8C7 are both dogs, so R9C7 must be a cat (no three in a row).
  17. R3C10 and R5C10 are both dogs with one square between them, so R4C10 must be a cat.
  18. Imagine R1C7 were a dog: following the rules from there soon forces a contradiction, so R1C7 must be a cat.
  19. R1C7 and R2C7 are both cats, so R3C7 must be a dog (no three in a row).
  20. R3C7 and R5C7 are both dogs with one square between them, so R4C7 must be a cat.
  21. The × clue between R4C7 and R4C8 means they are different. R4C7 is a cat, so R4C8 is a dog.
  22. R4C8 and R5C8 are both dogs, so R3C8 must be a cat (no three in a row).
  23. R4C8 and R5C8 are both dogs, so R6C8 must be a cat (no three in a row).
  24. R6C7 and R6C8 are both cats, so R6C6 must be a dog (no three in a row).
  25. R6C7 and R6C8 are both cats, so R6C9 must be a dog (no three in a row).
  26. Imagine R2C2 were a cat: following the rules from there soon forces a contradiction, so R2C2 must be a dog.
  27. The = clue between R2C2 and R2C3 means they are the same. R2C2 is a dog, so R2C3 is a dog.
  28. R2C2 and R2C3 are both dogs, so R2C1 must be a cat (no three in a row).
  29. The = clue between R2C1 and R1C1 means they are the same. R2C1 is a cat, so R1C1 is a cat.
  30. R1C1 and R2C1 are both cats, so R3C1 must be a dog (no three in a row).
  31. Imagine R2C8 were a cat: following the rules from there soon forces a contradiction, so R2C8 must be a dog.
  32. Row 2 already has its 5 dogs, so R2C9 must be cats.
  33. The = clue between R2C9 and R3C9 means they are the same. R2C9 is a cat, so R3C9 is a cat.
  34. R2C9 and R3C9 are both cats, so R1C9 must be a dog (no three in a row).
  35. R2C9 and R3C9 are both cats, so R4C9 must be a dog (no three in a row).
  36. Row 2 already has its 5 dogs, so R2C10 must be cats.
  37. Imagine R1C6 were a cat: following the rules from there soon forces a contradiction, so R1C6 must be a dog.
  38. R1C6 and R2C6 are both dogs, so R3C6 must be a cat (no three in a row).
  39. R3C6 and R5C6 are both cats with one square between them, so R4C6 must be a dog.
  40. Column 6 already has its 5 dogs, so R7C6 must be cats.
  41. Imagine R1C8 were a dog: following the rules from there soon forces a contradiction, so R1C8 must be a cat.
  42. Imagine R3C5 were a dog: following the rules from there soon forces a contradiction, so R3C5 must be a cat.
  43. Imagine R5C4 were a cat: following the rules from there soon forces a contradiction, so R5C4 must be a dog.
  44. Imagine R1C2 were a cat: following the rules from there soon forces a contradiction, so R1C2 must be a dog.
  45. R1C2 and R2C2 are both dogs, so R3C2 must be a cat (no three in a row).
  46. The × clue between R3C2 and R3C3 means they are different. R3C2 is a cat, so R3C3 is a dog.
  47. R2C3 and R3C3 are both dogs, so R1C3 must be a cat (no three in a row).
  48. R2C3 and R3C3 are both dogs, so R4C3 must be a cat (no three in a row).
  49. R4C3 and R4C4 are both cats, so R4C2 must be a dog (no three in a row).
  50. The × clue between R4C2 and R4C1 means they are different. R4C2 is a dog, so R4C1 is a cat.
  51. R4C3 and R4C4 are both cats, so R4C5 must be a dog (no three in a row).
  52. The × clue between R4C5 and R5C5 means they are different. R4C5 is a dog, so R5C5 is a cat.
  53. Imagine R1C10 were a cat: following the rules from there soon forces a contradiction, so R1C10 must be a dog.
  54. Imagine R5C2 were a dog: following the rules from there soon forces a contradiction, so R5C2 must be a cat.
  55. Imagine R6C1 were a cat: following the rules from there soon forces a contradiction, so R6C1 must be a dog.
  56. The = clue between R6C1 and R6C2 means they are the same. R6C1 is a dog, so R6C2 is a dog.
  57. R6C1 and R6C2 are both dogs, so R6C3 must be a cat (no three in a row).
  58. The × clue between R6C3 and R6C4 means they are different. R6C3 is a cat, so R6C4 is a dog.
  59. The × clue between R6C4 and R7C4 means they are different. R6C4 is a dog, so R7C4 is a cat.
  60. R6C4 and R6C6 are both dogs with one square between them, so R6C5 must be a cat.
  61. R7C4 and R7C6 are both cats with one square between them, so R7C5 must be a dog.
  62. R4C3 and R6C3 are both cats with one square between them, so R5C3 must be a dog.
  63. R7C4 and R8C4 are both cats, so R9C4 must be a dog (no three in a row).
  64. R9C4 and R9C6 are both dogs with one square between them, so R9C5 must be a cat.
  65. Row 5 already has its 5 dogs, so R5C1 must be cats.
  66. Row 6 already has its 5 dogs, so R6C10 must be cats.
  67. Imagine R7C1 were a cat: following the rules from there soon forces a contradiction, so R7C1 must be a dog.
  68. R6C1 and R7C1 are both dogs, so R8C1 must be a cat (no three in a row).
  69. Column 1 already has its 5 cats, so R9C1 and R10C1 must be dogs.
  70. Imagine R1C4 were a dog: following the rules from there soon forces a contradiction, so R1C4 must be a cat.
  71. R1C3 and R1C4 are both cats, so R1C5 must be a dog (no three in a row).
  72. Column 4 already has its 5 cats, so R10C4 must be dogs.
  73. Row 10 already has its 5 dogs, so R10C2, R10C3 and R10C5 must be cats.
  74. Imagine R7C2 were a dog: following the rules from there soon forces a contradiction, so R7C2 must be a cat.
  75. R7C2 and R7C4 are both cats with one square between them, so R7C3 must be a dog.
  76. R7C3 and R8C3 are both dogs, so R9C3 must be a cat (no three in a row).
  77. Imagine R7C8 were a cat: following the rules from there soon forces a contradiction, so R7C8 must be a dog.
  78. R7C7 and R7C8 are both dogs, so R7C9 must be a cat (no three in a row).
  79. The = clue between R7C9 and R7C10 means they are the same. R7C9 is a cat, so R7C10 is a cat.
  80. R6C10 and R7C10 are both cats, so R8C10 must be a dog (no three in a row).
  81. R8C10 and R10C10 are both dogs with one square between them, so R9C10 must be a cat.
  82. Column 8 already has its 5 dogs, so R8C8 and R9C8 must be cats.
  83. R9C7 and R9C8 are both cats, so R9C9 must be a dog (no three in a row).
  84. Row 9 already has its 5 cats, so R9C2 must be dogs.
  85. Column 2 already has its 5 dogs, so R8C2 must be cats.
  86. Row 8 already has its 5 cats, so R8C9 must be dogs.

About this puzzle

This 10×10 grid starts with 10 filled squares and 19 = / × clues. It can be solved in 86 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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