Cats & Dogs #260: 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 R1C6 and R1C5 means they are different. R1C6 is a cat, so R1C5 is a dog.
  2. The × clue between R2C3 and R3C3 means they are different. R2C3 is a cat, so R3C3 is a dog.
  3. The × clue between R2C10 and R3C10 means they are different. R2C10 is a cat, so R3C10 is a dog.
  4. The = clue between R5C8 and R6C8 means they are the same. R5C8 is a dog, so R6C8 is a dog.
  5. The × clue between R7C2 and R7C1 means they are different. R7C2 is a dog, so R7C1 is a cat.
  6. The × clue between R7C5 and R7C4 means they are different. R7C5 is a cat, so R7C4 is a dog.
  7. R2C3 and R2C4 are both cats, so R2C2 must be a dog (no three in a row).
  8. R2C3 and R2C4 are both cats, so R2C5 must be a dog (no three in a row).
  9. R2C5 and R2C6 are both dogs, so R2C7 must be a cat (no three in a row).
  10. The × clue between R2C7 and R3C7 means they are different. R2C7 is a cat, so R3C7 is a dog.
  11. R3C3 and R3C4 are both dogs, so R3C2 must be a cat (no three in a row).
  12. R3C3 and R3C4 are both dogs, so R3C5 must be a cat (no three in a row).
  13. R6C8 and R6C10 are both dogs with one square between them, so R6C9 must be a cat.
  14. R7C2 and R7C4 are both dogs with one square between them, so R7C3 must be a cat.
  15. R3C3 and R4C3 are both dogs, so R5C3 must be a cat (no three in a row).
  16. R5C3 and R7C3 are both cats with one square between them, so R6C3 must be a dog.
  17. R5C8 and R6C8 are both dogs, so R4C8 must be a cat (no three in a row).
  18. R5C8 and R6C8 are both dogs, so R7C8 must be a cat (no three in a row).
  19. R7C8 and R8C8 are both cats, so R9C8 must be a dog (no three in a row).
  20. Imagine R1C8 were a cat: following the rules from there soon forces a contradiction, so R1C8 must be a dog.
  21. Imagine R2C1 were a cat: following the rules from there soon forces a contradiction, so R2C1 must be a dog.
  22. R1C1 and R2C1 are both dogs, so R3C1 must be a cat (no three in a row).
  23. The × clue between R3C1 and R4C1 means they are different. R3C1 is a cat, so R4C1 is a dog.
  24. R4C1 and R4C3 are both dogs with one square between them, so R4C2 must be a cat.
  25. R3C2 and R4C2 are both cats, so R5C2 must be a dog (no three in a row).
  26. R5C2 and R7C2 are both dogs with one square between them, so R6C2 must be a cat.
  27. Imagine R3C6 were a dog: following the rules from there soon forces a contradiction, so R3C6 must be a cat.
  28. Imagine R7C6 were a cat: following the rules from there soon forces a contradiction, so R7C6 must be a dog.
  29. The = clue between R7C6 and R8C6 means they are the same. R7C6 is a dog, so R8C6 is a dog.
  30. R7C6 and R8C6 are both dogs, so R6C6 must be a cat (no three in a row).
  31. R7C6 and R8C6 are both dogs, so R9C6 must be a cat (no three in a row).
  32. The × clue between R9C6 and R10C6 means they are different. R9C6 is a cat, so R10C6 is a dog.
  33. The = clue between R10C6 and R10C5 means they are the same. R10C6 is a dog, so R10C5 is a dog.
  34. R10C5 and R10C6 are both dogs, so R10C4 must be a cat (no three in a row).
  35. The × clue between R10C4 and R10C3 means they are different. R10C4 is a cat, so R10C3 is a dog.
  36. R10C5 and R10C6 are both dogs, so R10C7 must be a cat (no three in a row).
  37. R10C7 and R10C8 are both cats, so R10C9 must be a dog (no three in a row).
  38. Imagine R1C2 were a cat: following the rules from there soon forces a contradiction, so R1C2 must be a dog.
  39. The × clue between R1C2 and R1C3 means they are different. R1C2 is a dog, so R1C3 is a cat.
  40. Imagine R5C5 were a cat: following the rules from there soon forces a contradiction, so R5C5 must be a dog.
  41. Imagine R4C5 were a dog: following the rules from there soon forces a contradiction, so R4C5 must be a cat.
  42. Imagine R5C4 were a dog: following the rules from there soon forces a contradiction, so R5C4 must be a cat.
  43. Imagine R4C4 were a cat: following the rules from there soon forces a contradiction, so R4C4 must be a dog.
  44. Imagine R6C4 were a cat: following the rules from there soon forces a contradiction, so R6C4 must be a dog.
  45. R6C3 and R6C4 are both dogs, so R6C5 must be a cat (no three in a row).
  46. R6C5 and R6C6 are both cats, so R6C7 must be a dog (no three in a row).
  47. R6C4 and R7C4 are both dogs, so R8C4 must be a cat (no three in a row).
  48. R8C4 and R10C4 are both cats with one square between them, so R9C4 must be a dog.
  49. R6C5 and R7C5 are both cats, so R8C5 must be a dog (no three in a row).
  50. R8C5 and R8C6 are both dogs, so R8C7 must be a cat (no three in a row).
  51. R8C7 and R8C8 are both cats, so R8C9 must be a dog (no three in a row).
  52. R8C5 and R10C5 are both dogs with one square between them, so R9C5 must be a cat.
  53. R9C5 and R9C6 are both cats, so R9C7 must be a dog (no three in a row).
  54. R9C7 and R9C8 are both dogs, so R9C9 must be a cat (no three in a row).
  55. Row 6 already has its 5 dogs, so R6C1 must be cats.
  56. R6C1 and R7C1 are both cats, so R5C1 must be a dog (no three in a row).
  57. R6C1 and R7C1 are both cats, so R8C1 must be a dog (no three in a row).
  58. The × clue between R8C1 and R8C2 means they are different. R8C1 is a dog, so R8C2 is a cat.
  59. R8C2 and R8C4 are both cats with one square between them, so R8C3 must be a dog.
  60. R8C3 and R10C3 are both dogs with one square between them, so R9C3 must be a cat.
  61. Row 8 already has its 5 dogs, so R8C10 must be cats.
  62. The × clue between R8C10 and R7C10 means they are different. R8C10 is a cat, so R7C10 is a dog.
  63. R6C10 and R7C10 are both dogs, so R5C10 must be a cat (no three in a row).
  64. Column 1 already has its 5 dogs, so R9C1 must be cats.
  65. R9C1 and R9C3 are both cats with one square between them, so R9C2 must be a dog.
  66. Row 9 already has its 5 cats, so R9C10 must be dogs.
  67. Column 1 already has its 5 dogs, so R10C1 must be cats.
  68. Column 2 already has its 5 dogs, so R10C2 must be cats.
  69. Row 10 already has its 5 cats, so R10C10 must be dogs.
  70. Column 4 already has its 5 dogs, so R1C4 must be cats.
  71. Column 10 already has its 5 dogs, so R1C10 and R4C10 must be cats.
  72. R4C8 and R4C10 are both cats with one square between them, so R4C9 must be a dog.
  73. Imagine R1C7 were a cat: following the rules from there soon forces a contradiction, so R1C7 must be a dog.
  74. R1C7 and R1C8 are both dogs, so R1C9 must be a cat (no three in a row).
  75. The = clue between R1C9 and R2C9 means they are the same. R1C9 is a cat, so R2C9 is a cat.
  76. The × clue between R2C9 and R2C8 means they are different. R2C9 is a cat, so R2C8 is a dog.
  77. R1C8 and R2C8 are both dogs, so R3C8 must be a cat (no three in a row).
  78. R1C9 and R2C9 are both cats, so R3C9 must be a dog (no three in a row).
  79. R3C9 and R4C9 are both dogs, so R5C9 must be a cat (no three in a row).
  80. R5C9 and R6C9 are both cats, so R7C9 must be a dog (no three in a row).
  81. Row 5 already has its 5 cats, so R5C6 must be dogs.
  82. Row 7 already has its 5 dogs, so R7C7 must be cats.
  83. Column 6 already has its 5 dogs, so R4C6 must be cats.
  84. R4C5 and R4C6 are both cats, so R4C7 must be a dog (no three in a row).

About this puzzle

This 10×10 grid starts with 15 filled squares and 17 = / × clues. It can be solved in 84 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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