Cats & Dogs #241: 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

A 10x10 logic grid: 5 cats and 5 dogs in every row and column, no three of a kind in a row, and a few = and × clues to point the way.

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

About this puzzle

This 10×10 grid starts with 12 filled squares and 10 = / × clues. It can be solved in 87 steps using a "what if" trial of one square on top of the basic rules.

Count as you go. Once a row or column has all of one animal, every remaining empty square in it must be the other.

Every puzzle on this site has exactly one solution that can be reached by deduction. If you are guessing, look again at the rows and columns that are nearly full.

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