Cats & Dogs #218: 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. The × clue between R2C6 and R2C5 means they are different. R2C6 is a cat, so R2C5 is a dog.
  2. The × clue between R10C4 and R10C5 means they are different. R10C4 is a cat, so R10C5 is a dog.
  3. R10C2 and R10C4 are both cats with one square between them, so R10C3 must be a dog.
  4. R9C3 and R10C3 are both dogs, so R8C3 must be a cat (no three in a row).
  5. R6C3 and R8C3 are both cats with one square between them, so R7C3 must be a dog.
  6. R3C4 and R5C4 are both cats with one square between them, so R4C4 must be a dog.
  7. R2C9 and R3C9 are both cats, so R1C9 must be a dog (no three in a row).
  8. The = clue between R1C9 and R1C10 means they are the same. R1C9 is a dog, so R1C10 is a dog.
  9. R1C9 and R1C10 are both dogs, so R1C8 must be a cat (no three in a row).
  10. R2C9 and R3C9 are both cats, so R4C9 must be a dog (no three in a row).
  11. The = clue between R4C9 and R5C9 means they are the same. R4C9 is a dog, so R5C9 is a dog.
  12. R4C9 and R5C9 are both dogs, so R6C9 must be a cat (no three in a row).
  13. The = clue between R6C9 and R6C10 means they are the same. R6C9 is a cat, so R6C10 is a cat.
  14. R6C9 and R6C10 are both cats, so R6C8 must be a dog (no three in a row).
  15. The × clue between R6C8 and R6C7 means they are different. R6C8 is a dog, so R6C7 is a cat.
  16. Imagine R1C5 were a dog: following the rules from there soon forces a contradiction, so R1C5 must be a cat.
  17. Imagine R2C3 were a dog: following the rules from there soon forces a contradiction, so R2C3 must be a cat.
  18. Imagine R3C2 were a cat: following the rules from there soon forces a contradiction, so R3C2 must be a dog.
  19. Imagine R3C3 were a dog: following the rules from there soon forces a contradiction, so R3C3 must be a cat.
  20. R3C3 and R3C4 are both cats, so R3C5 must be a dog (no three in a row).
  21. R2C3 and R3C3 are both cats, so R4C3 must be a dog (no three in a row).
  22. R4C3 and R4C4 are both dogs, so R4C2 must be a cat (no three in a row).
  23. R4C3 and R4C4 are both dogs, so R4C5 must be a cat (no three in a row).
  24. Column 3 already has its 5 dogs, so R5C3 must be cats.
  25. R5C3 and R5C4 are both cats, so R5C2 must be a dog (no three in a row).
  26. R5C3 and R5C4 are both cats, so R5C5 must be a dog (no three in a row).
  27. Imagine R5C6 were a dog: following the rules from there soon forces a contradiction, so R5C6 must be a cat.
  28. The × clue between R5C6 and R6C6 means they are different. R5C6 is a cat, so R6C6 is a dog.
  29. Imagine R6C1 were a cat: following the rules from there soon forces a contradiction, so R6C1 must be a dog.
  30. Imagine R6C2 were a cat: following the rules from there soon forces a contradiction, so R6C2 must be a dog.
  31. R5C2 and R6C2 are both dogs, so R7C2 must be a cat (no three in a row).
  32. Imagine R6C4 were a cat: following the rules from there soon forces a contradiction, so R6C4 must be a dog.
  33. R6C4 and R6C6 are both dogs with one square between them, so R6C5 must be a cat.
  34. Imagine R7C6 were a dog: following the rules from there soon forces a contradiction, so R7C6 must be a cat.
  35. The = clue between R7C6 and R8C6 means they are the same. R7C6 is a cat, so R8C6 is a cat.
  36. R7C6 and R8C6 are both cats, so R9C6 must be a dog (no three in a row).
  37. R9C6 and R9C7 are both dogs, so R9C5 must be a cat (no three in a row).
  38. R9C6 and R9C7 are both dogs, so R9C8 must be a cat (no three in a row).
  39. Imagine R5C7 were a cat: following the rules from there soon forces a contradiction, so R5C7 must be a dog.
  40. R5C7 and R5C9 are both dogs with one square between them, so R5C8 must be a cat.
  41. Imagine R7C10 were a cat: following the rules from there soon forces a contradiction, so R7C10 must be a dog.
  42. Imagine R7C4 were a cat: following the rules from there soon forces a contradiction, so R7C4 must be a dog.
  43. R7C3 and R7C4 are both dogs, so R7C5 must be a cat (no three in a row).
  44. R7C5 and R7C6 are both cats, so R7C7 must be a dog (no three in a row).
  45. R6C4 and R7C4 are both dogs, so R8C4 must be a cat (no three in a row).
  46. R8C3 and R8C4 are both cats, so R8C2 must be a dog (no three in a row).
  47. R8C3 and R8C4 are both cats, so R8C5 must be a dog (no three in a row).
  48. R8C4 and R10C4 are both cats with one square between them, so R9C4 must be a dog.
  49. R9C3 and R9C4 are both dogs, so R9C2 must be a cat (no three in a row).
  50. R7C7 and R9C7 are both dogs with one square between them, so R8C7 must be a cat.
  51. R8C6 and R8C7 are both cats, so R8C8 must be a dog (no three in a row).
  52. R8C8 and R8C9 are both dogs, so R8C10 must be a cat (no three in a row).
  53. R6C8 and R8C8 are both dogs with one square between them, so R7C8 must be a cat.
  54. Row 8 already has its 5 cats, so R8C1 must be dogs.
  55. R6C1 and R8C1 are both dogs with one square between them, so R7C1 must be a cat.
  56. Row 7 already has its 5 cats, so R7C9 must be dogs.
  57. R7C9 and R8C9 are both dogs, so R9C9 must be a cat (no three in a row).
  58. R9C8 and R9C9 are both cats, so R9C10 must be a dog (no three in a row).
  59. Row 9 already has its 5 dogs, so R9C1 must be cats.
  60. Column 9 already has its 5 dogs, so R10C9 must be cats.
  61. The × clue between R10C9 and R10C10 means they are different. R10C9 is a cat, so R10C10 is a dog.
  62. Imagine R2C7 were a dog: following the rules from there soon forces a contradiction, so R2C7 must be a cat.
  63. The × clue between R2C7 and R2C8 means they are different. R2C7 is a cat, so R2C8 is a dog.
  64. Imagine R1C2 were a dog: following the rules from there soon forces a contradiction, so R1C2 must be a cat.
  65. Column 2 already has its 5 cats, so R2C2 must be dogs.
  66. Imagine R1C4 were a dog: following the rules from there soon forces a contradiction, so R1C4 must be a cat.
  67. R1C4 and R1C5 are both cats, so R1C6 must be a dog (no three in a row).
  68. R1C4 and R3C4 are both cats with one square between them, so R2C4 must be a dog.
  69. Imagine R1C1 were a dog: following the rules from there soon forces a contradiction, so R1C1 must be a cat.
  70. Row 1 already has its 5 cats, so R1C7 must be dogs.
  71. Imagine R2C1 were a cat: following the rules from there soon forces a contradiction, so R2C1 must be a dog.
  72. Row 2 already has its 5 dogs, so R2C10 must be cats.
  73. Imagine R3C7 were a dog: following the rules from there soon forces a contradiction, so R3C7 must be a cat.
  74. The × clue between R3C7 and R3C8 means they are different. R3C7 is a cat, so R3C8 is a dog.
  75. R2C7 and R3C7 are both cats, so R4C7 must be a dog (no three in a row).
  76. R4C7 and R4C9 are both dogs with one square between them, so R4C8 must be a cat.
  77. Column 7 already has its 5 dogs, so R10C7 must be cats.
  78. R10C7 and R10C9 are both cats with one square between them, so R10C8 must be a dog.
  79. Imagine R3C1 were a cat: following the rules from there soon forces a contradiction, so R3C1 must be a dog.
  80. R2C1 and R3C1 are both dogs, so R4C1 must be a cat (no three in a row).
  81. Imagine R3C6 were a cat: following the rules from there soon forces a contradiction, so R3C6 must be a dog.
  82. Row 3 already has its 5 dogs, so R3C10 must be cats.
  83. R2C10 and R3C10 are both cats, so R4C10 must be a dog (no three in a row).
  84. Row 4 already has its 5 dogs, so R4C6 must be cats.
  85. Column 6 already has its 5 cats, so R10C6 must be dogs.
  86. Row 10 already has its 5 dogs, so R10C1 must be cats.
  87. Column 1 already has its 5 cats, so R5C1 must be dogs.
  88. Row 5 already has its 5 dogs, so R5C10 must be cats.

About this puzzle

This 10×10 grid starts with 12 filled squares and 11 = / × clues. It can be solved in 88 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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