Cats & Dogs #230: 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

Use pure logic to place every cat and dog. Each row and column holds 5 of each animal, three in a row is never allowed, and the clues between squares settle the rest.

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

About this puzzle

This 10×10 grid starts with 7 filled squares and 14 = / × clues. It can be solved in 91 steps using a "what if" trial of one square on top of the basic rules.

Whenever two of the same animal sit side by side, the squares on both ends must be the other animal. Look for these pairs first.

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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