Cats & Dogs #226: 10x10 Grid Puzzle (Hard)

hard

Tap a square: 🐱 cat → 🐶 dog → clear

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

About this puzzle

This 10×10 grid starts with 9 filled squares and 20 = / × clues. It can be solved in 90 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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