Cats & Dogs #247: 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. The = clue between R6C6 and R6C5 means they are the same. R6C6 is a cat, so R6C5 is a cat.
  2. The = clue between R10C9 and R9C9 means they are the same. R10C9 is a cat, so R9C9 is a cat.
  3. The × clue between R10C9 and R10C8 means they are different. R10C9 is a cat, so R10C8 is a dog.
  4. R6C5 and R6C6 are both cats, so R6C4 must be a dog (no three in a row).
  5. R6C5 and R6C6 are both cats, so R6C7 must be a dog (no three in a row).
  6. The = clue between R6C7 and R5C7 means they are the same. R6C7 is a dog, so R5C7 is a dog.
  7. R10C7 and R10C8 are both dogs, so R10C6 must be a cat (no three in a row).
  8. R6C5 and R7C5 are both cats, so R5C5 must be a dog (no three in a row).
  9. R5C5 and R5C7 are both dogs with one square between them, so R5C6 must be a cat.
  10. R6C5 and R7C5 are both cats, so R8C5 must be a dog (no three in a row).
  11. R5C6 and R6C6 are both cats, so R4C6 must be a dog (no three in a row).
  12. R5C6 and R6C6 are both cats, so R7C6 must be a dog (no three in a row).
  13. R5C7 and R6C7 are both dogs, so R4C7 must be a cat (no three in a row).
  14. R5C7 and R6C7 are both dogs, so R7C7 must be a cat (no three in a row).
  15. The × clue between R7C7 and R7C8 means they are different. R7C7 is a cat, so R7C8 is a dog.
  16. R7C8 and R8C8 are both dogs, so R6C8 must be a cat (no three in a row).
  17. R7C8 and R8C8 are both dogs, so R9C8 must be a cat (no three in a row).
  18. R9C8 and R9C9 are both cats, so R9C7 must be a dog (no three in a row).
  19. R9C8 and R9C9 are both cats, so R9C10 must be a dog (no three in a row).
  20. R9C7 and R10C7 are both dogs, so R8C7 must be a cat (no three in a row).
  21. R9C9 and R10C9 are both cats, so R8C9 must be a dog (no three in a row).
  22. R8C8 and R8C9 are both dogs, so R8C10 must be a cat (no three in a row).
  23. Imagine R1C5 were a cat: following the rules from there soon forces a contradiction, so R1C5 must be a dog.
  24. The = clue between R1C5 and R2C5 means they are the same. R1C5 is a dog, so R2C5 is a dog.
  25. R2C4 and R2C5 are both dogs, so R2C3 must be a cat (no three in a row).
  26. R2C4 and R2C5 are both dogs, so R2C6 must be a cat (no three in a row).
  27. The = clue between R2C6 and R2C7 means they are the same. R2C6 is a cat, so R2C7 is a cat.
  28. R2C6 and R2C7 are both cats, so R2C8 must be a dog (no three in a row).
  29. R1C3 and R2C3 are both cats, so R3C3 must be a dog (no three in a row).
  30. R1C5 and R2C5 are both dogs, so R3C5 must be a cat (no three in a row).
  31. The × clue between R3C5 and R4C5 means they are different. R3C5 is a cat, so R4C5 is a dog.
  32. R4C5 and R4C6 are both dogs, so R4C4 must be a cat (no three in a row).
  33. R2C7 and R4C7 are both cats with one square between them, so R3C7 must be a dog.
  34. Column 5 already has its 5 dogs, so R9C5 and R10C5 must be cats.
  35. R10C5 and R10C6 are both cats, so R10C4 must be a dog (no three in a row).
  36. Column 7 already has its 5 dogs, so R1C7 must be cats.
  37. Imagine R1C2 were a cat: following the rules from there soon forces a contradiction, so R1C2 must be a dog.
  38. Imagine R1C4 were a dog: following the rules from there soon forces a contradiction, so R1C4 must be a cat.
  39. Imagine R1C6 were a cat: following the rules from there soon forces a contradiction, so R1C6 must be a dog.
  40. Imagine R1C8 were a dog: following the rules from there soon forces a contradiction, so R1C8 must be a cat.
  41. R1C7 and R1C8 are both cats, so R1C9 must be a dog (no three in a row).
  42. Imagine R3C6 were a cat: following the rules from there soon forces a contradiction, so R3C6 must be a dog.
  43. R3C6 and R3C7 are both dogs, so R3C8 must be a cat (no three in a row).
  44. Imagine R8C4 were a dog: following the rules from there soon forces a contradiction, so R8C4 must be a cat.
  45. Imagine R2C2 were a cat: following the rules from there soon forces a contradiction, so R2C2 must be a dog.
  46. The × clue between R2C2 and R3C2 means they are different. R2C2 is a dog, so R3C2 is a cat.
  47. Imagine R3C1 were a dog: following the rules from there soon forces a contradiction, so R3C1 must be a cat.
  48. Imagine R3C4 were a cat: following the rules from there soon forces a contradiction, so R3C4 must be a dog.
  49. Row 3 already has its 5 dogs, so R3C9 must be cats.
  50. Imagine R5C4 were a dog: following the rules from there soon forces a contradiction, so R5C4 must be a cat.
  51. Imagine R7C2 were a dog: following the rules from there soon forces a contradiction, so R7C2 must be a cat.
  52. The × clue between R7C2 and R8C2 means they are different. R7C2 is a cat, so R8C2 is a dog.
  53. The × clue between R8C2 and R8C3 means they are different. R8C2 is a dog, so R8C3 is a cat.
  54. The × clue between R8C3 and R9C3 means they are different. R8C3 is a cat, so R9C3 is a dog.
  55. R9C2 and R9C3 are both dogs, so R9C1 must be a cat (no three in a row).
  56. The × clue between R9C1 and R8C1 means they are different. R9C1 is a cat, so R8C1 is a dog.
  57. R9C2 and R9C3 are both dogs, so R9C4 must be a cat (no three in a row).
  58. R9C4 and R9C5 are both cats, so R9C6 must be a dog (no three in a row).
  59. R8C2 and R9C2 are both dogs, so R10C2 must be a cat (no three in a row).
  60. R8C4 and R9C4 are both cats, so R7C4 must be a dog (no three in a row).
  61. The × clue between R7C4 and R7C3 means they are different. R7C4 is a dog, so R7C3 is a cat.
  62. R7C2 and R7C3 are both cats, so R7C1 must be a dog (no three in a row).
  63. R7C1 and R8C1 are both dogs, so R6C1 must be a cat (no three in a row).
  64. R7C3 and R8C3 are both cats, so R6C3 must be a dog (no three in a row).
  65. The × clue between R6C3 and R6C2 means they are different. R6C3 is a dog, so R6C2 is a cat.
  66. R6C2 and R7C2 are both cats, so R5C2 must be a dog (no three in a row).
  67. The = clue between R5C2 and R5C1 means they are the same. R5C2 is a dog, so R5C1 is a dog.
  68. R5C1 and R5C2 are both dogs, so R5C3 must be a cat (no three in a row).
  69. R7C6 and R9C6 are both dogs with one square between them, so R8C6 must be a cat.
  70. Row 6 already has its 5 cats, so R6C9 must be dogs.
  71. R4C9 and R6C9 are both dogs with one square between them, so R5C9 must be a cat.
  72. R6C9 and R8C9 are both dogs with one square between them, so R7C9 must be a cat.
  73. Row 6 already has its 5 cats, so R6C10 must be dogs.
  74. Row 7 already has its 5 cats, so R7C10 must be dogs.
  75. R6C10 and R7C10 are both dogs, so R5C10 must be a cat (no three in a row).
  76. R5C9 and R5C10 are both cats, so R5C8 must be a dog (no three in a row).
  77. Column 2 already has its 5 dogs, so R4C2 must be cats.
  78. R4C2 and R4C4 are both cats with one square between them, so R4C3 must be a dog.
  79. Column 3 already has its 5 cats, so R10C3 must be dogs.
  80. Column 8 already has its 5 dogs, so R4C8 must be cats.
  81. Column 9 already has its 5 cats, so R2C9 must be dogs.
  82. R2C8 and R2C9 are both dogs, so R2C10 must be a cat (no three in a row).
  83. Row 2 already has its 5 dogs, so R2C1 must be cats.
  84. R2C1 and R3C1 are both cats, so R1C1 must be a dog (no three in a row).
  85. R2C1 and R3C1 are both cats, so R4C1 must be a dog (no three in a row).
  86. Row 1 already has its 5 dogs, so R1C10 must be cats.
  87. Row 4 already has its 5 dogs, so R4C10 must be cats.
  88. Column 1 already has its 5 dogs, so R10C1 must be cats.
  89. Row 10 already has its 5 cats, so R10C10 must be dogs.

About this puzzle

This 10×10 grid starts with 10 filled squares and 16 = / × clues. It can be solved in 89 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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