Cats & Dogs #285: 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 R3C8 and R3C7 means they are the same. R3C8 is a dog, so R3C7 is a dog.
  2. The × clue between R10C2 and R9C2 means they are different. R10C2 is a cat, so R9C2 is a dog.
  3. The × clue between R9C2 and R8C2 means they are different. R9C2 is a dog, so R8C2 is a cat.
  4. The × clue between R8C2 and R8C1 means they are different. R8C2 is a cat, so R8C1 is a dog.
  5. The × clue between R9C9 and R10C9 means they are different. R9C9 is a cat, so R10C9 is a dog.
  6. R3C7 and R3C8 are both dogs, so R3C6 must be a cat (no three in a row).
  7. R3C4 and R3C6 are both cats with one square between them, so R3C5 must be a dog.
  8. R3C7 and R3C8 are both dogs, so R3C9 must be a cat (no three in a row).
  9. R5C1 and R7C1 are both dogs with one square between them, so R6C1 must be a cat.
  10. R7C1 and R8C1 are both dogs, so R9C1 must be a cat (no three in a row).
  11. R2C4 and R3C4 are both cats, so R1C4 must be a dog (no three in a row).
  12. R2C4 and R3C4 are both cats, so R4C4 must be a dog (no three in a row).
  13. R3C9 and R5C9 are both cats with one square between them, so R4C9 must be a dog.
  14. Imagine R1C5 were a dog: following the rules from there soon forces a contradiction, so R1C5 must be a cat.
  15. The = clue between R1C5 and R1C6 means they are the same. R1C5 is a cat, so R1C6 is a cat.
  16. R1C5 and R1C6 are both cats, so R1C7 must be a dog (no three in a row).
  17. R1C7 and R1C9 are both dogs with one square between them, so R1C8 must be a cat.
  18. R1C6 and R3C6 are both cats with one square between them, so R2C6 must be a dog.
  19. R1C7 and R3C7 are both dogs with one square between them, so R2C7 must be a cat.
  20. Imagine R3C10 were a cat: following the rules from there soon forces a contradiction, so R3C10 must be a dog.
  21. Imagine R4C8 were a dog: following the rules from there soon forces a contradiction, so R4C8 must be a cat.
  22. Imagine R4C5 were a dog: following the rules from there soon forces a contradiction, so R4C5 must be a cat.
  23. Imagine R5C7 were a dog: following the rules from there soon forces a contradiction, so R5C7 must be a cat.
  24. R5C7 and R5C9 are both cats with one square between them, so R5C8 must be a dog.
  25. The = clue between R5C8 and R6C8 means they are the same. R5C8 is a dog, so R6C8 is a dog.
  26. R5C8 and R6C8 are both dogs, so R7C8 must be a cat (no three in a row).
  27. R7C8 and R7C10 are both cats with one square between them, so R7C9 must be a dog.
  28. Imagine R3C2 were a dog: following the rules from there soon forces a contradiction, so R3C2 must be a cat.
  29. R3C1 and R3C2 are both cats, so R3C3 must be a dog (no three in a row).
  30. The = clue between R3C3 and R4C3 means they are the same. R3C3 is a dog, so R4C3 is a dog.
  31. R4C3 and R4C4 are both dogs, so R4C2 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. The × clue between R2C2 and R2C1 means they are different. R2C2 is a dog, so R2C1 is a cat.
  34. R2C1 and R3C1 are both cats, so R1C1 must be a dog (no three in a row).
  35. R2C1 and R3C1 are both cats, so R4C1 must be a dog (no three in a row).
  36. R3C2 and R4C2 are both cats, so R5C2 must be a dog (no three in a row).
  37. The = clue between R5C2 and R6C2 means they are the same. R5C2 is a dog, so R6C2 is a dog.
  38. R5C1 and R5C2 are both dogs, so R5C3 must be a cat (no three in a row).
  39. R5C3 and R5C4 are both cats, so R5C5 must be a dog (no three in a row).
  40. R5C2 and R6C2 are both dogs, so R7C2 must be a cat (no three in a row).
  41. R3C3 and R4C3 are both dogs, so R2C3 must be a cat (no three in a row).
  42. R2C3 and R2C4 are both cats, so R2C5 must be a dog (no three in a row).
  43. Row 5 already has its 5 dogs, so R5C10 must be cats.
  44. R5C10 and R7C10 are both cats with one square between them, so R6C10 must be a dog.
  45. R6C8 and R6C10 are both dogs with one square between them, so R6C9 must be a cat.
  46. Column 1 already has its 5 dogs, so R10C1 must be cats.
  47. R10C1 and R10C2 are both cats, so R10C3 must be a dog (no three in a row).
  48. R8C3 and R10C3 are both dogs with one square between them, so R9C3 must be a cat.
  49. Column 2 already has its 5 cats, so R1C2 must be dogs.
  50. R1C1 and R1C2 are both dogs, so R1C3 must be a cat (no three in a row).
  51. Row 1 already has its 5 dogs, so R1C10 must be cats.
  52. Imagine R4C10 were a dog: following the rules from there soon forces a contradiction, so R4C10 must be a cat.
  53. Imagine R2C10 were a cat: following the rules from there soon forces a contradiction, so R2C10 must be a dog.
  54. Imagine R6C5 were a dog: following the rules from there soon forces a contradiction, so R6C5 must be a cat.
  55. Imagine R7C7 were a cat: following the rules from there soon forces a contradiction, so R7C7 must be a dog.
  56. Imagine R2C8 were a cat: following the rules from there soon forces a contradiction, so R2C8 must be a dog.
  57. R2C8 and R2C10 are both dogs with one square between them, so R2C9 must be a cat.
  58. Column 9 already has its 5 cats, so R8C9 must be dogs.
  59. The = clue between R8C9 and R8C8 means they are the same. R8C9 is a dog, so R8C8 is a dog.
  60. R8C8 and R8C9 are both dogs, so R8C7 must be a cat (no three in a row).
  61. R8C8 and R8C9 are both dogs, so R8C10 must be a cat (no three in a row).
  62. R7C10 and R8C10 are both cats, so R9C10 must be a dog (no three in a row).
  63. Column 8 already has its 5 dogs, so R9C8 must be cats.
  64. R9C8 and R9C9 are both cats, so R9C7 must be a dog (no three in a row).
  65. Column 8 already has its 5 dogs, so R10C8 must be cats.
  66. Column 10 already has its 5 cats, so R10C10 must be dogs.
  67. Imagine R4C6 were a cat: following the rules from there soon forces a contradiction, so R4C6 must be a dog.
  68. R4C6 and R5C6 are both dogs, so R6C6 must be a cat (no three in a row).
  69. R6C5 and R6C6 are both cats, so R6C4 must be a dog (no three in a row).
  70. R6C2 and R6C4 are both dogs with one square between them, so R6C3 must be a cat.
  71. R6C5 and R6C6 are both cats, so R6C7 must be a dog (no three in a row).
  72. R5C3 and R6C3 are both cats, so R7C3 must be a dog (no three in a row).
  73. The × clue between R7C3 and R7C4 means they are different. R7C3 is a dog, so R7C4 is a cat.
  74. The = clue between R7C4 and R7C5 means they are the same. R7C4 is a cat, so R7C5 is a cat.
  75. The = clue between R7C4 and R8C4 means they are the same. R7C4 is a cat, so R8C4 is a cat.
  76. R7C4 and R7C5 are both cats, so R7C6 must be a dog (no three in a row).
  77. The × clue between R7C6 and R8C6 means they are different. R7C6 is a dog, so R8C6 is a cat.
  78. R8C4 and R8C6 are both cats with one square between them, so R8C5 must be a dog.
  79. R7C4 and R8C4 are both cats, so R9C4 must be a dog (no three in a row).
  80. Row 4 already has its 5 dogs, so R4C7 must be cats.
  81. Column 4 already has its 5 cats, so R10C4 must be dogs.
  82. R10C3 and R10C4 are both dogs, so R10C5 must be a cat (no three in a row).
  83. Column 5 already has its 5 cats, so R9C5 must be dogs.
  84. R9C4 and R9C5 are both dogs, so R9C6 must be a cat (no three in a row).
  85. The × clue between R9C6 and R10C6 means they are different. R9C6 is a cat, so R10C6 is a dog.
  86. Row 10 already has its 5 dogs, so R10C7 must be cats.

About this puzzle

This 10×10 grid starts with 14 filled squares and 16 = / × clues. It can be solved in 86 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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