Cats & Dogs #274: 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 R8C2 and R8C1 means they are different. R8C2 is a dog, so R8C1 is a cat.
  2. The × clue between R9C8 and R10C8 means they are different. R9C8 is a dog, so R10C8 is a cat.
  3. The = clue between R10C8 and R10C7 means they are the same. R10C8 is a cat, so R10C7 is a cat.
  4. The × clue between R10C7 and R9C7 means they are different. R10C7 is a cat, so R9C7 is a dog.
  5. R8C2 and R8C4 are both dogs with one square between them, so R8C3 must be a cat.
  6. The = clue between R8C3 and R7C3 means they are the same. R8C3 is a cat, so R7C3 is a cat.
  7. R9C7 and R9C8 are both dogs, so R9C6 must be a cat (no three in a row).
  8. R9C7 and R9C8 are both dogs, so R9C9 must be a cat (no three in a row).
  9. R10C7 and R10C8 are both cats, so R10C6 must be a dog (no three in a row).
  10. R10C7 and R10C8 are both cats, so R10C9 must be a dog (no three in a row).
  11. R7C3 and R8C3 are both cats, so R6C3 must be a dog (no three in a row).
  12. R7C3 and R8C3 are both cats, so R9C3 must be a dog (no three in a row).
  13. The × clue between R9C3 and R10C3 means they are different. R9C3 is a dog, so R10C3 is a cat.
  14. R8C6 and R9C6 are both cats, so R7C6 must be a dog (no three in a row).
  15. Imagine R2C3 were a dog: following the rules from there soon forces a contradiction, so R2C3 must be a cat.
  16. Imagine R1C2 were a cat: following the rules from there soon forces a contradiction, so R1C2 must be a dog.
  17. The = clue between R1C2 and R1C3 means they are the same. R1C2 is a dog, so R1C3 is a dog.
  18. R1C2 and R1C3 are both dogs, so R1C1 must be a cat (no three in a row).
  19. R1C2 and R1C3 are both dogs, so R1C4 must be a cat (no three in a row).
  20. R1C2 and R2C2 are both dogs, so R3C2 must be a cat (no three in a row).
  21. R3C2 and R3C4 are both cats with one square between them, so R3C3 must be a dog.
  22. R1C4 and R3C4 are both cats with one square between them, so R2C4 must be a dog.
  23. Imagine R4C3 were a cat: following the rules from there soon forces a contradiction, so R4C3 must be a dog.
  24. The = clue between R4C3 and R4C4 means they are the same. R4C3 is a dog, so R4C4 is a dog.
  25. R4C3 and R4C4 are both dogs, so R4C2 must be a cat (no three in a row).
  26. R4C3 and R4C4 are both dogs, so R4C5 must be a cat (no three in a row).
  27. R3C2 and R4C2 are both cats, so R5C2 must be a dog (no three in a row).
  28. R3C3 and R4C3 are both dogs, so R5C3 must be a cat (no three in a row).
  29. Imagine R5C4 were a dog: following the rules from there soon forces a contradiction, so R5C4 must be a cat.
  30. The = clue between R5C4 and R6C4 means they are the same. R5C4 is a cat, so R6C4 is a cat.
  31. R5C3 and R5C4 are both cats, so R5C5 must be a dog (no three in a row).
  32. The = clue between R5C5 and R5C6 means they are the same. R5C5 is a dog, so R5C6 is a dog.
  33. R5C5 and R5C6 are both dogs, so R5C7 must be a cat (no three in a row).
  34. R5C4 and R6C4 are both cats, so R7C4 must be a dog (no three in a row).
  35. R7C4 and R7C6 are both dogs with one square between them, so R7C5 must be a cat.
  36. R7C4 and R8C4 are both dogs, so R9C4 must be a cat (no three in a row).
  37. R9C4 and R9C6 are both cats with one square between them, so R9C5 must be a dog.
  38. R5C6 and R7C6 are both dogs with one square between them, so R6C6 must be a cat.
  39. R6C4 and R6C6 are both cats with one square between them, so R6C5 must be a dog.
  40. Column 4 already has its 5 cats, so R10C4 must be dogs.
  41. R10C4 and R10C6 are both dogs with one square between them, so R10C5 must be a cat.
  42. Imagine R6C1 were a dog: following the rules from there soon forces a contradiction, so R6C1 must be a cat.
  43. R6C1 and R8C1 are both cats with one square between them, so R7C1 must be a dog.
  44. Imagine R6C2 were a cat: following the rules from there soon forces a contradiction, so R6C2 must be a dog.
  45. The × clue between R6C2 and R7C2 means they are different. R6C2 is a dog, so R7C2 is a cat.
  46. Column 2 already has its 5 dogs, so R9C2 must be cats.
  47. The = clue between R9C2 and R9C1 means they are the same. R9C2 is a cat, so R9C1 is a cat.
  48. R8C1 and R9C1 are both cats, so R10C1 must be a dog (no three in a row).
  49. Row 9 already has its 5 cats, so R9C10 must be dogs.
  50. Column 2 already has its 5 dogs, so R10C2 must be cats.
  51. Row 10 already has its 5 cats, so R10C10 must be dogs.
  52. R9C10 and R10C10 are both dogs, so R8C10 must be a cat (no three in a row).
  53. The × clue between R8C10 and R7C10 means they are different. R8C10 is a cat, so R7C10 is a dog.
  54. Imagine R1C10 were a dog: following the rules from there soon forces a contradiction, so R1C10 must be a cat.
  55. Imagine R2C1 were a cat: following the rules from there soon forces a contradiction, so R2C1 must be a dog.
  56. Imagine R2C5 were a dog: following the rules from there soon forces a contradiction, so R2C5 must be a cat.
  57. R2C5 and R4C5 are both cats with one square between them, so R3C5 must be a dog.
  58. Imagine R1C5 were a dog: following the rules from there soon forces a contradiction, so R1C5 must be a cat.
  59. R1C4 and R1C5 are both cats, so R1C6 must be a dog (no three in a row).
  60. The = clue between R1C6 and R1C7 means they are the same. R1C6 is a dog, so R1C7 is a dog.
  61. R1C6 and R1C7 are both dogs, so R1C8 must be a cat (no three in a row).
  62. R1C8 and R1C10 are both cats with one square between them, so R1C9 must be a dog.
  63. R1C8 and R3C8 are both cats with one square between them, so R2C8 must be a dog.
  64. Column 5 already has its 5 cats, so R8C5 must be dogs.
  65. Imagine R2C6 were a cat: following the rules from there soon forces a contradiction, so R2C6 must be a dog.
  66. The × clue between R2C6 and R2C7 means they are different. R2C6 is a dog, so R2C7 is a cat.
  67. R1C6 and R2C6 are both dogs, so R3C6 must be a cat (no three in a row).
  68. R3C6 and R3C8 are both cats with one square between them, so R3C7 must be a dog.
  69. Row 2 already has its 5 dogs, so R2C9 and R2C10 must be cats.
  70. Column 6 already has its 5 dogs, so R4C6 must be cats.
  71. R4C5 and R4C6 are both cats, so R4C7 must be a dog (no three in a row).
  72. Column 7 already has its 5 dogs, so R7C7 and R8C7 must be cats.
  73. R8C6 and R8C7 are both cats, so R8C8 must be a dog (no three in a row).
  74. R8C8 and R9C8 are both dogs, so R7C8 must be a cat (no three in a row).
  75. R7C7 and R7C8 are both cats, so R7C9 must be a dog (no three in a row).
  76. Row 8 already has its 5 cats, so R8C9 must be dogs.
  77. R7C9 and R8C9 are both dogs, so R6C9 must be a cat (no three in a row).
  78. Imagine R3C1 were a cat: following the rules from there soon forces a contradiction, so R3C1 must be a dog.
  79. R2C1 and R3C1 are both dogs, so R4C1 must be a cat (no three in a row).
  80. R4C1 and R6C1 are both cats with one square between them, so R5C1 must be a dog.
  81. Row 3 already has its 5 dogs, so R3C9 must be cats.
  82. R2C9 and R3C9 are both cats, so R4C9 must be a dog (no three in a row).
  83. R4C7 and R4C9 are both dogs with one square between them, so R4C8 must be a cat.
  84. R3C8 and R4C8 are both cats, so R5C8 must be a dog (no three in a row).
  85. Row 4 already has its 5 cats, so R4C10 must be dogs.
  86. R3C10 and R4C10 are both dogs, so R5C10 must be a cat (no three in a row).
  87. Row 5 already has its 5 dogs, so R5C9 must be cats.
  88. Column 8 already has its 5 cats, so R6C8 must be dogs.
  89. Row 6 already has its 5 dogs, so R6C10 must be cats.

About this puzzle

This 10×10 grid starts with 9 filled squares and 15 = / × 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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