Cats & Dogs #288: 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. R1C8 and R1C10 are both cats with one square between them, so R1C9 must be a dog.
  2. R4C2 and R4C4 are both dogs with one square between them, so R4C3 must be a cat.
  3. Imagine R2C2 were a cat: following the rules from there soon forces a contradiction, so R2C2 must be a dog.
  4. The = clue between R2C2 and R2C3 means they are the same. R2C2 is a dog, so R2C3 is a dog.
  5. The × clue between R2C3 and R3C3 means they are different. R2C3 is a dog, so R3C3 is a cat.
  6. R2C2 and R2C3 are both dogs, so R2C4 must be a cat (no three in a row).
  7. R2C2 and R4C2 are both dogs with one square between them, so R3C2 must be a cat.
  8. R3C2 and R3C3 are both cats, so R3C1 must be a dog (no three in a row).
  9. R3C2 and R3C3 are both cats, so R3C4 must be a dog (no three in a row).
  10. R3C3 and R4C3 are both cats, so R5C3 must be a dog (no three in a row).
  11. R3C4 and R4C4 are both dogs, so R5C4 must be a cat (no three in a row).
  12. R5C4 and R5C5 are both cats, so R5C6 must be a dog (no three in a row).
  13. Imagine R2C9 were a dog: following the rules from there soon forces a contradiction, so R2C9 must be a cat.
  14. The = clue between R2C9 and R3C9 means they are the same. R2C9 is a cat, so R3C9 is a cat.
  15. The = clue between R3C9 and R3C10 means they are the same. R3C9 is a cat, so R3C10 is a cat.
  16. R3C9 and R3C10 are both cats, so R3C8 must be a dog (no three in a row).
  17. R2C9 and R3C9 are both cats, so R4C9 must be a dog (no three in a row).
  18. R1C10 and R3C10 are both cats with one square between them, so R2C10 must be a dog.
  19. Imagine R3C5 were a cat: following the rules from there soon forces a contradiction, so R3C5 must be a dog.
  20. R3C4 and R3C5 are both dogs, so R3C6 must be a cat (no three in a row).
  21. Row 3 already has its 5 cats, so R3C7 must be dogs.
  22. The = clue between R3C7 and R4C7 means they are the same. R3C7 is a dog, so R4C7 is a dog.
  23. R4C7 and R4C9 are both dogs with one square between them, so R4C8 must be a cat.
  24. R3C7 and R4C7 are both dogs, so R2C7 must be a cat (no three in a row).
  25. R2C7 and R2C9 are both cats with one square between them, so R2C8 must be a dog.
  26. R3C7 and R4C7 are both dogs, so R5C7 must be a cat (no three in a row).
  27. R5C7 and R5C9 are both cats with one square between them, so R5C8 must be a dog.
  28. R5C7 and R7C7 are both cats with one square between them, so R6C7 must be a dog.
  29. Imagine R4C1 were a dog: following the rules from there soon forces a contradiction, so R4C1 must be a cat.
  30. Imagine R5C10 were a cat: following the rules from there soon forces a contradiction, so R5C10 must be a dog.
  31. Imagine R6C2 were a dog: following the rules from there soon forces a contradiction, so R6C2 must be a cat.
  32. The = clue between R6C2 and R6C3 means they are the same. R6C2 is a cat, so R6C3 is a cat.
  33. The = clue between R6C2 and R7C2 means they are the same. R6C2 is a cat, so R7C2 is a cat.
  34. The × clue between R6C3 and R7C3 means they are different. R6C3 is a cat, so R7C3 is a dog.
  35. R6C2 and R6C3 are both cats, so R6C1 must be a dog (no three in a row).
  36. R6C2 and R6C3 are both cats, so R6C4 must be a dog (no three in a row).
  37. R6C1 and R7C1 are both dogs, so R5C1 must be a cat (no three in a row).
  38. R6C1 and R7C1 are both dogs, so R8C1 must be a cat (no three in a row).
  39. R6C2 and R7C2 are both cats, so R5C2 must be a dog (no three in a row).
  40. R6C2 and R7C2 are both cats, so R8C2 must be a dog (no three in a row).
  41. The = clue between R8C2 and R8C3 means they are the same. R8C2 is a dog, so R8C3 is a dog.
  42. The × clue between R8C2 and R9C2 means they are different. R8C2 is a dog, so R9C2 is a cat.
  43. R8C2 and R8C3 are both dogs, so R8C4 must be a cat (no three in a row).
  44. R7C3 and R8C3 are both dogs, so R9C3 must be a cat (no three in a row).
  45. R9C2 and R9C3 are both cats, so R9C1 must be a dog (no three in a row).
  46. R9C2 and R9C3 are both cats, so R9C4 must be a dog (no three in a row).
  47. Column 1 already has its 5 dogs, so R1C1 must be cats.
  48. Column 3 already has its 5 cats, so R1C3 must be dogs.
  49. Imagine R7C4 were a dog: following the rules from there soon forces a contradiction, so R7C4 must be a cat.
  50. The × clue between R7C4 and R7C5 means they are different. R7C4 is a cat, so R7C5 is a dog.
  51. Imagine R4C10 were a dog: following the rules from there soon forces a contradiction, so R4C10 must be a cat.
  52. Imagine R8C9 were a dog: following the rules from there soon forces a contradiction, so R8C9 must be a cat.
  53. The × clue between R8C9 and R9C9 means they are different. R8C9 is a cat, so R9C9 is a dog.
  54. The = clue between R9C9 and R9C10 means they are the same. R9C9 is a dog, so R9C10 is a dog.
  55. The × clue between R9C9 and R10C9 means they are different. R9C9 is a dog, so R10C9 is a cat.
  56. R9C9 and R9C10 are both dogs, so R9C8 must be a cat (no three in a row).
  57. Column 9 already has its 5 cats, so R6C9 must be dogs.
  58. R6C7 and R6C9 are both dogs with one square between them, so R6C8 must be a cat.
  59. Column 9 already has its 5 cats, so R7C9 must be dogs.
  60. Imagine R2C5 were a dog: following the rules from there soon forces a contradiction, so R2C5 must be a cat.
  61. R2C4 and R2C5 are both cats, so R2C6 must be a dog (no three in a row).
  62. Imagine R4C5 were a cat: following the rules from there soon forces a contradiction, so R4C5 must be a dog.
  63. R4C4 and R4C5 are both dogs, so R4C6 must be a cat (no three in a row).
  64. Imagine R6C5 were a dog: following the rules from there soon forces a contradiction, so R6C5 must be a cat.
  65. Imagine R6C6 were a dog: following the rules from there soon forces a contradiction, so R6C6 must be a cat.
  66. Row 6 already has its 5 cats, so R6C10 must be dogs.
  67. R5C10 and R6C10 are both dogs, so R7C10 must be a cat (no three in a row).
  68. Imagine R8C5 were a cat: following the rules from there soon forces a contradiction, so R8C5 must be a dog.
  69. Imagine R7C6 were a cat: following the rules from there soon forces a contradiction, so R7C6 must be a dog.
  70. The × clue between R7C6 and R8C6 means they are different. R7C6 is a dog, so R8C6 is a cat.
  71. Row 7 already has its 5 dogs, so R7C8 must be cats.
  72. R6C8 and R7C8 are both cats, so R8C8 must be a dog (no three in a row).
  73. Column 8 already has its 5 cats, so R10C8 must be dogs.
  74. Imagine R8C7 were a cat: following the rules from there soon forces a contradiction, so R8C7 must be a dog.
  75. Row 8 already has its 5 dogs, so R8C10 must be cats.
  76. Column 10 already has its 5 cats, so R10C10 must be dogs.
  77. Imagine R1C4 were a dog: following the rules from there soon forces a contradiction, so R1C4 must be a cat.
  78. Column 4 already has its 5 cats, so R10C4 must be dogs.
  79. Imagine R1C2 were a cat: following the rules from there soon forces a contradiction, so R1C2 must be a dog.
  80. Column 2 already has its 5 dogs, so R10C2 must be cats.
  81. Imagine R1C5 were a cat: following the rules from there soon forces a contradiction, so R1C5 must be a dog.
  82. Column 5 already has its 5 dogs, so R10C5 must be cats.
  83. Imagine R9C6 were a cat: following the rules from there soon forces a contradiction, so R9C6 must be a dog.
  84. The = clue between R9C6 and R10C6 means they are the same. R9C6 is a dog, so R10C6 is a dog.
  85. R10C6 and R10C8 are both dogs with one square between them, so R10C7 must be a cat.
  86. Row 9 already has its 5 dogs, so R9C7 must be cats.
  87. Column 6 already has its 5 dogs, so R1C6 must be cats.
  88. R1C6 and R1C8 are both cats with one square between them, so R1C7 must be a dog.

About this puzzle

This 10×10 grid starts with 12 filled squares and 16 = / × clues. It can be solved in 88 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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