Cats & Dogs #214: 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 R8C1 and R7C1 means they are the same. R8C1 is a cat, so R7C1 is a cat.
  2. R2C4 and R2C5 are both cats, so R2C3 must be a dog (no three in a row).
  3. R2C4 and R2C5 are both cats, so R2C6 must be a dog (no three in a row).
  4. R7C1 and R7C2 are both cats, so R7C3 must be a dog (no three in a row).
  5. R7C1 and R8C1 are both cats, so R6C1 must be a dog (no three in a row).
  6. R7C1 and R8C1 are both cats, so R9C1 must be a dog (no three in a row).
  7. R2C5 and R3C5 are both cats, so R1C5 must be a dog (no three in a row).
  8. R2C5 and R3C5 are both cats, so R4C5 must be a dog (no three in a row).
  9. R4C5 and R4C6 are both dogs, so R4C4 must be a cat (no three in a row).
  10. R4C5 and R4C6 are both dogs, so R4C7 must be a cat (no three in a row).
  11. R2C4 and R4C4 are both cats with one square between them, so R3C4 must be a dog.
  12. R7C5 and R8C5 are both cats, so R6C5 must be a dog (no three in a row).
  13. The = clue between R6C5 and R6C6 means they are the same. R6C5 is a dog, so R6C6 is a dog.
  14. R6C5 and R6C6 are both dogs, so R6C4 must be a cat (no three in a row).
  15. R6C5 and R6C6 are both dogs, so R6C7 must be a cat (no three in a row).
  16. R4C4 and R6C4 are both cats with one square between them, so R5C4 must be a dog.
  17. R4C5 and R6C5 are both dogs with one square between them, so R5C5 must be a cat.
  18. R7C5 and R8C5 are both cats, so R9C5 must be a dog (no three in a row).
  19. R2C6 and R4C6 are both dogs with one square between them, so R3C6 must be a cat.
  20. R3C5 and R3C6 are both cats, so R3C7 must be a dog (no three in a row).
  21. R4C6 and R6C6 are both dogs with one square between them, so R5C6 must be a cat.
  22. R5C5 and R5C6 are both cats, so R5C7 must be a dog (no three in a row).
  23. Column 5 already has its 5 cats, so R10C5 must be dogs.
  24. Imagine R1C1 were a dog: following the rules from there soon forces a contradiction, so R1C1 must be a cat.
  25. The = clue between R1C1 and R2C1 means they are the same. R1C1 is a cat, so R2C1 is a cat.
  26. R1C1 and R2C1 are both cats, so R3C1 must be a dog (no three in a row).
  27. Column 1 already has its 5 cats, so R5C1 must be dogs.
  28. Imagine R6C9 were a dog: following the rules from there soon forces a contradiction, so R6C9 must be a cat.
  29. Imagine R6C10 were a dog: following the rules from there soon forces a contradiction, so R6C10 must be a cat.
  30. Imagine R7C7 were a cat: following the rules from there soon forces a contradiction, so R7C7 must be a dog.
  31. The = clue between R7C7 and R8C7 means they are the same. R7C7 is a dog, so R8C7 is a dog.
  32. R7C7 and R8C7 are both dogs, so R9C7 must be a cat (no three in a row).
  33. Imagine R8C8 were a dog: following the rules from there soon forces a contradiction, so R8C8 must be a cat.
  34. Imagine R8C9 were a cat: following the rules from there soon forces a contradiction, so R8C9 must be a dog.
  35. The = clue between R8C9 and R8C10 means they are the same. R8C9 is a dog, so R8C10 is a dog.
  36. Imagine R8C3 were a dog: following the rules from there soon forces a contradiction, so R8C3 must be a cat.
  37. R8C3 and R8C5 are both cats with one square between them, so R8C4 must be a dog.
  38. Row 8 already has its 5 dogs, so R8C6 must be cats.
  39. Imagine R9C2 were a dog: following the rules from there soon forces a contradiction, so R9C2 must be a cat.
  40. Imagine R9C3 were a cat: following the rules from there soon forces a contradiction, so R9C3 must be a dog.
  41. R9C3 and R9C5 are both dogs with one square between them, so R9C4 must be a cat.
  42. The × clue between R9C4 and R10C4 means they are different. R9C4 is a cat, so R10C4 is a dog.
  43. R10C4 and R10C5 are both dogs, so R10C3 must be a cat (no three in a row).
  44. R10C4 and R10C5 are both dogs, so R10C6 must be a cat (no three in a row).
  45. R10C6 and R10C7 are both cats, so R10C8 must be a dog (no three in a row).
  46. R8C6 and R10C6 are both cats with one square between them, so R9C6 must be a dog.
  47. Imagine R3C9 were a dog: following the rules from there soon forces a contradiction, so R3C9 must be a cat.
  48. Imagine R3C8 were a cat: following the rules from there soon forces a contradiction, so R3C8 must be a dog.
  49. The = clue between R3C8 and R4C8 means they are the same. R3C8 is a dog, so R4C8 is a dog.
  50. R3C8 and R4C8 are both dogs, so R2C8 must be a cat (no three in a row).
  51. R3C8 and R4C8 are both dogs, so R5C8 must be a cat (no three in a row).
  52. Imagine R1C8 were a dog: following the rules from there soon forces a contradiction, so R1C8 must be a cat.
  53. Imagine R1C9 were a cat: following the rules from there soon forces a contradiction, so R1C9 must be a dog.
  54. Imagine R9C10 were a dog: following the rules from there soon forces a contradiction, so R9C10 must be a cat.
  55. Imagine R10C9 were a dog: following the rules from there soon forces a contradiction, so R10C9 must be a cat.
  56. The = clue between R10C9 and R10C10 means they are the same. R10C9 is a cat, so R10C10 is a cat.
  57. Row 10 already has its 5 cats, so R10C2 must be dogs.
  58. Imagine R1C2 were a dog: following the rules from there soon forces a contradiction, so R1C2 must be a cat.
  59. The = clue between R1C2 and R2C2 means they are the same. R1C2 is a cat, so R2C2 is a cat.
  60. R1C1 and R1C2 are both cats, so R1C3 must be a dog (no three in a row).
  61. R1C3 and R1C5 are both dogs with one square between them, so R1C4 must be a cat.
  62. R1C2 and R2C2 are both cats, so R3C2 must be a dog (no three in a row).
  63. The × clue between R3C2 and R4C2 means they are different. R3C2 is a dog, so R4C2 is a cat.
  64. R3C1 and R3C2 are both dogs, so R3C3 must be a cat (no three in a row).
  65. R4C1 and R4C2 are both cats, so R4C3 must be a dog (no three in a row).
  66. Row 2 already has its 5 cats, so R2C7 must be dogs.
  67. R2C7 and R3C7 are both dogs, so R1C7 must be a cat (no three in a row).
  68. R1C7 and R1C8 are both cats, so R1C6 must be a dog (no three in a row).
  69. Row 1 already has its 5 cats, so R1C10 must be dogs.
  70. Row 2 already has its 5 cats, so R2C9 and R2C10 must be dogs.
  71. R1C10 and R2C10 are both dogs, so R3C10 must be a cat (no three in a row).
  72. Column 2 already has its 5 cats, so R5C2 must be dogs.
  73. R5C1 and R5C2 are both dogs, so R5C3 must be a cat (no three in a row).
  74. Row 5 already has its 5 dogs, so R5C9 must be cats.
  75. R3C9 and R5C9 are both cats with one square between them, so R4C9 must be a dog.
  76. R4C8 and R4C9 are both dogs, so R4C10 must be a cat (no three in a row).
  77. R5C9 and R6C9 are both cats, so R7C9 must be a dog (no three in a row).
  78. R7C7 and R7C9 are both dogs with one square between them, so R7C8 must be a cat.
  79. R7C8 and R8C8 are both cats, so R9C8 must be a dog (no three in a row).
  80. R7C9 and R8C9 are both dogs, so R9C9 must be a cat (no three in a row).
  81. Column 2 already has its 5 cats, so R6C2 must be dogs.
  82. R6C1 and R6C2 are both dogs, so R6C3 must be a cat (no three in a row).
  83. Column 4 already has its 5 cats, so R7C4 must be dogs.
  84. Column 6 already has its 5 dogs, so R7C6 must be cats.
  85. Row 7 already has its 5 cats, so R7C10 must be dogs.

About this puzzle

This 10×10 grid starts with 14 filled squares and 10 = / × clues. It can be solved in 85 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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