Cats & Dogs #259: 10x10 Grid Puzzle (Hard)

hard

Tap a square: 🐱 cat → 🐶 dog → clear

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🐱 5 cats and 🐶 5 dogs in every row and column = same   × different

A 10x10 logic grid: 5 cats and 5 dogs in every row and column, no three of a kind in a row, and a few = and × clues to point the way.

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

About this puzzle

This 10×10 grid starts with 16 filled squares and 12 = / × clues. It can be solved in 84 steps using a "what if" trial of one square on top of the basic rules.

Count as you go. Once a row or column has all of one animal, every remaining empty square in it must be the other.

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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