Cats & Dogs #223: 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 R7C3 and R7C4 means they are different. R7C3 is a cat, so R7C4 is a dog.
  2. The = clue between R7C4 and R6C4 means they are the same. R7C4 is a dog, so R6C4 is a dog.
  3. The × clue between R7C7 and R7C8 means they are different. R7C7 is a dog, so R7C8 is a cat.
  4. The = clue between R10C3 and R10C2 means they are the same. R10C3 is a cat, so R10C2 is a cat.
  5. R10C2 and R10C3 are both cats, so R10C1 must be a dog (no three in a row).
  6. R10C2 and R10C3 are both cats, so R10C4 must be a dog (no three in a row).
  7. R6C4 and R7C4 are both dogs, so R5C4 must be a cat (no three in a row).
  8. R6C4 and R7C4 are both dogs, so R8C4 must be a cat (no three in a row).
  9. Imagine R3C2 were a cat: following the rules from there soon forces a contradiction, so R3C2 must be a dog.
  10. Imagine R3C3 were a dog: following the rules from there soon forces a contradiction, so R3C3 must be a cat.
  11. Imagine R3C4 were a cat: following the rules from there soon forces a contradiction, so R3C4 must be a dog.
  12. The = clue between R3C4 and R4C4 means they are the same. R3C4 is a dog, so R4C4 is a dog.
  13. R3C4 and R4C4 are both dogs, so R2C4 must be a cat (no three in a row).
  14. Column 4 already has its 5 dogs, so R1C4 must be cats.
  15. R1C2 and R1C4 are both cats with one square between them, so R1C3 must be a dog.
  16. Column 4 already has its 5 dogs, so R9C4 must be cats.
  17. R9C4 and R9C6 are both cats with one square between them, so R9C5 must be a dog.
  18. Imagine R4C3 were a cat: following the rules from there soon forces a contradiction, so R4C3 must be a dog.
  19. R4C3 and R4C4 are both dogs, so R4C5 must be a cat (no three in a row).
  20. Imagine R7C9 were a cat: following the rules from there soon forces a contradiction, so R7C9 must be a dog.
  21. The = clue between R7C9 and R7C10 means they are the same. R7C9 is a dog, so R7C10 is a dog.
  22. Imagine R7C5 were a dog: following the rules from there soon forces a contradiction, so R7C5 must be a cat.
  23. Imagine R7C6 were a dog: following the rules from there soon forces a contradiction, so R7C6 must be a cat.
  24. R7C6 and R9C6 are both cats with one square between them, so R8C6 must be a dog.
  25. Imagine R8C7 were a dog: following the rules from there soon forces a contradiction, so R8C7 must be a cat.
  26. Imagine R8C8 were a cat: following the rules from there soon forces a contradiction, so R8C8 must be a dog.
  27. The × clue between R8C8 and R8C9 means they are different. R8C8 is a dog, so R8C9 is a cat.
  28. The = clue between R8C8 and R9C8 means they are the same. R8C8 is a dog, so R9C8 is a dog.
  29. R8C8 and R9C8 are both dogs, so R10C8 must be a cat (no three in a row).
  30. R10C8 and R10C10 are both cats with one square between them, so R10C9 must be a dog.
  31. The × clue between R10C9 and R9C9 means they are different. R10C9 is a dog, so R9C9 is a cat.
  32. The × clue between R9C9 and R9C10 means they are different. R9C9 is a cat, so R9C10 is a dog.
  33. R7C10 and R9C10 are both dogs with one square between them, so R8C10 must be a cat.
  34. Imagine R8C1 were a cat: following the rules from there soon forces a contradiction, so R8C1 must be a dog.
  35. R8C1 and R10C1 are both dogs with one square between them, so R9C1 must be a cat.
  36. Imagine R8C5 were a cat: following the rules from there soon forces a contradiction, so R8C5 must be a dog.
  37. R8C5 and R9C5 are both dogs, so R10C5 must be a cat (no three in a row).
  38. Row 10 already has its 5 cats, so R10C6 and R10C7 must be dogs.
  39. Imagine R9C7 were a cat: following the rules from there soon forces a contradiction, so R9C7 must be a dog.
  40. Imagine R2C7 were a dog: following the rules from there soon forces a contradiction, so R2C7 must be a cat.
  41. The = clue between R2C7 and R3C7 means they are the same. R2C7 is a cat, so R3C7 is a cat.
  42. R2C7 and R3C7 are both cats, so R1C7 must be a dog (no three in a row).
  43. R1C6 and R1C7 are both dogs, so R1C5 must be a cat (no three in a row).
  44. R1C6 and R1C7 are both dogs, so R1C8 must be a cat (no three in a row).
  45. R2C7 and R3C7 are both cats, so R4C7 must be a dog (no three in a row).
  46. Column 7 already has its 5 dogs, so R5C7 must be cats.
  47. The = clue between R5C7 and R5C8 means they are the same. R5C7 is a cat, so R5C8 is a cat.
  48. R5C7 and R5C8 are both cats, so R5C6 must be a dog (no three in a row).
  49. R5C7 and R5C8 are both cats, so R5C9 must be a dog (no three in a row).
  50. R5C8 and R7C8 are both cats with one square between them, so R6C8 must be a dog.
  51. R5C9 and R7C9 are both dogs with one square between them, so R6C9 must be a cat.
  52. Column 7 already has its 5 dogs, so R6C7 must be cats.
  53. Imagine R1C9 were a cat: following the rules from there soon forces a contradiction, so R1C9 must be a dog.
  54. R1C9 and R2C9 are both dogs, so R3C9 must be a cat (no three in a row).
  55. R3C7 and R3C9 are both cats with one square between them, so R3C8 must be a dog.
  56. Column 9 already has its 5 dogs, so R4C9 must be cats.
  57. Imagine R3C5 were a cat: following the rules from there soon forces a contradiction, so R3C5 must be a dog.
  58. R3C4 and R3C5 are both dogs, so R3C6 must be a cat (no three in a row).
  59. Imagine R2C6 were a cat: following the rules from there soon forces a contradiction, so R2C6 must be a dog.
  60. Column 6 already has its 5 dogs, so R4C6 and R6C6 must be cats.
  61. R6C6 and R6C7 are both cats, so R6C5 must be a dog (no three in a row).
  62. R6C4 and R6C5 are both dogs, so R6C3 must be a cat (no three in a row).
  63. R6C3 and R7C3 are both cats, so R5C3 must be a dog (no three in a row).
  64. R5C1 and R5C3 are both dogs with one square between them, so R5C2 must be a cat.
  65. R4C2 and R5C2 are both cats, so R6C2 must be a dog (no three in a row).
  66. R6C3 and R7C3 are both cats, so R8C3 must be a dog (no three in a row).
  67. R8C1 and R8C3 are both dogs with one square between them, so R8C2 must be a cat.
  68. The × clue between R8C2 and R9C2 means they are different. R8C2 is a cat, so R9C2 is a dog.
  69. Row 9 already has its 5 dogs, so R9C3 must be cats.
  70. Column 2 already has its 5 cats, so R2C2 must be dogs.
  71. R2C2 and R2C3 are both dogs, so R2C1 must be a cat (no three in a row).
  72. The × clue between R2C1 and R3C1 means they are different. R2C1 is a cat, so R3C1 is a dog.
  73. R3C1 and R5C1 are both dogs with one square between them, so R4C1 must be a cat.
  74. Row 3 already has its 5 dogs, so R3C10 must be cats.
  75. Row 4 already has its 5 cats, so R4C8 must be dogs.
  76. R3C8 and R4C8 are both dogs, so R2C8 must be a cat (no three in a row).
  77. Row 4 already has its 5 cats, so R4C10 must be dogs.
  78. Column 2 already has its 5 cats, so R7C2 must be dogs.
  79. Row 7 already has its 5 dogs, so R7C1 must be cats.
  80. Imagine R1C1 were a dog: following the rules from there soon forces a contradiction, so R1C1 must be a cat.
  81. Row 1 already has its 5 cats, so R1C10 must be dogs.
  82. The = clue between R1C10 and R2C10 means they are the same. R1C10 is a dog, so R2C10 is a dog.
  83. Row 2 already has its 5 dogs, so R2C5 must be cats.
  84. Column 1 already has its 5 cats, so R6C1 must be dogs.
  85. Row 6 already has its 5 dogs, so R6C10 must be cats.
  86. Column 5 already has its 5 cats, so R5C5 must be dogs.
  87. Row 5 already has its 5 dogs, so R5C10 must be cats.

About this puzzle

This 10×10 grid starts with 11 filled squares and 15 = / × clues. It can be solved in 87 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.

More hard puzzles