Cats & Dogs #204: 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

Can you finish the grid? Cats and dogs must balance in every line, no animal may appear three times in a row, and = / × signs tell you whether two neighbors match.

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

About this puzzle

This 10×10 grid starts with 13 filled squares and 14 = / × clues. It can be solved in 85 steps using a "what if" trial of one square on top of the basic rules.

Start with the clues and the squares already filled in. An = or × next to a known animal gives you its neighbor immediately.

Stuck? Open the step-by-step solution below -- each step names the squares involved, so you can use it as a hint and finish the puzzle yourself.

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