Cats & Dogs #224: 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. R1C2 and R3C2 are both cats with one square between them, so R2C2 must be a dog.
  2. The = clue between R2C2 and R2C1 means they are the same. R2C2 is a dog, so R2C1 is a dog.
  3. The = clue between R2C1 and R1C1 means they are the same. R2C1 is a dog, so R1C1 is a dog.
  4. R2C1 and R2C2 are both dogs, so R2C3 must be a cat (no three in a row).
  5. R1C1 and R2C1 are both dogs, so R3C1 must be a cat (no three in a row).
  6. R3C1 and R3C2 are both cats, so R3C3 must be a dog (no three in a row).
  7. The × clue between R3C3 and R3C4 means they are different. R3C3 is a dog, so R3C4 is a cat.
  8. Imagine R3C8 were a cat: following the rules from there soon forces a contradiction, so R3C8 must be a dog.
  9. The = clue between R3C8 and R4C8 means they are the same. R3C8 is a dog, so R4C8 is a dog.
  10. R3C8 and R4C8 are both dogs, so R2C8 must be a cat (no three in a row).
  11. R3C8 and R4C8 are both dogs, so R5C8 must be a cat (no three in a row).
  12. The = clue between R5C8 and R5C7 means they are the same. R5C8 is a cat, so R5C7 is a cat.
  13. R5C7 and R5C8 are both cats, so R5C6 must be a dog (no three in a row).
  14. The = clue between R5C6 and R6C6 means they are the same. R5C6 is a dog, so R6C6 is a dog.
  15. R5C7 and R5C8 are both cats, so R5C9 must be a dog (no three in a row).
  16. R5C6 and R6C6 are both dogs, so R4C6 must be a cat (no three in a row).
  17. Imagine R2C6 were a cat: following the rules from there soon forces a contradiction, so R2C6 must be a dog.
  18. Imagine R2C7 were a dog: following the rules from there soon forces a contradiction, so R2C7 must be a cat.
  19. R2C7 and R2C8 are both cats, so R2C9 must be a dog (no three in a row).
  20. Imagine R1C10 were a cat: following the rules from there soon forces a contradiction, so R1C10 must be a dog.
  21. The × clue between R1C10 and R2C10 means they are different. R1C10 is a dog, so R2C10 is a cat.
  22. Imagine R3C5 were a cat: following the rules from there soon forces a contradiction, so R3C5 must be a dog.
  23. The × clue between R3C5 and R3C6 means they are different. R3C5 is a dog, so R3C6 is a cat.
  24. Imagine R3C7 were a cat: following the rules from there soon forces a contradiction, so R3C7 must be a dog.
  25. R3C7 and R3C8 are both dogs, so R3C9 must be a cat (no three in a row).
  26. Row 3 already has its 5 cats, so R3C10 must be dogs.
  27. Imagine R4C3 were a dog: following the rules from there soon forces a contradiction, so R4C3 must be a cat.
  28. The = clue between R4C3 and R5C3 means they are the same. R4C3 is a cat, so R5C3 is a cat.
  29. R4C3 and R5C3 are both cats, so R6C3 must be a dog (no three in a row).
  30. The × clue between R6C3 and R6C4 means they are different. R6C3 is a dog, so R6C4 is a cat.
  31. Imagine R4C9 were a dog: following the rules from there soon forces a contradiction, so R4C9 must be a cat.
  32. Imagine R9C9 were a dog: following the rules from there soon forces a contradiction, so R9C9 must be a cat.
  33. The = clue between R9C9 and R10C9 means they are the same. R9C9 is a cat, so R10C9 is a cat.
  34. Imagine R1C7 were a cat: following the rules from there soon forces a contradiction, so R1C7 must be a dog.
  35. The × clue between R1C7 and R1C8 means they are different. R1C7 is a dog, so R1C8 is a cat.
  36. Imagine R1C5 were a dog: following the rules from there soon forces a contradiction, so R1C5 must be a cat.
  37. Imagine R1C4 were a cat: following the rules from there soon forces a contradiction, so R1C4 must be a dog.
  38. The × clue between R1C4 and R2C4 means they are different. R1C4 is a dog, so R2C4 is a cat.
  39. R2C3 and R2C4 are both cats, so R2C5 must be a dog (no three in a row).
  40. R2C4 and R3C4 are both cats, so R4C4 must be a dog (no three in a row).
  41. R2C5 and R3C5 are both dogs, so R4C5 must be a cat (no three in a row).
  42. R4C5 and R4C6 are both cats, so R4C7 must be a dog (no three in a row).
  43. Imagine R1C3 were a dog: following the rules from there soon forces a contradiction, so R1C3 must be a cat.
  44. Imagine R1C6 were a dog: following the rules from there soon forces a contradiction, so R1C6 must be a cat.
  45. Row 1 already has its 5 cats, so R1C9 must be dogs.
  46. Imagine R7C3 were a cat: following the rules from there soon forces a contradiction, so R7C3 must be a dog.
  47. R6C3 and R7C3 are both dogs, so R8C3 must be a cat (no three in a row).
  48. Column 3 already has its 5 cats, so R9C3 and R10C3 must be dogs.
  49. The = clue between R10C3 and R10C4 means they are the same. R10C3 is a dog, so R10C4 is a dog.
  50. R10C3 and R10C4 are both dogs, so R10C2 must be a cat (no three in a row).
  51. R10C3 and R10C4 are both dogs, so R10C5 must be a cat (no three in a row).
  52. The = clue between R10C5 and R10C6 means they are the same. R10C5 is a cat, so R10C6 is a cat.
  53. R10C5 and R10C6 are both cats, so R10C7 must be a dog (no three in a row).
  54. Column 6 already has its 5 cats, so R8C6 and R9C6 must be dogs.
  55. Imagine R6C5 were a cat: following the rules from there soon forces a contradiction, so R6C5 must be a dog.
  56. R6C5 and R6C6 are both dogs, so R6C7 must be a cat (no three in a row).
  57. R5C7 and R6C7 are both cats, so R7C7 must be a dog (no three in a row).
  58. Column 7 already has its 5 dogs, so R8C7 and R9C7 must be cats.
  59. R9C7 and R9C9 are both cats with one square between them, so R9C8 must be a dog.
  60. Imagine R8C2 were a cat: following the rules from there soon forces a contradiction, so R8C2 must be a dog.
  61. Imagine R8C8 were a dog: following the rules from there soon forces a contradiction, so R8C8 must be a cat.
  62. Imagine R9C1 were a dog: following the rules from there soon forces a contradiction, so R9C1 must be a cat.
  63. Imagine R9C2 were a dog: following the rules from there soon forces a contradiction, so R9C2 must be a cat.
  64. Imagine R4C2 were a cat: following the rules from there soon forces a contradiction, so R4C2 must be a dog.
  65. Imagine R5C1 were a cat: following the rules from there soon forces a contradiction, so R5C1 must be a dog.
  66. Imagine R5C2 were a cat: following the rules from there soon forces a contradiction, so R5C2 must be a dog.
  67. R4C2 and R5C2 are both dogs, so R6C2 must be a cat (no three in a row).
  68. Column 2 already has its 5 cats, so R7C2 must be dogs.
  69. R7C2 and R7C3 are both dogs, so R7C1 must be a cat (no three in a row).
  70. R7C2 and R7C3 are both dogs, so R7C4 must be a cat (no three in a row).
  71. R7C4 and R7C6 are both cats with one square between them, so R7C5 must be a dog.
  72. R7C1 and R9C1 are both cats with one square between them, so R8C1 must be a dog.
  73. R6C4 and R7C4 are both cats, so R5C4 must be a dog (no three in a row).
  74. R5C4 and R5C6 are both dogs with one square between them, so R5C5 must be a cat.
  75. R6C4 and R7C4 are both cats, so R8C4 must be a dog (no three in a row).
  76. R8C4 and R8C6 are both dogs with one square between them, so R8C5 must be a cat.
  77. R8C4 and R10C4 are both dogs with one square between them, so R9C4 must be a cat.
  78. R8C5 and R10C5 are both cats with one square between them, so R9C5 must be a dog.
  79. Row 5 already has its 5 dogs, so R5C10 must be cats.
  80. The × clue between R5C10 and R4C10 means they are different. R5C10 is a cat, so R4C10 is a dog.
  81. Row 4 already has its 5 dogs, so R4C1 must be cats.
  82. Row 8 already has its 5 dogs, so R8C10 must be cats.
  83. Imagine R6C1 were a dog: following the rules from there soon forces a contradiction, so R6C1 must be a cat.
  84. Column 1 already has its 5 cats, so R10C1 must be dogs.
  85. Imagine R6C8 were a cat: following the rules from there soon forces a contradiction, so R6C8 must be a dog.
  86. Imagine R6C9 were a dog: following the rules from there soon forces a contradiction, so R6C9 must be a cat.
  87. Row 6 already has its 5 cats, so R6C10 must be dogs.
  88. Column 9 already has its 5 cats, so R7C9 must be dogs.
  89. The × clue between R7C9 and R7C8 means they are different. R7C9 is a dog, so R7C8 is a cat.
  90. The × clue between R7C9 and R7C10 means they are different. R7C9 is a dog, so R7C10 is a cat.
  91. Column 8 already has its 5 cats, so R10C8 must be dogs.
  92. Row 10 already has its 5 dogs, so R10C10 must be cats.

About this puzzle

This 10×10 grid starts with 5 filled squares and 18 = / × clues. It can be solved in 92 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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