Cats & Dogs #253: 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. The = clue between R3C10 and R2C10 means they are the same. R3C10 is a dog, so R2C10 is a dog.
  2. The × clue between R9C3 and R8C3 means they are different. R9C3 is a dog, so R8C3 is a cat.
  3. R2C10 and R3C10 are both dogs, so R1C10 must be a cat (no three in a row).
  4. R2C10 and R3C10 are both dogs, so R4C10 must be a cat (no three in a row).
  5. Imagine R1C6 were a cat: following the rules from there soon forces a contradiction, so R1C6 must be a dog.
  6. The = clue between R1C6 and R2C6 means they are the same. R1C6 is a dog, so R2C6 is a dog.
  7. The = clue between R2C6 and R2C7 means they are the same. R2C6 is a dog, so R2C7 is a dog.
  8. R2C6 and R2C7 are both dogs, so R2C5 must be a cat (no three in a row).
  9. The × clue between R2C5 and R2C4 means they are different. R2C5 is a cat, so R2C4 is a dog.
  10. R2C6 and R2C7 are both dogs, so R2C8 must be a cat (no three in a row).
  11. R1C6 and R2C6 are both dogs, so R3C6 must be a cat (no three in a row).
  12. Imagine R2C9 were a dog: following the rules from there soon forces a contradiction, so R2C9 must be a cat.
  13. Imagine R3C5 were a cat: following the rules from there soon forces a contradiction, so R3C5 must be a dog.
  14. Imagine R6C6 were a dog: following the rules from there soon forces a contradiction, so R6C6 must be a cat.
  15. The = clue between R6C6 and R7C6 means they are the same. R6C6 is a cat, so R7C6 is a cat.
  16. R6C6 and R7C6 are both cats, so R5C6 must be a dog (no three in a row).
  17. R6C6 and R7C6 are both cats, so R8C6 must be a dog (no three in a row).
  18. The = clue between R8C6 and R8C5 means they are the same. R8C6 is a dog, so R8C5 is a dog.
  19. R8C5 and R8C6 are both dogs, so R8C4 must be a cat (no three in a row).
  20. R8C3 and R8C4 are both cats, so R8C2 must be a dog (no three in a row).
  21. The = clue between R8C2 and R8C1 means they are the same. R8C2 is a dog, so R8C1 is a dog.
  22. R8C5 and R8C6 are both dogs, so R8C7 must be a cat (no three in a row).
  23. The × clue between R8C7 and R9C7 means they are different. R8C7 is a cat, so R9C7 is a dog.
  24. The × clue between R9C7 and R10C7 means they are different. R9C7 is a dog, so R10C7 is a cat.
  25. Imagine R6C9 were a cat: following the rules from there soon forces a contradiction, so R6C9 must be a dog.
  26. The = clue between R6C9 and R7C9 means they are the same. R6C9 is a dog, so R7C9 is a dog.
  27. The = clue between R7C9 and R7C10 means they are the same. R7C9 is a dog, so R7C10 is a dog.
  28. R7C9 and R7C10 are both dogs, so R7C8 must be a cat (no three in a row).
  29. The × clue between R7C8 and R7C7 means they are different. R7C8 is a cat, so R7C7 is a dog.
  30. R6C9 and R7C9 are both dogs, so R5C9 must be a cat (no three in a row).
  31. R6C9 and R7C9 are both dogs, so R8C9 must be a cat (no three in a row).
  32. R8C7 and R8C9 are both cats with one square between them, so R8C8 must be a dog.
  33. Row 8 already has its 5 dogs, so R8C10 must be cats.
  34. The × clue between R8C10 and R9C10 means they are different. R8C10 is a cat, so R9C10 is a dog.
  35. Imagine R6C5 were a cat: following the rules from there soon forces a contradiction, so R6C5 must be a dog.
  36. R6C5 and R8C5 are both dogs with one square between them, so R7C5 must be a cat.
  37. R7C5 and R7C6 are both cats, so R7C4 must be a dog (no three in a row).
  38. Imagine R7C1 were a dog: following the rules from there soon forces a contradiction, so R7C1 must be a cat.
  39. Imagine R9C5 were a dog: following the rules from there soon forces a contradiction, so R9C5 must be a cat.
  40. The = clue between R9C5 and R9C6 means they are the same. R9C5 is a cat, so R9C6 is a cat.
  41. R9C5 and R9C6 are both cats, so R9C4 must be a dog (no three in a row).
  42. R9C3 and R9C4 are both dogs, so R9C2 must be a cat (no three in a row).
  43. The × clue between R9C2 and R10C2 means they are different. R9C2 is a cat, so R10C2 is a dog.
  44. The × clue between R10C2 and R10C1 means they are different. R10C2 is a dog, so R10C1 is a cat.
  45. Imagine R9C1 were a dog: following the rules from there soon forces a contradiction, so R9C1 must be a cat.
  46. Imagine R4C1 were a cat: following the rules from there soon forces a contradiction, so R4C1 must be a dog.
  47. The = clue between R4C1 and R5C1 means they are the same. R4C1 is a dog, so R5C1 is a dog.
  48. R4C1 and R5C1 are both dogs, so R3C1 must be a cat (no three in a row).
  49. R4C1 and R5C1 are both dogs, so R6C1 must be a cat (no three in a row).
  50. Column 1 already has its 5 cats, so R1C1 and R2C1 must be dogs.
  51. Row 2 already has its 5 dogs, so R2C2 must be cats.
  52. Imagine R3C3 were a cat: following the rules from there soon forces a contradiction, so R3C3 must be a dog.
  53. R3C3 and R3C5 are both dogs with one square between them, so R3C4 must be a cat.
  54. Imagine R4C3 were a dog: following the rules from there soon forces a contradiction, so R4C3 must be a cat.
  55. Imagine R4C4 were a cat: following the rules from there soon forces a contradiction, so R4C4 must be a dog.
  56. The = clue between R4C4 and R4C5 means they are the same. R4C4 is a dog, so R4C5 is a dog.
  57. R4C4 and R4C5 are both dogs, so R4C6 must be a cat (no three in a row).
  58. Column 6 already has its 5 cats, so R10C6 must be dogs.
  59. Imagine R10C4 were a dog: following the rules from there soon forces a contradiction, so R10C4 must be a cat.
  60. Imagine R10C10 were a dog: following the rules from there soon forces a contradiction, so R10C10 must be a cat.
  61. Imagine R4C7 were a dog: following the rules from there soon forces a contradiction, so R4C7 must be a cat.
  62. R4C6 and R4C7 are both cats, so R4C8 must be a dog (no three in a row).
  63. Imagine R1C7 were a dog: following the rules from there soon forces a contradiction, so R1C7 must be a cat.
  64. Imagine R1C8 were a cat: following the rules from there soon forces a contradiction, so R1C8 must be a dog.
  65. Imagine R3C7 were a cat: following the rules from there soon forces a contradiction, so R3C7 must be a dog.
  66. Imagine R1C2 were a cat: following the rules from there soon forces a contradiction, so R1C2 must be a dog.
  67. R1C1 and R1C2 are both dogs, so R1C3 must be a cat (no three in a row).
  68. R1C3 and R1C4 are both cats, so R1C5 must be a dog (no three in a row).
  69. Row 1 already has its 5 dogs, so R1C9 must be cats.
  70. R1C9 and R2C9 are both cats, so R3C9 must be a dog (no three in a row).
  71. R3C7 and R3C9 are both dogs with one square between them, so R3C8 must be a cat.
  72. Row 3 already has its 5 dogs, so R3C2 must be cats.
  73. R2C2 and R3C2 are both cats, so R4C2 must be a dog (no three in a row).
  74. The = clue between R4C2 and R5C2 means they are the same. R4C2 is a dog, so R5C2 is a dog.
  75. The × clue between R5C2 and R5C3 means they are different. R5C2 is a dog, so R5C3 is a cat.
  76. R5C3 and R5C5 are both cats with one square between them, so R5C4 must be a dog.
  77. R4C2 and R5C2 are both dogs, so R6C2 must be a cat (no three in a row).
  78. R6C1 and R6C2 are both cats, so R6C3 must be a dog (no three in a row).
  79. R6C3 and R6C5 are both dogs with one square between them, so R6C4 must be a cat.
  80. Row 4 already has its 5 dogs, so R4C9 must be cats.
  81. Column 2 already has its 5 dogs, so R7C2 must be cats.
  82. The × clue between R7C2 and R7C3 means they are different. R7C2 is a cat, so R7C3 is a dog.
  83. Column 3 already has its 5 cats, so R10C3 must be dogs.
  84. Column 5 already has its 5 dogs, so R10C5 must be cats.
  85. Row 10 already has its 5 cats, so R10C8 must be dogs.
  86. R8C8 and R10C8 are both dogs with one square between them, so R9C8 must be a cat.
  87. The × clue between R9C8 and R9C9 means they are different. R9C8 is a cat, so R9C9 is a dog.
  88. Row 10 already has its 5 cats, so R10C9 must be dogs.
  89. Imagine R5C7 were a dog: following the rules from there soon forces a contradiction, so R5C7 must be a cat.
  90. R5C7 and R5C9 are both cats with one square between them, so R5C8 must be a dog.
  91. R4C7 and R5C7 are both cats, so R6C7 must be a dog (no three in a row).
  92. R6C7 and R6C9 are both dogs with one square between them, so R6C8 must be a cat.
  93. Row 5 already has its 5 dogs, so R5C10 must be cats.
  94. R4C10 and R5C10 are both cats, so R6C10 must be a dog (no three in a row).

About this puzzle

This 10×10 grid starts with 5 filled squares and 23 = / × clues. It can be solved in 94 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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