Cats & Dogs #219: 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 R4C1 and R4C2 means they are different. R4C1 is a cat, so R4C2 is a dog.
  2. The × clue between R10C4 and R9C4 means they are different. R10C4 is a cat, so R9C4 is a dog.
  3. The = clue between R9C4 and R9C5 means they are the same. R9C4 is a dog, so R9C5 is a dog.
  4. R3C5 and R3C6 are both cats, so R3C4 must be a dog (no three in a row).
  5. The = clue between R3C4 and R3C3 means they are the same. R3C4 is a dog, so R3C3 is a dog.
  6. R3C3 and R3C4 are both dogs, so R3C2 must be a cat (no three in a row).
  7. The × clue between R3C2 and R2C2 means they are different. R3C2 is a cat, so R2C2 is a dog.
  8. R3C5 and R3C6 are both cats, so R3C7 must be a dog (no three in a row).
  9. R9C4 and R9C5 are both dogs, so R9C3 must be a cat (no three in a row).
  10. R9C4 and R9C5 are both dogs, so R9C6 must be a cat (no three in a row).
  11. The = clue between R9C6 and R8C6 means they are the same. R9C6 is a cat, so R8C6 is a cat.
  12. The × clue between R9C6 and R9C7 means they are different. R9C6 is a cat, so R9C7 is a dog.
  13. R8C6 and R9C6 are both cats, so R7C6 must be a dog (no three in a row).
  14. The = clue between R7C6 and R6C6 means they are the same. R7C6 is a dog, so R6C6 is a dog.
  15. R6C6 and R7C6 are both dogs, so R5C6 must be a cat (no three in a row).
  16. The × clue between R5C6 and R5C7 means they are different. R5C6 is a cat, so R5C7 is a dog.
  17. The × clue between R5C7 and R5C8 means they are different. R5C7 is a dog, so R5C8 is a cat.
  18. R3C6 and R5C6 are both cats with one square between them, so R4C6 must be a dog.
  19. R8C6 and R9C6 are both cats, so R10C6 must be a dog (no three in a row).
  20. R3C7 and R5C7 are both dogs with one square between them, so R4C7 must be a cat.
  21. R5C8 and R6C8 are both cats, so R4C8 must be a dog (no three in a row).
  22. The = clue between R4C8 and R3C8 means they are the same. R4C8 is a dog, so R3C8 is a dog.
  23. R3C7 and R3C8 are both dogs, so R3C9 must be a cat (no three in a row).
  24. R3C8 and R4C8 are both dogs, so R2C8 must be a cat (no three in a row).
  25. R5C8 and R6C8 are both cats, so R7C8 must be a dog (no three in a row).
  26. The × clue between R7C8 and R7C9 means they are different. R7C8 is a dog, so R7C9 is a cat.
  27. R7C6 and R7C8 are both dogs with one square between them, so R7C7 must be a cat.
  28. Imagine R1C3 were a dog: following the rules from there soon forces a contradiction, so R1C3 must be a cat.
  29. The = clue between R1C3 and R2C3 means they are the same. R1C3 is a cat, so R2C3 is a cat.
  30. The × clue between R2C3 and R2C4 means they are different. R2C3 is a cat, so R2C4 is a dog.
  31. R2C4 and R3C4 are both dogs, so R1C4 must be a cat (no three in a row).
  32. R1C3 and R1C4 are both cats, so R1C2 must be a dog (no three in a row).
  33. R1C3 and R1C4 are both cats, so R1C5 must be a dog (no three in a row).
  34. R2C4 and R3C4 are both dogs, so R4C4 must be a cat (no three in a row).
  35. Imagine R1C8 were a cat: following the rules from there soon forces a contradiction, so R1C8 must be a dog.
  36. Imagine R8C8 were a cat: following the rules from there soon forces a contradiction, so R8C8 must be a dog.
  37. The = clue between R8C8 and R8C9 means they are the same. R8C8 is a dog, so R8C9 is a dog.
  38. R8C8 and R8C9 are both dogs, so R8C7 must be a cat (no three in a row).
  39. R8C6 and R8C7 are both cats, so R8C5 must be a dog (no three in a row).
  40. R8C8 and R8C9 are both dogs, so R8C10 must be a cat (no three in a row).
  41. R8C5 and R9C5 are both dogs, so R7C5 must be a cat (no three in a row).
  42. R8C5 and R9C5 are both dogs, so R10C5 must be a cat (no three in a row).
  43. R10C4 and R10C5 are both cats, so R10C3 must be a dog (no three in a row).
  44. R7C7 and R8C7 are both cats, so R6C7 must be a dog (no three in a row).
  45. R6C6 and R6C7 are both dogs, so R6C5 must be a cat (no three in a row).
  46. R6C5 and R7C5 are both cats, so R5C5 must be a dog (no three in a row).
  47. The × clue between R5C5 and R5C4 means they are different. R5C5 is a dog, so R5C4 is a cat.
  48. R4C4 and R5C4 are both cats, so R6C4 must be a dog (no three in a row).
  49. R7C8 and R8C8 are both dogs, so R9C8 must be a cat (no three in a row).
  50. Imagine R6C2 were a dog: following the rules from there soon forces a contradiction, so R6C2 must be a cat.
  51. Imagine R7C3 were a cat: following the rules from there soon forces a contradiction, so R7C3 must be a dog.
  52. Imagine R5C2 were a cat: following the rules from there soon forces a contradiction, so R5C2 must be a dog.
  53. Imagine R5C3 were a dog: following the rules from there soon forces a contradiction, so R5C3 must be a cat.
  54. Imagine R4C3 were a cat: following the rules from there soon forces a contradiction, so R4C3 must be a dog.
  55. Imagine R6C3 were a cat: following the rules from there soon forces a contradiction, so R6C3 must be a dog.
  56. R6C3 and R7C3 are both dogs, so R8C3 must be a cat (no three in a row).
  57. The = clue between R8C3 and R8C4 means they are the same. R8C3 is a cat, so R8C4 is a cat.
  58. R8C3 and R8C4 are both cats, so R8C2 must be a dog (no three in a row).
  59. Row 8 already has its 5 cats, so R8C1 must be dogs.
  60. Column 2 already has its 5 dogs, so R7C2 and R9C2 must be cats.
  61. R9C2 and R9C3 are both cats, so R9C1 must be a dog (no three in a row).
  62. R8C1 and R9C1 are both dogs, so R7C1 must be a cat (no three in a row).
  63. R8C1 and R9C1 are both dogs, so R10C1 must be a cat (no three in a row).
  64. Row 7 already has its 5 cats, so R7C4 and R7C10 must be dogs.
  65. Column 2 already has its 5 dogs, so R10C2 must be cats.
  66. Row 10 already has its 5 cats, so R10C7 and R10C9 must be dogs.
  67. R8C9 and R10C9 are both dogs with one square between them, so R9C9 must be a cat.
  68. R9C8 and R9C9 are both cats, so R9C10 must be a dog (no three in a row).
  69. Row 10 already has its 5 cats, so R10C10 must be dogs.
  70. Column 7 already has its 5 dogs, so R1C7 and R2C7 must be cats.
  71. R2C7 and R2C8 are both cats, so R2C6 must be a dog (no three in a row).
  72. R2C4 and R2C6 are both dogs with one square between them, so R2C5 must be a cat.
  73. R2C7 and R2C8 are both cats, so R2C9 must be a dog (no three in a row).
  74. R2C5 and R3C5 are both cats, so R4C5 must be a dog (no three in a row).
  75. Row 4 already has its 5 dogs, so R4C9 must be cats.
  76. R3C9 and R4C9 are both cats, so R5C9 must be a dog (no three in a row).
  77. Row 4 already has its 5 dogs, so R4C10 must be cats.
  78. Column 6 already has its 5 dogs, so R1C6 must be cats.
  79. Imagine R1C1 were a cat: following the rules from there soon forces a contradiction, so R1C1 must be a dog.
  80. Imagine R1C9 were a cat: following the rules from there soon forces a contradiction, so R1C9 must be a dog.
  81. R1C8 and R1C9 are both dogs, so R1C10 must be a cat (no three in a row).
  82. Column 9 already has its 5 dogs, so R6C9 must be cats.
  83. R6C8 and R6C9 are both cats, so R6C10 must be a dog (no three in a row).
  84. R6C10 and R7C10 are both dogs, so R5C10 must be a cat (no three in a row).
  85. R4C10 and R5C10 are both cats, so R3C10 must be a dog (no three in a row).
  86. Row 3 already has its 5 dogs, so R3C1 must be cats.
  87. R3C1 and R4C1 are both cats, so R2C1 must be a dog (no three in a row).
  88. R3C1 and R4C1 are both cats, so R5C1 must be a dog (no three in a row).
  89. Row 2 already has its 5 dogs, so R2C10 must be cats.
  90. Row 6 already has its 5 dogs, so R6C1 must be cats.

About this puzzle

This 10×10 grid starts with 6 filled squares and 17 = / × clues. It can be solved in 90 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.

More hard puzzles