Cats & Dogs #290: 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 R1C1 and R1C2 means they are different. R1C1 is a dog, so R1C2 is a cat.
  2. The × clue between R1C5 and R1C4 means they are different. R1C5 is a dog, so R1C4 is a cat.
  3. The × clue between R3C3 and R4C3 means they are different. R3C3 is a cat, so R4C3 is a dog.
  4. The = clue between R6C4 and R5C4 means they are the same. R6C4 is a cat, so R5C4 is a cat.
  5. The = clue between R10C2 and R10C1 means they are the same. R10C2 is a dog, so R10C1 is a dog.
  6. The × clue between R10C8 and R10C9 means they are different. R10C8 is a cat, so R10C9 is a dog.
  7. R1C2 and R1C4 are both cats with one square between them, so R1C3 must be a dog.
  8. R10C1 and R10C2 are both dogs, so R10C3 must be a cat (no three in a row).
  9. R5C4 and R6C4 are both cats, so R4C4 must be a dog (no three in a row).
  10. R4C3 and R4C4 are both dogs, so R4C2 must be a cat (no three in a row).
  11. R4C3 and R4C4 are both dogs, so R4C5 must be a cat (no three in a row).
  12. R5C4 and R6C4 are both cats, so R7C4 must be a dog (no three in a row).
  13. The × clue between R7C4 and R8C4 means they are different. R7C4 is a dog, so R8C4 is a cat.
  14. The = clue between R8C4 and R8C5 means they are the same. R8C4 is a cat, so R8C5 is a cat.
  15. R8C4 and R8C5 are both cats, so R8C3 must be a dog (no three in a row).
  16. R8C4 and R8C5 are both cats, so R8C6 must be a dog (no three in a row).
  17. R8C6 and R8C8 are both dogs with one square between them, so R8C7 must be a cat.
  18. Imagine R2C1 were a dog: following the rules from there soon forces a contradiction, so R2C1 must be a cat.
  19. The = clue between R2C1 and R3C1 means they are the same. R2C1 is a cat, so R3C1 is a cat.
  20. R3C1 and R3C3 are both cats with one square between them, so R3C2 must be a dog.
  21. R2C1 and R3C1 are both cats, so R4C1 must be a dog (no three in a row).
  22. The = clue between R4C1 and R5C1 means they are the same. R4C1 is a dog, so R5C1 is a dog.
  23. R4C1 and R5C1 are both dogs, so R6C1 must be a cat (no three in a row).
  24. Imagine R6C5 were a cat: following the rules from there soon forces a contradiction, so R6C5 must be a dog.
  25. Imagine R8C2 were a dog: following the rules from there soon forces a contradiction, so R8C2 must be a cat.
  26. Imagine R5C2 were a dog: following the rules from there soon forces a contradiction, so R5C2 must be a cat.
  27. The × clue between R5C2 and R6C2 means they are different. R5C2 is a cat, so R6C2 is a dog.
  28. R5C2 and R5C4 are both cats with one square between them, so R5C3 must be a dog.
  29. R4C3 and R5C3 are both dogs, so R6C3 must be a cat (no three in a row).
  30. Imagine R2C2 were a cat: following the rules from there soon forces a contradiction, so R2C2 must be a dog.
  31. Imagine R7C1 were a dog: following the rules from there soon forces a contradiction, so R7C1 must be a cat.
  32. The = clue between R7C1 and R7C2 means they are the same. R7C1 is a cat, so R7C2 is a cat.
  33. R7C1 and R7C2 are both cats, so R7C3 must be a dog (no three in a row).
  34. R7C3 and R7C4 are both dogs, so R7C5 must be a cat (no three in a row).
  35. R6C1 and R7C1 are both cats, so R8C1 must be a dog (no three in a row).
  36. R8C1 and R10C1 are both dogs with one square between them, so R9C1 must be a cat.
  37. R7C2 and R8C2 are both cats, so R9C2 must be a dog (no three in a row).
  38. R7C3 and R8C3 are both dogs, so R9C3 must be a cat (no three in a row).
  39. R7C5 and R8C5 are both cats, so R9C5 must be a dog (no three in a row).
  40. Column 3 already has its 5 dogs, so R2C3 must be cats.
  41. Imagine R5C5 were a cat: following the rules from there soon forces a contradiction, so R5C5 must be a dog.
  42. R5C5 and R5C6 are both dogs, so R5C7 must be a cat (no three in a row).
  43. The × clue between R5C7 and R5C8 means they are different. R5C7 is a cat, so R5C8 is a dog.
  44. The = clue between R5C8 and R6C8 means they are the same. R5C8 is a dog, so R6C8 is a dog.
  45. The × clue between R6C8 and R6C7 means they are different. R6C8 is a dog, so R6C7 is a cat.
  46. R5C7 and R6C7 are both cats, so R4C7 must be a dog (no three in a row).
  47. R5C7 and R6C7 are both cats, so R7C7 must be a dog (no three in a row).
  48. R5C8 and R6C8 are both dogs, so R4C8 must be a cat (no three in a row).
  49. R5C8 and R6C8 are both dogs, so R7C8 must be a cat (no three in a row).
  50. Row 5 already has its 5 dogs, so R5C9 and R5C10 must be cats.
  51. Imagine R4C6 were a dog: following the rules from there soon forces a contradiction, so R4C6 must be a cat.
  52. Imagine R6C6 were a cat: following the rules from there soon forces a contradiction, so R6C6 must be a dog.
  53. R5C6 and R6C6 are both dogs, so R7C6 must be a cat (no three in a row).
  54. Row 7 already has its 5 cats, so R7C9 and R7C10 must be dogs.
  55. Imagine R9C4 were a cat: following the rules from there soon forces a contradiction, so R9C4 must be a dog.
  56. R9C4 and R9C5 are both dogs, so R9C6 must be a cat (no three in a row).
  57. Imagine R10C4 were a cat: following the rules from there soon forces a contradiction, so R10C4 must be a dog.
  58. Imagine R2C10 were a cat: following the rules from there soon forces a contradiction, so R2C10 must be a dog.
  59. The = clue between R2C10 and R3C10 means they are the same. R2C10 is a dog, so R3C10 is a dog.
  60. R2C10 and R3C10 are both dogs, so R1C10 must be a cat (no three in a row).
  61. R2C10 and R3C10 are both dogs, so R4C10 must be a cat (no three in a row).
  62. R4C8 and R4C10 are both cats with one square between them, so R4C9 must be a dog.
  63. The × clue between R4C9 and R3C9 means they are different. R4C9 is a dog, so R3C9 is a cat.
  64. R4C10 and R5C10 are both cats, so R6C10 must be a dog (no three in a row).
  65. R6C8 and R6C10 are both dogs with one square between them, so R6C9 must be a cat.
  66. R6C10 and R7C10 are both dogs, so R8C10 must be a cat (no three in a row).
  67. Row 8 already has its 5 cats, so R8C9 must be dogs.
  68. R7C9 and R8C9 are both dogs, so R9C9 must be a cat (no three in a row).
  69. Imagine R1C8 were a cat: following the rules from there soon forces a contradiction, so R1C8 must be a dog.
  70. The = clue between R1C8 and R2C8 means they are the same. R1C8 is a dog, so R2C8 is a dog.
  71. The × clue between R2C8 and R2C9 means they are different. R2C8 is a dog, so R2C9 is a cat.
  72. R1C8 and R2C8 are both dogs, so R3C8 must be a cat (no three in a row).
  73. R3C8 and R3C9 are both cats, so R3C7 must be a dog (no three in a row).
  74. R3C7 and R4C7 are both dogs, so R2C7 must be a cat (no three in a row).
  75. R2C9 and R3C9 are both cats, so R1C9 must be a dog (no three in a row).
  76. R1C8 and R1C9 are both dogs, so R1C7 must be a cat (no three in a row).
  77. Row 1 already has its 5 dogs, so R1C6 must be cats.
  78. Column 7 already has its 5 cats, so R9C7 and R10C7 must be dogs.
  79. Row 10 already has its 5 dogs, so R10C5, R10C6 and R10C10 must be cats.
  80. R8C10 and R10C10 are both cats with one square between them, so R9C10 must be a dog.
  81. Row 9 already has its 5 dogs, so R9C8 must be cats.
  82. Column 6 already has its 5 cats, so R2C6 and R3C6 must be dogs.
  83. R3C6 and R3C7 are both dogs, so R3C5 must be a cat (no three in a row).
  84. R3C3 and R3C5 are both cats with one square between them, so R3C4 must be a dog.
  85. R3C4 and R4C4 are both dogs, so R2C4 must be a cat (no three in a row).
  86. R2C3 and R2C4 are both cats, so R2C5 must be a dog (no three in a row).

About this puzzle

This 10×10 grid starts with 8 filled squares and 19 = / × clues. It can be solved in 86 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