Cats & Dogs #206: 10x10 Grid Puzzle (Hard)

Step-by-step solution

Squares are written as R<row>C<column>, counting from the top-left.

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