Cats & Dogs #292: 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 R4C1 and R3C1 means they are different. R4C1 is a dog, so R3C1 is a cat.
2. Imagine R3C5 were a dog: following the rules from there soon forces a contradiction, so R3C5 must be a cat.
3. The = clue between R3C5 and R4C5 means they are the same. R3C5 is a cat, so R4C5 is a cat.
4. R3C5 and R4C5 are both cats, so R2C5 must be a dog (no three in a row).
5. R3C5 and R4C5 are both cats, so R5C5 must be a dog (no three in a row).
6. Imagine R3C9 were a dog: following the rules from there soon forces a contradiction, so R3C9 must be a cat.
7. The = clue between R3C9 and R4C9 means they are the same. R3C9 is a cat, so R4C9 is a cat.
8. R4C8 and R4C9 are both cats, so R4C7 must be a dog (no three in a row).
9. R4C8 and R4C9 are both cats, so R4C10 must be a dog (no three in a row).
10. R3C9 and R4C9 are both cats, so R5C9 must be a dog (no three in a row).
11. The × clue between R5C9 and R6C9 means they are different. R5C9 is a dog, so R6C9 is a cat.
12. Imagine R3C6 were a cat: following the rules from there soon forces a contradiction, so R3C6 must be a dog.
13. Imagine R2C10 were a dog: following the rules from there soon forces a contradiction, so R2C10 must be a cat.
14. Imagine R3C7 were a dog: following the rules from there soon forces a contradiction, so R3C7 must be a cat.
15. R3C7 and R3C9 are both cats with one square between them, so R3C8 must be a dog.
16. Imagine R3C10 were a cat: following the rules from there soon forces a contradiction, so R3C10 must be a dog.
17. R3C10 and R4C10 are both dogs, so R5C10 must be a cat (no three in a row).
18. Imagine R4C6 were a dog: following the rules from there soon forces a contradiction, so R4C6 must be a cat.
19. The = clue between R4C6 and R5C6 means they are the same. R4C6 is a cat, so R5C6 is a cat.
20. The × clue between R5C6 and R5C7 means they are different. R5C6 is a cat, so R5C7 is a dog.
21. R5C7 and R5C9 are both dogs with one square between them, so R5C8 must be a cat.
22. R4C6 and R5C6 are both cats, so R6C6 must be a dog (no three in a row).
23. R4C7 and R5C7 are both dogs, so R6C7 must be a cat (no three in a row).
24. R6C7 and R6C9 are both cats with one square between them, so R6C8 must be a dog.
25. Imagine R7C3 were a cat: following the rules from there soon forces a contradiction, so R7C3 must be a dog.
26. Imagine R7C7 were a cat: following the rules from there soon forces a contradiction, so R7C7 must be a dog.
27. The = clue between R7C7 and R8C7 means they are the same. R7C7 is a dog, so R8C7 is a dog.
28. R7C7 and R8C7 are both dogs, so R9C7 must be a cat (no three in a row).
29. Imagine R5C2 were a cat: following the rules from there soon forces a contradiction, so R5C2 must be a dog.
30. The = clue between R5C2 and R6C2 means they are the same. R5C2 is a dog, so R6C2 is a dog.
31. R5C2 and R6C2 are both dogs, so R4C2 must be a cat (no three in a row).
32. The × clue between R4C2 and R4C3 means they are different. R4C2 is a cat, so R4C3 is a dog.
33. R5C2 and R6C2 are both dogs, so R7C2 must be a cat (no three in a row).
34. Imagine R7C8 were a dog: following the rules from there soon forces a contradiction, so R7C8 must be a cat.
35. The = clue between R7C8 and R7C9 means they are the same. R7C8 is a cat, so R7C9 is a cat.
36. R7C8 and R7C9 are both cats, so R7C10 must be a dog (no three in a row).
37. R6C9 and R7C9 are both cats, so R8C9 must be a dog (no three in a row).
38. The = clue between R8C9 and R8C10 means they are the same. R8C9 is a dog, so R8C10 is a dog.
39. R8C7 and R8C9 are both dogs with one square between them, so R8C8 must be a cat.
40. R7C8 and R8C8 are both cats, so R9C8 must be a dog (no three in a row).
41. R7C10 and R8C10 are both dogs, so R6C10 must be a cat (no three in a row).
42. R7C10 and R8C10 are both dogs, so R9C10 must be a cat (no three in a row).
43. Imagine R1C7 were a cat: following the rules from there soon forces a contradiction, so R1C7 must be a dog.
44. Column 7 already has its 5 dogs, so R2C7 and R10C7 must be cats.
45. Imagine R1C8 were a dog: following the rules from there soon forces a contradiction, so R1C8 must be a cat.
46. Column 8 already has its 5 cats, so R2C8 and R10C8 must be dogs.
47. The = clue between R10C8 and R10C9 means they are the same. R10C8 is a dog, so R10C9 is a dog.
48. R10C8 and R10C9 are both dogs, so R10C10 must be a cat (no three in a row).
49. R8C9 and R10C9 are both dogs with one square between them, so R9C9 must be a cat.
50. Column 9 already has its 5 cats, so R1C9 must be dogs.
51. Column 10 already has its 5 cats, so R1C10 must be dogs.
52. Imagine R2C2 were a cat: following the rules from there soon forces a contradiction, so R2C2 must be a dog.
53. The × clue between R2C2 and R2C3 means they are different. R2C2 is a dog, so R2C3 is a cat.
54. Imagine R1C2 were a dog: following the rules from there soon forces a contradiction, so R1C2 must be a cat.
55. Imagine R3C2 were a cat: following the rules from there soon forces a contradiction, so R3C2 must be a dog.
56. Column 2 already has its 5 dogs, so R9C2 and R10C2 must be cats.
57. Imagine R3C3 were a cat: following the rules from there soon forces a contradiction, so R3C3 must be a dog.
58. R3C2 and R3C3 are both dogs, so R3C4 must be a cat (no three in a row).
59. Imagine R1C4 were a cat: following the rules from there soon forces a contradiction, so R1C4 must be a dog.
60. Imagine R1C5 were a dog: following the rules from there soon forces a contradiction, so R1C5 must be a cat.
61. Imagine R1C6 were a dog: following the rules from there soon forces a contradiction, so R1C6 must be a cat.
62. Imagine R5C1 were a dog: following the rules from there soon forces a contradiction, so R5C1 must be a cat.
63. Row 5 already has its 5 cats, so R5C4 must be dogs.
64. R4C4 and R5C4 are both dogs, so R6C4 must be a cat (no three in a row).
65. R6C4 and R7C4 are both cats, so R8C4 must be a dog (no three in a row).
66. R8C2 and R8C4 are both dogs with one square between them, so R8C3 must be a cat.
67. Row 8 already has its 5 dogs, so R8C1, R8C5 and R8C6 must be cats.
68. Imagine R1C1 were a cat: following the rules from there soon forces a contradiction, so R1C1 must be a dog.
69. Row 1 already has its 5 dogs, so R1C3 must be cats.
70. Imagine R2C1 were a dog: following the rules from there soon forces a contradiction, so R2C1 must be a cat.
71. Imagine R6C1 were a cat: following the rules from there soon forces a contradiction, so R6C1 must be a dog.
72. R6C1 and R6C2 are both dogs, so R6C3 must be a cat (no three in a row).
73. R6C3 and R6C4 are both cats, so R6C5 must be a dog (no three in a row).
74. R5C5 and R6C5 are both dogs, so R7C5 must be a cat (no three in a row).
75. R7C4 and R7C5 are both cats, so R7C6 must be a dog (no three in a row).
76. R7C5 and R8C5 are both cats, so R9C5 must be a dog (no three in a row).
77. Row 7 already has its 5 cats, so R7C1 must be dogs.
78. Column 3 already has its 5 cats, so R9C3 must be dogs.
79. R9C3 and R9C5 are both dogs with one square between them, so R9C4 must be a cat.
80. Row 9 already has its 5 cats, so R9C1 must be dogs.
81. The × clue between R9C1 and R10C1 means they are different. R9C1 is a dog, so R10C1 is a cat.
82. R10C1 and R10C2 are both cats, so R10C3 must be a dog (no three in a row).
83. Row 9 already has its 5 cats, so R9C6 must be dogs.
84. Column 5 already has its 5 cats, so R10C5 must be dogs.
85. R10C3 and R10C5 are both dogs with one square between them, so R10C4 must be a cat.
86. Row 10 already has its 5 cats, so R10C6 must be dogs.
87. Column 4 already has its 5 cats, so R2C4 must be dogs.
88. R2C4 and R2C5 are both dogs, so R2C6 must be a cat (no three in a row).