Cats & Dogs #275: 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 R5C3 and R5C2 means they are different. R5C3 is a cat, so R5C2 is a dog.
2. The × clue between R5C2 and R6C2 means they are different. R5C2 is a dog, so R6C2 is a cat.
3. The = clue between R6C6 and R6C7 means they are the same. R6C6 is a cat, so R6C7 is a cat.
4. R6C6 and R6C7 are both cats, so R6C5 must be a dog (no three in a row).
5. The × clue between R6C5 and R5C5 means they are different. R6C5 is a dog, so R5C5 is a cat.
6. The × clue between R5C5 and R5C6 means they are different. R5C5 is a cat, so R5C6 is a dog.
7. R5C3 and R5C5 are both cats with one square between them, so R5C4 must be a dog.
8. The = clue between R5C4 and R4C4 means they are the same. R5C4 is a dog, so R4C4 is a dog.
9. R6C6 and R6C7 are both cats, so R6C8 must be a dog (no three in a row).
10. R3C2 and R5C2 are both dogs with one square between them, so R4C2 must be a cat.
11. R4C4 and R5C4 are both dogs, so R3C4 must be a cat (no three in a row).
12. R4C4 and R5C4 are both dogs, so R6C4 must be a cat (no three in a row).
13. R6C2 and R6C4 are both cats with one square between them, so R6C3 must be a dog.
14. Imagine R3C5 were a cat: following the rules from there soon forces a contradiction, so R3C5 must be a dog.
15. Imagine R3C6 were a dog: following the rules from there soon forces a contradiction, so R3C6 must be a cat.
16. The = clue between R3C6 and R3C7 means they are the same. R3C6 is a cat, so R3C7 is a cat.
17. R3C6 and R3C7 are both cats, so R3C8 must be a dog (no three in a row).
18. Imagine R4C1 were a dog: following the rules from there soon forces a contradiction, so R4C1 must be a cat.
19. R4C1 and R4C2 are both cats, so R4C3 must be a dog (no three in a row).
20. R4C3 and R4C4 are both dogs, so R4C5 must be a cat (no three in a row).
21. Imagine R4C7 were a cat: following the rules from there soon forces a contradiction, so R4C7 must be a dog.
22. The × clue between R4C7 and R4C8 means they are different. R4C7 is a dog, so R4C8 is a cat.
23. Imagine R5C7 were a dog: following the rules from there soon forces a contradiction, so R5C7 must be a cat.
24. R5C7 and R6C7 are both cats, so R7C7 must be a dog (no three in a row).
25. The = clue between R7C7 and R7C6 means they are the same. R7C7 is a dog, so R7C6 is a dog.
26. R7C6 and R7C7 are both dogs, so R7C5 must be a cat (no three in a row).
27. The = clue between R7C5 and R7C4 means they are the same. R7C5 is a cat, so R7C4 is a cat.
28. R7C4 and R7C5 are both cats, so R7C3 must be a dog (no three in a row).
29. R7C6 and R7C7 are both dogs, so R7C8 must be a cat (no three in a row).
30. R6C3 and R7C3 are both dogs, so R8C3 must be a cat (no three in a row).
31. R6C4 and R7C4 are both cats, so R8C4 must be a dog (no three in a row).
32. Imagine R5C10 were a dog: following the rules from there soon forces a contradiction, so R5C10 must be a cat.
33. Imagine R6C1 were a cat: following the rules from there soon forces a contradiction, so R6C1 must be a dog.
34. R5C1 and R6C1 are both dogs, so R7C1 must be a cat (no three in a row).
35. The = clue between R7C1 and R8C1 means they are the same. R7C1 is a cat, so R8C1 is a cat.
36. R8C1 and R8C3 are both cats with one square between them, so R8C2 must be a dog.
37. R7C1 and R8C1 are both cats, so R9C1 must be a dog (no three in a row).
38. Imagine R8C5 were a cat: following the rules from there soon forces a contradiction, so R8C5 must be a dog.
39. The = clue between R8C5 and R9C5 means they are the same. R8C5 is a dog, so R9C5 is a dog.
40. R8C4 and R8C5 are both dogs, so R8C6 must be a cat (no three in a row).
41. R8C5 and R9C5 are both dogs, so R10C5 must be a cat (no three in a row).
42. Imagine R8C7 were a dog: following the rules from there soon forces a contradiction, so R8C7 must be a cat.
43. R8C6 and R8C7 are both cats, so R8C8 must be a dog (no three in a row).
44. The = clue between R8C8 and R9C8 means they are the same. R8C8 is a dog, so R9C8 is a dog.
45. The = clue between R9C8 and R9C7 means they are the same. R9C8 is a dog, so R9C7 is a dog.
46. R9C5 and R9C7 are both dogs with one square between them, so R9C6 must be a cat.
47. R9C7 and R9C8 are both dogs, so R9C9 must be a cat (no three in a row).
48. R8C6 and R9C6 are both cats, so R10C6 must be a dog (no three in a row).
49. R8C8 and R9C8 are both dogs, so R10C8 must be a cat (no three in a row).
50. The × clue between R10C8 and R10C9 means they are different. R10C8 is a cat, so R10C9 is a dog.
51. Row 8 already has its 5 cats, so R8C9 must be dogs.
52. Imagine R7C10 were a cat: following the rules from there soon forces a contradiction, so R7C10 must be a dog.
53. Imagine R9C10 were a dog: following the rules from there soon forces a contradiction, so R9C10 must be a cat.
54. R8C10 and R9C10 are both cats, so R10C10 must be a dog (no three in a row).
55. Imagine R6C9 were a dog: following the rules from there soon forces a contradiction, so R6C9 must be a cat.
56. Row 6 already has its 5 cats, so R6C10 must be dogs.
57. Imagine R5C8 were a dog: following the rules from there soon forces a contradiction, so R5C8 must be a cat.
58. R5C7 and R5C8 are both cats, so R5C9 must be a dog (no three in a row).
59. Imagine R10C7 were a cat: following the rules from there soon forces a contradiction, so R10C7 must be a dog.
60. Imagine R9C2 were a dog: following the rules from there soon forces a contradiction, so R9C2 must be a cat.
61. Imagine R10C1 were a dog: following the rules from there soon forces a contradiction, so R10C1 must be a cat.
62. Imagine R10C2 were a dog: following the rules from there soon forces a contradiction, so R10C2 must be a cat.
63. R10C1 and R10C2 are both cats, so R10C3 must be a dog (no three in a row).
64. Row 10 already has its 5 dogs, so R10C4 must be cats.
65. Imagine R2C3 were a dog: following the rules from there soon forces a contradiction, so R2C3 must be a cat.
66. Imagine R1C5 were a cat: following the rules from there soon forces a contradiction, so R1C5 must be a dog.
67. The = clue between R1C5 and R1C6 means they are the same. R1C5 is a dog, so R1C6 is a dog.
68. R1C5 and R1C6 are both dogs, so R1C4 must be a cat (no three in a row).
69. R1C5 and R1C6 are both dogs, so R1C7 must be a cat (no three in a row).
70. R1C4 and R3C4 are both cats with one square between them, so R2C4 must be a dog.
71. R2C4 and R2C6 are both dogs with one square between them, so R2C5 must be a cat.
72. R1C7 and R3C7 are both cats with one square between them, so R2C7 must be a dog.
73. R2C6 and R2C7 are both dogs, so R2C8 must be a cat (no three in a row).
74. Column 4 already has its 5 cats, so R9C4 must be dogs.
75. R9C4 and R9C5 are both dogs, so R9C3 must be a cat (no three in a row).
76. Column 6 already has its 5 dogs, so R4C6 must be cats.
77. Row 4 already has its 5 cats, so R4C9 must be dogs.
78. R4C9 and R5C9 are both dogs, so R3C9 must be a cat (no three in a row).
79. Row 4 already has its 5 cats, so R4C10 must be dogs.
80. Column 8 already has its 5 cats, so R1C8 must be dogs.
81. Imagine R1C1 were a cat: following the rules from there soon forces a contradiction, so R1C1 must be a dog.
82. The = clue between R1C1 and R1C2 means they are the same. R1C1 is a dog, so R1C2 is a dog.
83. R1C1 and R1C2 are both dogs, so R1C3 must be a cat (no three in a row).
84. R1C1 and R2C1 are both dogs, so R3C1 must be a cat (no three in a row).
85. R1C2 and R3C2 are both dogs with one square between them, so R2C2 must be a cat.
86. R1C3 and R2C3 are both cats, so R3C3 must be a dog (no three in a row).
87. Row 1 already has its 5 dogs, so R1C9 must be cats.
88. R1C9 and R3C9 are both cats with one square between them, so R2C9 must be a dog.
89. Row 2 already has its 5 dogs, so R2C10 must be cats.
90. R1C10 and R2C10 are both cats, so R3C10 must be a dog (no three in a row).
91. Column 2 already has its 5 cats, so R7C2 must be dogs.
92. Row 7 already has its 5 dogs, so R7C9 must be cats.