Cats & Dogs #267: 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 R10C2 and R10C3 means they are the same. R10C2 is a cat, so R10C3 is a cat.
2. R10C2 and R10C3 are both cats, so R10C1 must be a dog (no three in a row).
3. R10C2 and R10C3 are both cats, so R10C4 must be a dog (no three in a row).
4. Imagine R3C6 were a dog: following the rules from there soon forces a contradiction, so R3C6 must be a cat.
5. The × clue between R3C6 and R3C7 means they are different. R3C6 is a cat, so R3C7 is a dog.
6. The = clue between R3C6 and R4C6 means they are the same. R3C6 is a cat, so R4C6 is a cat.
7. R3C7 and R3C8 are both dogs, so R3C9 must be a cat (no three in a row).
8. R3C6 and R4C6 are both cats, so R5C6 must be a dog (no three in a row).
9. Imagine R1C8 were a dog: following the rules from there soon forces a contradiction, so R1C8 must be a cat.
10. Imagine R2C7 were a dog: following the rules from there soon forces a contradiction, so R2C7 must be a cat.
11. The × clue between R2C7 and R2C8 means they are different. R2C7 is a cat, so R2C8 is a dog.
12. R2C8 and R3C8 are both dogs, so R4C8 must be a cat (no three in a row).
13. The = clue between R4C8 and R5C8 means they are the same. R4C8 is a cat, so R5C8 is a cat.
14. R4C6 and R4C8 are both cats with one square between them, so R4C7 must be a dog.
15. R3C7 and R4C7 are both dogs, so R5C7 must be a cat (no three in a row).
16. R5C7 and R5C8 are both cats, so R5C9 must be a dog (no three in a row).
17. R4C8 and R5C8 are both cats, so R6C8 must be a dog (no three in a row).
18. Imagine R4C4 were a cat: following the rules from there soon forces a contradiction, so R4C4 must be a dog.
19. Imagine R5C3 were a cat: following the rules from there soon forces a contradiction, so R5C3 must be a dog.
20. The = clue between R5C3 and R6C3 means they are the same. R5C3 is a dog, so R6C3 is a dog.
21. R5C3 and R6C3 are both dogs, so R4C3 must be a cat (no three in a row).
22. R5C3 and R6C3 are both dogs, so R7C3 must be a cat (no three in a row).
23. The × clue between R7C3 and R7C4 means they are different. R7C3 is a cat, so R7C4 is a dog.
24. R7C2 and R7C3 are both cats, so R7C1 must be a dog (no three in a row).
25. Imagine R5C4 were a dog: following the rules from there soon forces a contradiction, so R5C4 must be a cat.
26. Imagine R5C5 were a cat: following the rules from there soon forces a contradiction, so R5C5 must be a dog.
27. The = clue between R5C5 and R6C5 means they are the same. R5C5 is a dog, so R6C5 is a dog.
28. R5C5 and R6C5 are both dogs, so R4C5 must be a cat (no three in a row).
29. R5C5 and R6C5 are both dogs, so R7C5 must be a cat (no three in a row).
30. The = clue between R7C5 and R7C6 means they are the same. R7C5 is a cat, so R7C6 is a cat.
31. R7C5 and R7C6 are both cats, so R7C7 must be a dog (no three in a row).
32. Imagine R2C1 were a dog: following the rules from there soon forces a contradiction, so R2C1 must be a cat.
33. Imagine R4C1 were a cat: following the rules from there soon forces a contradiction, so R4C1 must be a dog.
34. R3C1 and R4C1 are both dogs, so R5C1 must be a cat (no three in a row).
35. The × clue between R5C1 and R5C2 means they are different. R5C1 is a cat, so R5C2 is a dog.
36. Row 5 already has its 5 dogs, so R5C10 must be cats.
37. The = clue between R5C10 and R4C10 means they are the same. R5C10 is a cat, so R4C10 is a cat.
38. R4C8 and R4C10 are both cats with one square between them, so R4C9 must be a dog.
39. R4C9 and R5C9 are both dogs, so R6C9 must be a cat (no three in a row).
40. R4C10 and R5C10 are both cats, so R3C10 must be a dog (no three in a row).
41. R4C10 and R5C10 are both cats, so R6C10 must be a dog (no three in a row).
42. Row 4 already has its 5 cats, so R4C2 must be dogs.
43. R4C2 and R5C2 are both dogs, so R3C2 must be a cat (no three in a row).
44. R4C2 and R5C2 are both dogs, so R6C2 must be a cat (no three in a row).
45. R6C2 and R7C2 are both cats, so R8C2 must be a dog (no three in a row).
46. The × clue between R8C2 and R8C1 means they are different. R8C2 is a dog, so R8C1 is a cat.
47. Imagine R2C3 were a cat: following the rules from there soon forces a contradiction, so R2C3 must be a dog.
48. Imagine R2C4 were a dog: following the rules from there soon forces a contradiction, so R2C4 must be a cat.
49. Imagine R2C5 were a cat: following the rules from there soon forces a contradiction, so R2C5 must be a dog.
50. Imagine R3C3 were a dog: following the rules from there soon forces a contradiction, so R3C3 must be a cat.
51. R3C2 and R3C3 are both cats, so R3C4 must be a dog (no three in a row).
52. Row 3 already has its 5 dogs, so R3C5 must be cats.
53. Imagine R1C3 were a cat: following the rules from there soon forces a contradiction, so R1C3 must be a dog.
54. Imagine R7C10 were a cat: following the rules from there soon forces a contradiction, so R7C10 must be a dog.
55. R6C10 and R7C10 are both dogs, so R8C10 must be a cat (no three in a row).
56. R8C10 and R10C10 are both cats with one square between them, so R9C10 must be a dog.
57. Imagine R8C3 were a dog: following the rules from there soon forces a contradiction, so R8C3 must be a cat.
58. The = clue between R8C3 and R8C4 means they are the same. R8C3 is a cat, so R8C4 is a cat.
59. R8C3 and R8C4 are both cats, so R8C5 must be a dog (no three in a row).
60. R7C3 and R8C3 are both cats, so R9C3 must be a dog (no three in a row).
61. Imagine R1C1 were a dog: following the rules from there soon forces a contradiction, so R1C1 must be a cat.
62. Imagine R1C5 were a dog: following the rules from there soon forces a contradiction, so R1C5 must be a cat.
63. Imagine R1C6 were a cat: following the rules from there soon forces a contradiction, so R1C6 must be a dog.
64. Imagine R1C2 were a cat: following the rules from there soon forces a contradiction, so R1C2 must be a dog.
65. R1C2 and R1C3 are both dogs, so R1C4 must be a cat (no three in a row).
66. Column 4 already has its 5 cats, so R9C4 must be dogs.
67. R9C3 and R9C4 are both dogs, so R9C2 must be a cat (no three in a row).
68. R9C3 and R9C4 are both dogs, so R9C5 must be a cat (no three in a row).
69. Column 2 already has its 5 cats, so R2C2 must be dogs.
70. Row 2 already has its 5 dogs, so R2C9 must be cats.
71. R2C9 and R3C9 are both cats, so R1C9 must be a dog (no three in a row).
72. Row 2 already has its 5 dogs, so R2C10 must be cats.
73. Column 5 already has its 5 cats, so R10C5 must be dogs.
74. R10C4 and R10C5 are both dogs, so R10C6 must be a cat (no three in a row).
75. The = clue between R10C6 and R9C6 means they are the same. R10C6 is a cat, so R9C6 is a cat.
76. R9C5 and R9C6 are both cats, so R9C7 must be a dog (no three in a row).
77. R7C6 and R9C6 are both cats with one square between them, so R8C6 must be a dog.
78. R8C5 and R8C6 are both dogs, so R8C7 must be a cat (no three in a row).
79. Row 8 already has its 5 cats, so R8C8 must be dogs.
80. R6C8 and R8C8 are both dogs with one square between them, so R7C8 must be a cat.
81. Row 7 already has its 5 cats, so R7C9 must be dogs.
82. Row 8 already has its 5 cats, so R8C9 must be dogs.
83. R7C9 and R8C9 are both dogs, so R9C9 must be a cat (no three in a row).
84. Column 6 already has its 5 cats, so R6C6 must be dogs.
85. R6C5 and R6C6 are both dogs, so R6C7 must be a cat (no three in a row).
86. Row 6 already has its 5 dogs, so R6C1 must be cats.
87. Column 1 already has its 5 cats, so R9C1 must be dogs.
88. Row 9 already has its 5 dogs, so R9C8 must be cats.
89. Column 8 already has its 5 cats, so R10C8 must be dogs.
90. Column 9 already has its 5 dogs, so R10C9 must be cats.
91. Row 10 already has its 5 cats, so R10C7 must be dogs.
92. Column 7 already has its 5 dogs, so R1C7 must be cats.
93. Row 1 already has its 5 cats, so R1C10 must be dogs.