Cats & Dogs #249: 10x10 Grid Puzzle (Hard)

Step-by-step solution

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

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