Cats & Dogs #209: 10x10 Grid Puzzle (Hard)

Step-by-step solution

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

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