Cats & Dogs #256: 10x10 Grid Puzzle (Hard)

Step-by-step solution

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

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