Cats & Dogs #264: 10x10 Grid Puzzle (Hard)

Step-by-step solution

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

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