Cats & Dogs #257: 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 R10C7 and R9C7 means they are the same. R10C7 is a cat, so R9C7 is a cat.
2. The × clue between R9C7 and R9C6 means they are different. R9C7 is a cat, so R9C6 is a dog.
3. R1C9 and R1C10 are both dogs, so R1C8 must be a cat (no three in a row).
4. R7C9 and R7C10 are both dogs, so R7C8 must be a cat (no three in a row).
5. R9C4 and R9C6 are both dogs with one square between them, so R9C5 must be a cat.
6. R9C6 and R10C6 are both dogs, so R8C6 must be a cat (no three in a row).
7. R9C7 and R10C7 are both cats, so R8C7 must be a dog (no three in a row).
8. R1C9 and R2C9 are both dogs, so R3C9 must be a cat (no three in a row).
9. Imagine R4C2 were a cat: following the rules from there soon forces a contradiction, so R4C2 must be a dog.
10. The = clue between R4C2 and R5C2 means they are the same. R4C2 is a dog, so R5C2 is a dog.
11. R4C2 and R5C2 are both dogs, so R3C2 must be a cat (no three in a row).
12. Imagine R5C8 were a dog: following the rules from there soon forces a contradiction, so R5C8 must be a cat.
13. The × clue between R5C8 and R6C8 means they are different. R5C8 is a cat, so R6C8 is a dog.
14. Imagine R5C9 were a cat: following the rules from there soon forces a contradiction, so R5C9 must be a dog.
15. R5C9 and R7C9 are both dogs with one square between them, so R6C9 must be a cat.
16. Imagine R4C9 were a dog: following the rules from there soon forces a contradiction, so R4C9 must be a cat.
17. Imagine R5C10 were a dog: following the rules from there soon forces a contradiction, so R5C10 must be a cat.
18. The = clue between R5C10 and R6C10 means they are the same. R5C10 is a cat, so R6C10 is a cat.
19. R5C10 and R6C10 are both cats, so R4C10 must be a dog (no three in a row).
20. Imagine R6C7 were a dog: following the rules from there soon forces a contradiction, so R6C7 must be a cat.
21. Imagine R5C1 were a dog: following the rules from there soon forces a contradiction, so R5C1 must be a cat.
22. The × clue between R5C1 and R6C1 means they are different. R5C1 is a cat, so R6C1 is a dog.
23. Imagine R5C6 were a dog: following the rules from there soon forces a contradiction, so R5C6 must be a cat.
24. The × clue between R5C6 and R6C6 means they are different. R5C6 is a cat, so R6C6 is a dog.
25. Imagine R5C5 were a cat: following the rules from there soon forces a contradiction, so R5C5 must be a dog.
26. Imagine R4C4 were a cat: following the rules from there soon forces a contradiction, so R4C4 must be a dog.
27. Imagine R4C5 were a dog: following the rules from there soon forces a contradiction, so R4C5 must be a cat.
28. Imagine R6C3 were a cat: following the rules from there soon forces a contradiction, so R6C3 must be a dog.
29. The = clue between R6C3 and R7C3 means they are the same. R6C3 is a dog, so R7C3 is a dog.
30. R6C3 and R7C3 are both dogs, so R5C3 must be a cat (no three in a row).
31. R4C3 and R5C3 are both cats, so R3C3 must be a dog (no three in a row).
32. R6C3 and R7C3 are both dogs, so R8C3 must be a cat (no three in a row).
33. Row 5 already has its 5 cats, so R5C4 must be dogs.
34. R4C4 and R5C4 are both dogs, so R3C4 must be a cat (no three in a row).
35. R4C4 and R5C4 are both dogs, so R6C4 must be a cat (no three in a row).
36. Row 6 already has its 5 cats, so R6C5 must be dogs.
37. R5C5 and R6C5 are both dogs, so R7C5 must be a cat (no three in a row).
38. The × clue between R7C5 and R7C4 means they are different. R7C5 is a cat, so R7C4 is a dog.
39. The × clue between R7C5 and R7C6 means they are different. R7C5 is a cat, so R7C6 is a dog.
40. R7C3 and R7C4 are both dogs, so R7C2 must be a cat (no three in a row).
41. R6C2 and R7C2 are both cats, so R8C2 must be a dog (no three in a row).
42. R7C4 and R9C4 are both dogs with one square between them, so R8C4 must be a cat.
43. R8C3 and R8C4 are both cats, so R8C5 must be a dog (no three in a row).
44. Row 7 already has its 5 dogs, so R7C1 and R7C7 must be cats.
45. Imagine R1C6 were a dog: following the rules from there soon forces a contradiction, so R1C6 must be a cat.
46. R1C6 and R1C8 are both cats with one square between them, so R1C7 must be a dog.
47. Imagine R1C5 were a cat: following the rules from there soon forces a contradiction, so R1C5 must be a dog.
48. The = clue between R1C5 and R2C5 means they are the same. R1C5 is a dog, so R2C5 is a dog.
49. The × clue between R2C5 and R3C5 means they are different. R2C5 is a dog, so R3C5 is a cat.
50. R3C4 and R3C5 are both cats, so R3C6 must be a dog (no three in a row).
51. Column 5 already has its 5 dogs, so R10C5 must be cats.
52. Column 6 already has its 5 dogs, so R2C6 and R4C6 must be cats.
53. The × clue between R4C6 and R4C7 means they are different. R4C6 is a cat, so R4C7 is a dog.
54. R4C7 and R5C7 are both dogs, so R3C7 must be a cat (no three in a row).
55. R3C7 and R3C9 are both cats with one square between them, so R3C8 must be a dog.
56. Row 3 already has its 5 cats, so R3C1 and R3C10 must be dogs.
57. R1C10 and R3C10 are both dogs with one square between them, so R2C10 must be a cat.
58. Column 7 already has its 5 cats, so R2C7 must be dogs.
59. R2C7 and R2C9 are both dogs with one square between them, so R2C8 must be a cat.
60. Imagine R1C1 were a dog: following the rules from there soon forces a contradiction, so R1C1 must be a cat.
61. Imagine R1C4 were a dog: following the rules from there soon forces a contradiction, so R1C4 must be a cat.
62. R1C4 and R3C4 are both cats with one square between them, so R2C4 must be a dog.
63. R2C4 and R2C5 are both dogs, so R2C3 must be a cat (no three in a row).
64. Column 4 already has its 5 dogs, so R10C4 must be cats.
65. R10C4 and R10C5 are both cats, so R10C3 must be a dog (no three in a row).
66. Imagine R4C1 were a dog: following the rules from there soon forces a contradiction, so R4C1 must be a cat.
67. Row 4 already has its 5 cats, so R4C8 must be dogs.
68. Imagine R1C2 were a cat: following the rules from there soon forces a contradiction, so R1C2 must be a dog.
69. Row 1 already has its 5 dogs, so R1C3 must be cats.
70. Column 3 already has its 5 cats, so R9C3 must be dogs.
71. R9C3 and R9C4 are both dogs, so R9C2 must be a cat (no three in a row).
72. Imagine R2C1 were a cat: following the rules from there soon forces a contradiction, so R2C1 must be a dog.
73. Row 2 already has its 5 dogs, so R2C2 must be cats.
74. Column 2 already has its 5 cats, so R10C2 must be dogs.
75. R10C2 and R10C3 are both dogs, so R10C1 must be a cat (no three in a row).
76. Column 1 already has its 5 cats, so R8C1 and R9C1 must be dogs.
77. Imagine R8C8 were a dog: following the rules from there soon forces a contradiction, so R8C8 must be a cat.
78. The = clue between R8C8 and R8C9 means they are the same. R8C8 is a cat, so R8C9 is a cat.
79. R8C8 and R8C9 are both cats, so R8C10 must be a dog (no three in a row).
80. R7C8 and R8C8 are both cats, so R9C8 must be a dog (no three in a row).
81. R7C10 and R8C10 are both dogs, so R9C10 must be a cat (no three in a row).
82. Row 9 already has its 5 dogs, so R9C9 must be cats.
83. R8C9 and R9C9 are both cats, so R10C9 must be a dog (no three in a row).
84. Column 8 already has its 5 cats, so R10C8 must be dogs.
85. R10C8 and R10C9 are both dogs, so R10C10 must be a cat (no three in a row).