Cats & Dogs #258: 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 R1C1 and R1C2 means they are the same. R1C1 is a cat, so R1C2 is a cat.
2. The × clue between R6C5 and R5C5 means they are different. R6C5 is a dog, so R5C5 is a cat.
3. R1C1 and R1C2 are both cats, so R1C3 must be a dog (no three in a row).
4. Imagine R1C9 were a dog: following the rules from there soon forces a contradiction, so R1C9 must be a cat.
5. The = clue between R1C9 and R2C9 means they are the same. R1C9 is a cat, so R2C9 is a cat.
6. The × clue between R2C9 and R2C10 means they are different. R2C9 is a cat, so R2C10 is a dog.
7. R1C9 and R2C9 are both cats, so R3C9 must be a dog (no three in a row).
8. Imagine R2C6 were a dog: following the rules from there soon forces a contradiction, so R2C6 must be a cat.
9. Imagine R3C7 were a dog: following the rules from there soon forces a contradiction, so R3C7 must be a cat.
10. Imagine R4C1 were a dog: following the rules from there soon forces a contradiction, so R4C1 must be a cat.
11. The = clue between R4C1 and R5C1 means they are the same. R4C1 is a cat, so R5C1 is a cat.
12. R4C1 and R5C1 are both cats, so R6C1 must be a dog (no three in a row).
13. Imagine R2C1 were a cat: following the rules from there soon forces a contradiction, so R2C1 must be a dog.
14. Imagine R2C8 were a cat: following the rules from there soon forces a contradiction, so R2C8 must be a dog.
15. The = clue between R2C8 and R3C8 means they are the same. R2C8 is a dog, so R3C8 is a dog.
16. R3C8 and R3C9 are both dogs, so R3C10 must be a cat (no three in a row).
17. R2C8 and R3C8 are both dogs, so R1C8 must be a cat (no three in a row).
18. R1C8 and R1C9 are both cats, so R1C7 must be a dog (no three in a row).
19. R1C8 and R1C9 are both cats, so R1C10 must be a dog (no three in a row).
20. R2C8 and R3C8 are both dogs, so R4C8 must be a cat (no three in a row).
21. Imagine R1C4 were a cat: following the rules from there soon forces a contradiction, so R1C4 must be a dog.
22. R1C3 and R1C4 are both dogs, so R1C5 must be a cat (no three in a row).
23. Row 1 already has its 5 cats, so R1C6 must be dogs.
24. Imagine R2C2 were a dog: following the rules from there soon forces a contradiction, so R2C2 must be a cat.
25. R1C2 and R2C2 are both cats, so R3C2 must be a dog (no three in a row).
26. R3C1 and R3C2 are both dogs, so R3C3 must be a cat (no three in a row).
27. Imagine R2C3 were a dog: following the rules from there soon forces a contradiction, so R2C3 must be a cat.
28. R2C2 and R2C3 are both cats, so R2C4 must be a dog (no three in a row).
29. R2C3 and R3C3 are both cats, so R4C3 must be a dog (no three in a row).
30. R1C4 and R2C4 are both dogs, so R3C4 must be a cat (no three in a row).
31. R3C3 and R3C4 are both cats, so R3C5 must be a dog (no three in a row).
32. Row 2 already has its 5 dogs, so R2C5 must be cats.
33. Row 3 already has its 5 dogs, so R3C6 must be cats.
34. R2C6 and R3C6 are both cats, so R4C6 must be a dog (no three in a row).
35. Imagine R4C10 were a cat: following the rules from there soon forces a contradiction, so R4C10 must be a dog.
36. The = clue between R4C10 and R5C10 means they are the same. R4C10 is a dog, so R5C10 is a dog.
37. R5C8 and R5C10 are both dogs with one square between them, so R5C9 must be a cat.
38. R4C10 and R5C10 are both dogs, so R6C10 must be a cat (no three in a row).
39. Imagine R5C4 were a cat: following the rules from there soon forces a contradiction, so R5C4 must be a dog.
40. Imagine R5C6 were a dog: following the rules from there soon forces a contradiction, so R5C6 must be a cat.
41. The = clue between R5C6 and R6C6 means they are the same. R5C6 is a cat, so R6C6 is a cat.
42. R5C5 and R5C6 are both cats, so R5C7 must be a dog (no three in a row).
43. R5C6 and R6C6 are both cats, so R7C6 must be a dog (no three in a row).
44. Imagine R6C8 were a cat: following the rules from there soon forces a contradiction, so R6C8 must be a dog.
45. The × clue between R6C8 and R7C8 means they are different. R6C8 is a dog, so R7C8 is a cat.
46. Imagine R7C10 were a dog: following the rules from there soon forces a contradiction, so R7C10 must be a cat.
47. R6C10 and R7C10 are both cats, so R8C10 must be a dog (no three in a row).
48. Column 10 already has its 5 dogs, so R9C10 and R10C10 must be cats.
49. Imagine R7C2 were a cat: following the rules from there soon forces a contradiction, so R7C2 must be a dog.
50. The = clue between R7C2 and R7C3 means they are the same. R7C2 is a dog, so R7C3 is a dog.
51. R7C2 and R7C3 are both dogs, so R7C1 must be a cat (no three in a row).
52. R7C2 and R7C3 are both dogs, so R7C4 must be a cat (no three in a row).
53. Column 1 already has its 5 cats, so R8C1 and R9C1 must be dogs.
54. Imagine R8C5 were a dog: following the rules from there soon forces a contradiction, so R8C5 must be a cat.
55. Imagine R4C4 were a dog: following the rules from there soon forces a contradiction, so R4C4 must be a cat.
56. Imagine R4C5 were a cat: following the rules from there soon forces a contradiction, so R4C5 must be a dog.
57. R4C5 and R4C6 are both dogs, so R4C7 must be a cat (no three in a row).
58. R4C7 and R4C8 are both cats, so R4C9 must be a dog (no three in a row).
59. Row 4 already has its 5 dogs, so R4C2 must be cats.
60. Imagine R7C5 were a cat: following the rules from there soon forces a contradiction, so R7C5 must be a dog.
61. R7C5 and R7C6 are both dogs, so R7C7 must be a cat (no three in a row).
62. The = clue between R7C7 and R8C7 means they are the same. R7C7 is a cat, so R8C7 is a cat.
63. R8C5 and R8C7 are both cats with one square between them, so R8C6 must be a dog.
64. R7C6 and R8C6 are both dogs, so R9C6 must be a cat (no three in a row).
65. R7C7 and R8C7 are both cats, so R6C7 must be a dog (no three in a row).
66. R6C7 and R6C8 are both dogs, so R6C9 must be a cat (no three in a row).
67. R7C7 and R8C7 are both cats, so R9C7 must be a dog (no three in a row).
68. The = clue between R9C7 and R9C8 means they are the same. R9C7 is a dog, so R9C8 is a dog.
69. R9C7 and R9C8 are both dogs, so R9C9 must be a cat (no three in a row).
70. Column 6 already has its 5 cats, so R10C6 must be dogs.
71. Column 7 already has its 5 dogs, so R10C7 must be cats.
72. Column 8 already has its 5 dogs, so R8C8 must be cats.
73. R8C7 and R8C8 are both cats, so R8C9 must be a dog (no three in a row).
74. Column 8 already has its 5 dogs, so R10C8 must be cats.
75. R10C7 and R10C8 are both cats, so R10C9 must be a dog (no three in a row).
76. Imagine R5C2 were a cat: following the rules from there soon forces a contradiction, so R5C2 must be a dog.
77. R5C2 and R5C4 are both dogs with one square between them, so R5C3 must be a cat.
78. R5C2 and R7C2 are both dogs with one square between them, so R6C2 must be a cat.
79. Imagine R6C3 were a dog: following the rules from there soon forces a contradiction, so R6C3 must be a cat.
80. R6C2 and R6C3 are both cats, so R6C4 must be a dog (no three in a row).
81. Imagine R8C2 were a dog: following the rules from there soon forces a contradiction, so R8C2 must be a cat.
82. The × clue between R8C2 and R8C3 means they are different. R8C2 is a cat, so R8C3 is a dog.
83. R7C3 and R8C3 are both dogs, so R9C3 must be a cat (no three in a row).
84. Row 8 already has its 5 dogs, so R8C4 must be cats.
85. R7C4 and R8C4 are both cats, so R9C4 must be a dog (no three in a row).
86. Column 2 already has its 5 cats, so R9C2 must be dogs.
87. Row 9 already has its 5 dogs, so R9C5 must be cats.
88. R8C5 and R9C5 are both cats, so R10C5 must be a dog (no three in a row).
89. R10C5 and R10C6 are both dogs, so R10C4 must be a cat (no three in a row).
90. Row 10 already has its 5 cats, so R10C2 and R10C3 must be dogs.