Cats & Dogs #232: 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 R2C1 and R3C1 means they are different. R2C1 is a dog, so R3C1 is a cat.
2. The × clue between R2C3 and R2C4 means they are different. R2C3 is a cat, so R2C4 is a dog.
3. The × clue between R6C4 and R6C3 means they are different. R6C4 is a cat, so R6C3 is a dog.
4. R3C1 and R4C1 are both cats, so R5C1 must be a dog (no three in a row).
5. Imagine R2C5 were a dog: following the rules from there soon forces a contradiction, so R2C5 must be a cat.
6. The = clue between R2C5 and R2C6 means they are the same. R2C5 is a cat, so R2C6 is a cat.
7. R2C5 and R2C6 are both cats, so R2C7 must be a dog (no three in a row).
8. R2C7 and R3C7 are both dogs, so R1C7 must be a cat (no three in a row).
9. The × clue between R1C7 and R1C8 means they are different. R1C7 is a cat, so R1C8 is a dog.
10. R2C7 and R3C7 are both dogs, so R4C7 must be a cat (no three in a row).
11. R4C7 and R5C7 are both cats, so R6C7 must be a dog (no three in a row).
12. The × clue between R6C7 and R7C7 means they are different. R6C7 is a dog, so R7C7 is a cat.
13. R7C7 and R7C9 are both cats with one square between them, so R7C8 must be a dog.
14. Imagine R5C8 were a cat: following the rules from there soon forces a contradiction, so R5C8 must be a dog.
15. The = clue between R5C8 and R5C9 means they are the same. R5C8 is a dog, so R5C9 is a dog.
16. R5C8 and R5C9 are both dogs, so R5C10 must be a cat (no three in a row).
17. R5C8 and R7C8 are both dogs with one square between them, so R6C8 must be a cat.
18. Imagine R5C2 were a cat: following the rules from there soon forces a contradiction, so R5C2 must be a dog.
19. The × clue between R5C2 and R5C3 means they are different. R5C2 is a dog, so R5C3 is a cat.
20. Imagine R1C3 were a cat: following the rules from there soon forces a contradiction, so R1C3 must be a dog.
21. Imagine R3C2 were a cat: following the rules from there soon forces a contradiction, so R3C2 must be a dog.
22. R3C2 and R5C2 are both dogs with one square between them, so R4C2 must be a cat.
23. R4C1 and R4C2 are both cats, so R4C3 must be a dog (no three in a row).
24. Imagine R1C6 were a cat: following the rules from there soon forces a contradiction, so R1C6 must be a dog.
25. Imagine R3C3 were a dog: following the rules from there soon forces a contradiction, so R3C3 must be a cat.
26. The = clue between R3C3 and R3C4 means they are the same. R3C3 is a cat, so R3C4 is a cat.
27. R3C3 and R3C4 are both cats, so R3C5 must be a dog (no three in a row).
28. R3C5 and R3C7 are both dogs with one square between them, so R3C6 must be a cat.
29. R2C6 and R3C6 are both cats, so R4C6 must be a dog (no three in a row).
30. Imagine R2C8 were a dog: following the rules from there soon forces a contradiction, so R2C8 must be a cat.
31. Imagine R3C10 were a cat: following the rules from there soon forces a contradiction, so R3C10 must be a dog.
32. Imagine R4C4 were a cat: following the rules from there soon forces a contradiction, so R4C4 must be a dog.
33. R4C3 and R4C4 are both dogs, so R4C5 must be a cat (no three in a row).
34. Imagine R1C2 were a dog: following the rules from there soon forces a contradiction, so R1C2 must be a cat.
35. Imagine R2C2 were a cat: following the rules from there soon forces a contradiction, so R2C2 must be a dog.
36. Imagine R2C9 were a cat: following the rules from there soon forces a contradiction, so R2C9 must be a dog.
37. Row 2 already has its 5 dogs, so R2C10 must be cats.
38. Imagine R4C10 were a cat: following the rules from there soon forces a contradiction, so R4C10 must be a dog.
39. Imagine R5C4 were a dog: following the rules from there soon forces a contradiction, so R5C4 must be a cat.
40. R5C3 and R5C4 are both cats, so R5C5 must be a dog (no three in a row).
41. R5C4 and R6C4 are both cats, so R7C4 must be a dog (no three in a row).
42. Row 5 already has its 5 dogs, so R5C6 must be cats.
43. Imagine R6C5 were a dog: following the rules from there soon forces a contradiction, so R6C5 must be a cat.
44. R6C4 and R6C5 are both cats, so R6C6 must be a dog (no three in a row).
45. Imagine R8C4 were a dog: following the rules from there soon forces a contradiction, so R8C4 must be a cat.
46. The = clue between R8C4 and R9C4 means they are the same. R8C4 is a cat, so R9C4 is a cat.
47. R8C4 and R9C4 are both cats, so R10C4 must be a dog (no three in a row).
48. Column 4 already has its 5 cats, so R1C4 must be dogs.
49. R1C3 and R1C4 are both dogs, so R1C5 must be a cat (no three in a row).
50. Imagine R7C3 were a dog: following the rules from there soon forces a contradiction, so R7C3 must be a cat.
51. Imagine R7C5 were a cat: following the rules from there soon forces a contradiction, so R7C5 must be a dog.
52. R7C4 and R7C5 are both dogs, so R7C6 must be a cat (no three in a row).
53. Column 6 already has its 5 cats, so R8C6 and R9C6 must be dogs.
54. Imagine R1C1 were a cat: following the rules from there soon forces a contradiction, so R1C1 must be a dog.
55. Row 1 already has its 5 dogs, so R1C9 must be cats.
56. Imagine R3C8 were a dog: following the rules from there soon forces a contradiction, so R3C8 must be a cat.
57. R2C8 and R3C8 are both cats, so R4C8 must be a dog (no three in a row).
58. R4C8 and R4C10 are both dogs with one square between them, so R4C9 must be a cat.
59. Row 3 already has its 5 cats, so R3C9 must be dogs.
60. Imagine R6C9 were a cat: following the rules from there soon forces a contradiction, so R6C9 must be a dog.
61. The × clue between R6C9 and R6C10 means they are different. R6C9 is a dog, so R6C10 is a cat.
62. The × clue between R6C10 and R7C10 means they are different. R6C10 is a cat, so R7C10 is a dog.
63. The × clue between R7C10 and R8C10 means they are different. R7C10 is a dog, so R8C10 is a cat.
64. Column 10 already has its 5 cats, so R9C10 and R10C10 must be dogs.
65. Imagine R8C3 were a cat: following the rules from there soon forces a contradiction, so R8C3 must be a dog.
66. Imagine R8C5 were a cat: following the rules from there soon forces a contradiction, so R8C5 must be a dog.
67. R8C5 and R8C6 are both dogs, so R8C7 must be a cat (no three in a row).
68. R7C5 and R8C5 are both dogs, so R9C5 must be a cat (no three in a row).
69. The × clue between R9C5 and R10C5 means they are different. R9C5 is a cat, so R10C5 is a dog.
70. R9C4 and R9C5 are both cats, so R9C3 must be a dog (no three in a row).
71. R10C4 and R10C5 are both dogs, so R10C3 must be a cat (no three in a row).
72. R7C7 and R8C7 are both cats, so R9C7 must be a dog (no three in a row).
73. R9C6 and R9C7 are both dogs, so R9C8 must be a cat (no three in a row).
74. Column 7 already has its 5 cats, so R10C7 must be dogs.
75. Imagine R8C1 were a dog: following the rules from there soon forces a contradiction, so R8C1 must be a cat.
76. Imagine R6C1 were a dog: following the rules from there soon forces a contradiction, so R6C1 must be a cat.
77. R6C1 and R8C1 are both cats with one square between them, so R7C1 must be a dog.
78. Row 6 already has its 5 cats, so R6C2 must be dogs.
79. R5C2 and R6C2 are both dogs, so R7C2 must be a cat (no three in a row).
80. Imagine R8C2 were a cat: following the rules from there soon forces a contradiction, so R8C2 must be a dog.
81. The × clue between R8C2 and R9C2 means they are different. R8C2 is a dog, so R9C2 is a cat.
82. Column 2 already has its 5 dogs, so R10C2 must be cats.
83. R10C2 and R10C3 are both cats, so R10C1 must be a dog (no three in a row).
84. Row 10 already has its 5 dogs, so R10C8 must be cats.
85. R9C8 and R10C8 are both cats, so R8C8 must be a dog (no three in a row).
86. The × clue between R8C8 and R8C9 means they are different. R8C8 is a dog, so R8C9 is a cat.
87. R7C9 and R8C9 are both cats, so R9C9 must be a dog (no three in a row).
88. Row 9 already has its 5 dogs, so R9C1 must be cats.
89. Row 10 already has its 5 dogs, so R10C9 must be cats.