Cats & Dogs #269: 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 R6C7 and R6C6 means they are different. R6C7 is a cat, so R6C6 is a dog.
2. The × clue between R8C2 and R9C2 means they are different. R8C2 is a cat, so R9C2 is a dog.
3. The × clue between R8C10 and R8C9 means they are different. R8C10 is a dog, so R8C9 is a cat.
4. The × clue between R8C10 and R9C10 means they are different. R8C10 is a dog, so R9C10 is a cat.
5. The × clue between R9C7 and R9C6 means they are different. R9C7 is a cat, so R9C6 is a dog.
6. The = clue between R9C7 and R10C7 means they are the same. R9C7 is a cat, so R10C7 is a cat.
7. R9C7 and R10C7 are both cats, so R8C7 must be a dog (no three in a row).
8. Imagine R1C10 were a cat: following the rules from there soon forces a contradiction, so R1C10 must be a dog.
9. The = clue between R1C10 and R2C10 means they are the same. R1C10 is a dog, so R2C10 is a dog.
10. Imagine R2C3 were a dog: following the rules from there soon forces a contradiction, so R2C3 must be a cat.
11. The = clue between R2C3 and R3C3 means they are the same. R2C3 is a cat, so R3C3 is a cat.
12. R2C3 and R3C3 are both cats, so R4C3 must be a dog (no three in a row).
13. Imagine R2C2 were a cat: following the rules from there soon forces a contradiction, so R2C2 must be a dog.
14. The = clue between R2C2 and R3C2 means they are the same. R2C2 is a dog, so R3C2 is a dog.
15. R2C2 and R3C2 are both dogs, so R1C2 must be a cat (no three in a row).
16. R2C2 and R3C2 are both dogs, so R4C2 must be a cat (no three in a row).
17. Imagine R3C4 were a dog: following the rules from there soon forces a contradiction, so R3C4 must be a cat.
18. R3C3 and R3C4 are both cats, so R3C5 must be a dog (no three in a row).
19. R3C5 and R3C6 are both dogs, so R3C7 must be a cat (no three in a row).
20. Imagine R5C6 were a dog: following the rules from there soon forces a contradiction, so R5C6 must be a cat.
21. Imagine R7C6 were a cat: following the rules from there soon forces a contradiction, so R7C6 must be a dog.
22. The × clue between R7C6 and R8C6 means they are different. R7C6 is a dog, so R8C6 is a cat.
23. Imagine R1C7 were a cat: following the rules from there soon forces a contradiction, so R1C7 must be a dog.
24. Imagine R4C7 were a cat: following the rules from there soon forces a contradiction, so R4C7 must be a dog.
25. Imagine R7C4 were a dog: following the rules from there soon forces a contradiction, so R7C4 must be a cat.
26. Imagine R2C7 were a cat: following the rules from there soon forces a contradiction, so R2C7 must be a dog.
27. Imagine R2C1 were a dog: following the rules from there soon forces a contradiction, so R2C1 must be a cat.
28. Imagine R2C5 were a dog: following the rules from there soon forces a contradiction, so R2C5 must be a cat.
29. Imagine R2C6 were a dog: following the rules from there soon forces a contradiction, so R2C6 must be a cat.
30. Imagine R5C3 were a dog: following the rules from there soon forces a contradiction, so R5C3 must be a cat.
31. The × clue between R5C3 and R5C4 means they are different. R5C3 is a cat, so R5C4 is a dog.
32. The × clue between R5C3 and R6C3 means they are different. R5C3 is a cat, so R6C3 is a dog.
33. Imagine R1C4 were a cat: following the rules from there soon forces a contradiction, so R1C4 must be a dog.
34. Imagine R5C1 were a cat: following the rules from there soon forces a contradiction, so R5C1 must be a dog.
35. The × clue between R5C1 and R6C1 means they are different. R5C1 is a dog, so R6C1 is a cat.
36. Imagine R5C7 were a cat: following the rules from there soon forces a contradiction, so R5C7 must be a dog.
37. Column 7 already has its 5 dogs, so R7C7 must be cats.
38. Imagine R5C2 were a dog: following the rules from there soon forces a contradiction, so R5C2 must be a cat.
39. R4C2 and R5C2 are both cats, so R6C2 must be a dog (no three in a row).
40. R6C2 and R6C3 are both dogs, so R6C4 must be a cat (no three in a row).
41. The × clue between R6C4 and R6C5 means they are different. R6C4 is a cat, so R6C5 is a dog.
42. The = clue between R6C5 and R7C5 means they are the same. R6C5 is a dog, so R7C5 is a dog.
43. R6C4 and R7C4 are both cats, so R8C4 must be a dog (no three in a row).
44. R6C5 and R7C5 are both dogs, so R5C5 must be a cat (no three in a row).
45. R6C5 and R7C5 are both dogs, so R8C5 must be a cat (no three in a row).
46. Column 5 already has its 5 cats, so R9C5 must be dogs.
47. R9C5 and R9C6 are both dogs, so R9C4 must be a cat (no three in a row).
48. Column 5 already has its 5 cats, so R10C5 must be dogs.
49. Imagine R1C6 were a dog: following the rules from there soon forces a contradiction, so R1C6 must be a cat.
50. Imagine R4C4 were a cat: following the rules from there soon forces a contradiction, so R4C4 must be a dog.
51. Column 4 already has its 5 dogs, so R10C4 must be cats.
52. Imagine R4C6 were a dog: following the rules from there soon forces a contradiction, so R4C6 must be a cat.
53. Column 6 already has its 5 cats, so R10C6 must be dogs.
54. Imagine R6C10 were a dog: following the rules from there soon forces a contradiction, so R6C10 must be a cat.
55. Imagine R7C1 were a dog: following the rules from there soon forces a contradiction, so R7C1 must be a cat.
56. Imagine R1C1 were a cat: following the rules from there soon forces a contradiction, so R1C1 must be a dog.
57. Row 1 already has its 5 dogs, so R1C8 and R1C9 must be cats.
58. Imagine R7C2 were a dog: following the rules from there soon forces a contradiction, so R7C2 must be a cat.
59. The × clue between R7C2 and R7C3 means they are different. R7C2 is a cat, so R7C3 is a dog.
60. The × clue between R7C3 and R8C3 means they are different. R7C3 is a dog, so R8C3 is a cat.
61. Row 8 already has its 5 cats, so R8C8 must be dogs.
62. The × clue between R8C8 and R9C8 means they are different. R8C8 is a dog, so R9C8 is a cat.
63. The × clue between R9C8 and R10C8 means they are different. R9C8 is a cat, so R10C8 is a dog.
64. R9C7 and R9C8 are both cats, so R9C9 must be a dog (no three in a row).
65. The × clue between R9C9 and R10C9 means they are different. R9C9 is a dog, so R10C9 is a cat.
66. Column 2 already has its 5 cats, so R10C2 must be dogs.
67. The × clue between R10C2 and R10C1 means they are different. R10C2 is a dog, so R10C1 is a cat.
68. The × clue between R10C1 and R9C1 means they are different. R10C1 is a cat, so R9C1 is a dog.
69. R9C1 and R9C2 are both dogs, so R9C3 must be a cat (no three in a row).
70. R8C3 and R9C3 are both cats, so R10C3 must be a dog (no three in a row).
71. Row 10 already has its 5 dogs, so R10C10 must be cats.
72. Imagine R4C9 were a dog: following the rules from there soon forces a contradiction, so R4C9 must be a cat.
73. The × clue between R4C9 and R5C9 means they are different. R4C9 is a cat, so R5C9 is a dog.
74. R5C7 and R5C9 are both dogs with one square between them, so R5C8 must be a cat.
75. The = clue between R5C8 and R6C8 means they are the same. R5C8 is a cat, so R6C8 is a cat.
76. R6C7 and R6C8 are both cats, so R6C9 must be a dog (no three in a row).
77. R5C8 and R6C8 are both cats, so R4C8 must be a dog (no three in a row).
78. R5C8 and R6C8 are both cats, so R7C8 must be a dog (no three in a row).
79. R5C9 and R6C9 are both dogs, so R7C9 must be a cat (no three in a row).
80. Row 7 already has its 5 cats, so R7C10 must be dogs.
81. Column 9 already has its 5 cats, so R2C9 must be dogs.
82. The × clue between R2C9 and R2C8 means they are different. R2C9 is a dog, so R2C8 is a cat.
83. R1C8 and R2C8 are both cats, so R3C8 must be a dog (no three in a row).
84. Column 9 already has its 5 cats, so R3C9 must be dogs.
85. Row 3 already has its 5 dogs, so R3C1 must be cats.
86. R2C1 and R3C1 are both cats, so R4C1 must be a dog (no three in a row).
87. Row 4 already has its 5 dogs, so R4C10 must be cats.