Cats & Dogs #281: 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 R1C6 and R1C7 means they are different. R1C6 is a dog, so R1C7 is a cat.
2. The × clue between R2C8 and R3C8 means they are different. R2C8 is a cat, so R3C8 is a dog.
3. The × clue between R3C9 and R2C9 means they are different. R3C9 is a cat, so R2C9 is a dog.
4. The × clue between R2C9 and R1C9 means they are different. R2C9 is a dog, so R1C9 is a cat.
5. The × clue between R6C9 and R6C8 means they are different. R6C9 is a cat, so R6C8 is a dog.
6. R1C7 and R1C9 are both cats with one square between them, so R1C8 must be a dog.
7. Imagine R4C4 were a dog: following the rules from there soon forces a contradiction, so R4C4 must be a cat.
8. The = clue between R4C4 and R5C4 means they are the same. R4C4 is a cat, so R5C4 is a cat.
9. R4C4 and R5C4 are both cats, so R3C4 must be a dog (no three in a row).
10. Imagine R7C9 were a cat: following the rules from there soon forces a contradiction, so R7C9 must be a dog.
11. The = clue between R7C9 and R7C10 means they are the same. R7C9 is a dog, so R7C10 is a dog.
12. R7C9 and R7C10 are both dogs, so R7C8 must be a cat (no three in a row).
13. R7C7 and R7C8 are both cats, so R7C6 must be a dog (no three in a row).
14. Imagine R8C9 were a dog: following the rules from there soon forces a contradiction, so R8C9 must be a cat.
15. The = clue between R8C9 and R9C9 means they are the same. R8C9 is a cat, so R9C9 is a cat.
16. R8C9 and R9C9 are both cats, so R10C9 must be a dog (no three in a row).
17. Column 9 already has its 5 cats, so R4C9 must be dogs.
18. The = clue between R4C9 and R4C8 means they are the same. R4C9 is a dog, so R4C8 is a dog.
19. R4C8 and R4C9 are both dogs, so R4C7 must be a cat (no three in a row).
20. R4C8 and R4C9 are both dogs, so R4C10 must be a cat (no three in a row).
21. R3C8 and R4C8 are both dogs, so R5C8 must be a cat (no three in a row).
22. The × clue between R5C8 and R5C7 means they are different. R5C8 is a cat, so R5C7 is a dog.
23. Column 9 already has its 5 cats, so R5C9 must be dogs.
24. Imagine R6C5 were a dog: following the rules from there soon forces a contradiction, so R6C5 must be a cat.
25. The = clue between R6C5 and R7C5 means they are the same. R6C5 is a cat, so R7C5 is a cat.
26. R6C5 and R7C5 are both cats, so R5C5 must be a dog (no three in a row).
27. R5C5 and R5C7 are both dogs with one square between them, so R5C6 must be a cat.
28. R6C5 and R7C5 are both cats, so R8C5 must be a dog (no three in a row).
29. The × clue between R8C5 and R8C4 means they are different. R8C5 is a dog, so R8C4 is a cat.
30. The × clue between R8C4 and R8C3 means they are different. R8C4 is a cat, so R8C3 is a dog.
31. Imagine R4C6 were a cat: following the rules from there soon forces a contradiction, so R4C6 must be a dog.
32. Imagine R8C6 were a dog: following the rules from there soon forces a contradiction, so R8C6 must be a cat.
33. Imagine R8C7 were a cat: following the rules from there soon forces a contradiction, so R8C7 must be a dog.
34. Imagine R5C10 were a cat: following the rules from there soon forces a contradiction, so R5C10 must be a dog.
35. R5C10 and R7C10 are both dogs with one square between them, so R6C10 must be a cat.
36. Imagine R5C1 were a dog: following the rules from there soon forces a contradiction, so R5C1 must be a cat.
37. Imagine R6C1 were a cat: following the rules from there soon forces a contradiction, so R6C1 must be a dog.
38. The = clue between R6C1 and R7C1 means they are the same. R6C1 is a dog, so R7C1 is a dog.
39. R6C1 and R7C1 are both dogs, so R8C1 must be a cat (no three in a row).
40. Imagine R7C2 were a dog: following the rules from there soon forces a contradiction, so R7C2 must be a cat.
41. Imagine R8C2 were a cat: following the rules from there soon forces a contradiction, so R8C2 must be a dog.
42. Imagine R8C8 were a dog: following the rules from there soon forces a contradiction, so R8C8 must be a cat.
43. R8C8 and R8C9 are both cats, so R8C10 must be a dog (no three in a row).
44. R7C8 and R8C8 are both cats, so R9C8 must be a dog (no three in a row).
45. R7C10 and R8C10 are both dogs, so R9C10 must be a cat (no three in a row).
46. Column 8 already has its 5 dogs, so R10C8 must be cats.
47. Imagine R9C5 were a dog: following the rules from there soon forces a contradiction, so R9C5 must be a cat.
48. The × clue between R9C5 and R9C6 means they are different. R9C5 is a cat, so R9C6 is a dog.
49. The = clue between R9C5 and R10C5 means they are the same. R9C5 is a cat, so R10C5 is a cat.
50. The × clue between R10C5 and R10C6 means they are different. R10C5 is a cat, so R10C6 is a dog.
51. R9C6 and R9C8 are both dogs with one square between them, so R9C7 must be a cat.
52. Column 6 already has its 5 dogs, so R2C6 must be cats.
53. R2C6 and R2C8 are both cats with one square between them, so R2C7 must be a dog.
54. Column 6 already has its 5 dogs, so R3C6 and R6C6 must be cats.
55. R6C5 and R6C6 are both cats, so R6C7 must be a dog (no three in a row).
56. Imagine R1C4 were a dog: following the rules from there soon forces a contradiction, so R1C4 must be a cat.
57. Imagine R1C5 were a cat: following the rules from there soon forces a contradiction, so R1C5 must be a dog.
58. Imagine R2C5 were a cat: following the rules from there soon forces a contradiction, so R2C5 must be a dog.
59. R1C5 and R2C5 are both dogs, so R3C5 must be a cat (no three in a row).
60. R3C5 and R3C6 are both cats, so R3C7 must be a dog (no three in a row).
61. Column 5 already has its 5 cats, so R4C5 must be dogs.
62. Column 7 already has its 5 dogs, so R10C7 must be cats.
63. Imagine R3C1 were a cat: following the rules from there soon forces a contradiction, so R3C1 must be a dog.
64. Imagine R2C2 were a cat: following the rules from there soon forces a contradiction, so R2C2 must be a dog.
65. Imagine R4C1 were a dog: following the rules from there soon forces a contradiction, so R4C1 must be a cat.
66. Imagine R7C3 were a dog: following the rules from there soon forces a contradiction, so R7C3 must be a cat.
67. R7C2 and R7C3 are both cats, so R7C4 must be a dog (no three in a row).
68. Imagine R9C1 were a cat: following the rules from there soon forces a contradiction, so R9C1 must be a dog.
69. The = clue between R9C1 and R9C2 means they are the same. R9C1 is a dog, so R9C2 is a dog.
70. R9C1 and R9C2 are both dogs, so R9C3 must be a cat (no three in a row).
71. R9C3 and R9C5 are both cats with one square between them, so R9C4 must be a dog.
72. R8C2 and R9C2 are both dogs, so R10C2 must be a cat (no three in a row).
73. The = clue between R10C2 and R10C3 means they are the same. R10C2 is a cat, so R10C3 is a cat.
74. R10C2 and R10C3 are both cats, so R10C1 must be a dog (no three in a row).
75. R10C2 and R10C3 are both cats, so R10C4 must be a dog (no three in a row).
76. Row 10 already has its 5 cats, so R10C10 must be dogs.
77. Column 1 already has its 5 dogs, so R1C1 and R2C1 must be cats.
78. Column 4 already has its 5 dogs, so R2C4 must be cats.
79. Row 2 already has its 5 cats, so R2C10 must be dogs.
80. Column 10 already has its 5 dogs, so R1C10 must be cats.
81. Row 1 already has its 5 cats, so R1C2 must be dogs.
82. R1C2 and R2C2 are both dogs, so R3C2 must be a cat (no three in a row).
83. Row 1 already has its 5 cats, so R1C3 must be dogs.
84. Column 10 already has its 5 dogs, so R3C10 must be cats.
85. Row 3 already has its 5 cats, so R3C3 must be dogs.
86. Imagine R4C2 were a dog: following the rules from there soon forces a contradiction, so R4C2 must be a cat.
87. R4C1 and R4C2 are both cats, so R4C3 must be a dog (no three in a row).
88. R3C2 and R4C2 are both cats, so R5C2 must be a dog (no three in a row).
89. R3C3 and R4C3 are both dogs, so R5C3 must be a cat (no three in a row).
90. R5C3 and R7C3 are both cats with one square between them, so R6C3 must be a dog.
91. R6C1 and R6C3 are both dogs with one square between them, so R6C2 must be a cat.