Cats & Dogs #279: 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 R9C4 and R8C4 means they are different. R9C4 is a dog, so R8C4 is a cat.
2. The = clue between R9C1 and R10C1 means they are the same. R9C1 is a dog, so R10C1 is a dog.
3. The = clue between R10C4 and R10C5 means they are the same. R10C4 is a cat, so R10C5 is a cat.
4. R10C4 and R10C5 are both cats, so R10C3 must be a dog (no three in a row).
5. R10C1 and R10C3 are both dogs with one square between them, so R10C2 must be a cat.
6. R10C4 and R10C5 are both cats, so R10C6 must be a dog (no three in a row).
7. R9C1 and R10C1 are both dogs, so R8C1 must be a cat (no three in a row).
8. R4C10 and R5C10 are both dogs, so R3C10 must be a cat (no three in a row).
9. R4C10 and R5C10 are both dogs, so R6C10 must be a cat (no three in a row).
10. R6C9 and R6C10 are both cats, so R6C8 must be a dog (no three in a row).
11. Imagine R2C7 were a cat: following the rules from there soon forces a contradiction, so R2C7 must be a dog.
12. The = clue between R2C7 and R2C8 means they are the same. R2C7 is a dog, so R2C8 is a dog.
13. R2C7 and R2C8 are both dogs, so R2C9 must be a cat (no three in a row).
14. The × clue between R2C9 and R2C10 means they are different. R2C9 is a cat, so R2C10 is a dog.
15. Imagine R3C5 were a cat: following the rules from there soon forces a contradiction, so R3C5 must be a dog.
16. The = clue between R3C5 and R3C6 means they are the same. R3C5 is a dog, so R3C6 is a dog.
17. The = clue between R3C6 and R4C6 means they are the same. R3C6 is a dog, so R4C6 is a dog.
18. R3C5 and R3C6 are both dogs, so R3C4 must be a cat (no three in a row).
19. R3C5 and R3C6 are both dogs, so R3C7 must be a cat (no three in a row).
20. R3C6 and R4C6 are both dogs, so R5C6 must be a cat (no three in a row).
21. R5C6 and R6C6 are both cats, so R7C6 must be a dog (no three in a row).
22. Imagine R3C9 were a cat: following the rules from there soon forces a contradiction, so R3C9 must be a dog.
23. The = clue between R3C9 and R4C9 means they are the same. R3C9 is a dog, so R4C9 is a dog.
24. R4C9 and R4C10 are both dogs, so R4C8 must be a cat (no three in a row).
25. R3C9 and R4C9 are both dogs, so R5C9 must be a cat (no three in a row).
26. R5C9 and R6C9 are both cats, so R7C9 must be a dog (no three in a row).
27. Imagine R5C4 were a cat: following the rules from there soon forces a contradiction, so R5C4 must be a dog.
28. Imagine R5C5 were a dog: following the rules from there soon forces a contradiction, so R5C5 must be a cat.
29. The × clue between R5C5 and R6C5 means they are different. R5C5 is a cat, so R6C5 is a dog.
30. R5C5 and R5C6 are both cats, so R5C7 must be a dog (no three in a row).
31. Imagine R6C7 were a dog: following the rules from there soon forces a contradiction, so R6C7 must be a cat.
32. The = clue between R6C7 and R7C7 means they are the same. R6C7 is a cat, so R7C7 is a cat.
33. R6C7 and R7C7 are both cats, so R8C7 must be a dog (no three in a row).
34. The × clue between R8C7 and R8C8 means they are different. R8C7 is a dog, so R8C8 is a cat.
35. Imagine R2C4 were a cat: following the rules from there soon forces a contradiction, so R2C4 must be a dog.
36. Imagine R2C5 were a dog: following the rules from there soon forces a contradiction, so R2C5 must be a cat.
37. Imagine R4C4 were a dog: following the rules from there soon forces a contradiction, so R4C4 must be a cat.
38. Imagine R1C2 were a dog: following the rules from there soon forces a contradiction, so R1C2 must be a cat.
39. Imagine R1C4 were a cat: following the rules from there soon forces a contradiction, so R1C4 must be a dog.
40. R1C3 and R1C4 are both dogs, so R1C5 must be a cat (no three in a row).
41. Imagine R1C7 were a cat: following the rules from there soon forces a contradiction, so R1C7 must be a dog.
42. Imagine R4C5 were a cat: following the rules from there soon forces a contradiction, so R4C5 must be a dog.
43. R4C5 and R4C6 are both dogs, so R4C7 must be a cat (no three in a row).
44. Imagine R4C1 were a dog: following the rules from there soon forces a contradiction, so R4C1 must be a cat.
45. Imagine R6C1 were a cat: following the rules from there soon forces a contradiction, so R6C1 must be a dog.
46. Imagine R6C2 were a cat: following the rules from there soon forces a contradiction, so R6C2 must be a dog.
47. The × clue between R6C2 and R7C2 means they are different. R6C2 is a dog, so R7C2 is a cat.
48. R6C1 and R6C2 are both dogs, so R6C3 must be a cat (no three in a row).
49. Row 6 already has its 5 cats, so R6C4 must be dogs.
50. R5C4 and R6C4 are both dogs, so R7C4 must be a cat (no three in a row).
51. R7C2 and R7C4 are both cats with one square between them, so R7C3 must be a dog.
52. Imagine R9C2 were a cat: following the rules from there soon forces a contradiction, so R9C2 must be a dog.
53. The × clue between R9C2 and R9C3 means they are different. R9C2 is a dog, so R9C3 is a cat.
54. Imagine R9C5 were a cat: following the rules from there soon forces a contradiction, so R9C5 must be a dog.
55. R9C4 and R9C5 are both dogs, so R9C6 must be a cat (no three in a row).
56. Imagine R2C3 were a dog: following the rules from there soon forces a contradiction, so R2C3 must be a cat.
57. Imagine R3C2 were a cat: following the rules from there soon forces a contradiction, so R3C2 must be a dog.
58. Imagine R3C3 were a dog: following the rules from there soon forces a contradiction, so R3C3 must be a cat.
59. R2C3 and R3C3 are both cats, so R4C3 must be a dog (no three in a row).
60. Row 4 already has its 5 dogs, so R4C2 must be cats.
61. Imagine R5C2 were a cat: following the rules from there soon forces a contradiction, so R5C2 must be a dog.
62. R5C2 and R5C4 are both dogs with one square between them, so R5C3 must be a cat.
63. Column 3 already has its 5 cats, so R8C3 must be dogs.
64. Imagine R7C8 were a dog: following the rules from there soon forces a contradiction, so R7C8 must be a cat.
65. R7C8 and R8C8 are both cats, so R9C8 must be a dog (no three in a row).
66. Row 9 already has its 5 dogs, so R9C7, R9C9 and R9C10 must be cats.
67. Column 7 already has its 5 cats, so R10C7 must be dogs.
68. R10C6 and R10C7 are both dogs, so R10C8 must be a cat (no three in a row).
69. Imagine R1C6 were a dog: following the rules from there soon forces a contradiction, so R1C6 must be a cat.
70. Column 6 already has its 5 cats, so R8C6 must be dogs.
71. R8C6 and R8C7 are both dogs, so R8C5 must be a cat (no three in a row).
72. Column 5 already has its 5 cats, so R7C5 must be dogs.
73. Imagine R1C8 were a cat: following the rules from there soon forces a contradiction, so R1C8 must be a dog.
74. R1C7 and R1C8 are both dogs, so R1C9 must be a cat (no three in a row).
75. The × clue between R1C9 and R1C10 means they are different. R1C9 is a cat, so R1C10 is a dog.
76. R1C8 and R2C8 are both dogs, so R3C8 must be a cat (no three in a row).
77. R3C8 and R4C8 are both cats, so R5C8 must be a dog (no three in a row).
78. Row 1 already has its 5 dogs, so R1C1 must be cats.
79. Row 3 already has its 5 cats, so R3C1 must be dogs.
80. Row 5 already has its 5 dogs, so R5C1 must be cats.
81. Column 9 already has its 5 cats, so R8C9 and R10C9 must be dogs.
82. Row 10 already has its 5 dogs, so R10C10 must be cats.
83. R9C10 and R10C10 are both cats, so R8C10 must be a dog (no three in a row).
84. Row 8 already has its 5 dogs, so R8C2 must be cats.
85. Column 2 already has its 5 cats, so R2C2 must be dogs.
86. Row 2 already has its 5 dogs, so R2C1 must be cats.
87. Column 1 already has its 5 cats, so R7C1 must be dogs.
88. Row 7 already has its 5 dogs, so R7C10 must be cats.