Cats & Dogs #299: 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 R8C1 and R8C2 means they are different. R8C1 is a cat, so R8C2 is a dog.
2. Imagine R6C2 were a dog: following the rules from there soon forces a contradiction, so R6C2 must be a cat.
3. The = clue between R6C2 and R7C2 means they are the same. R6C2 is a cat, so R7C2 is a cat.
4. The × clue between R7C2 and R7C3 means they are different. R7C2 is a cat, so R7C3 is a dog.
5. R6C2 and R7C2 are both cats, so R5C2 must be a dog (no three in a row).
6. The = clue between R5C2 and R5C3 means they are the same. R5C2 is a dog, so R5C3 is a dog.
7. R5C2 and R5C3 are both dogs, so R5C1 must be a cat (no three in a row).
8. R5C2 and R5C3 are both dogs, so R5C4 must be a cat (no three in a row).
9. R5C4 and R5C6 are both cats with one square between them, so R5C5 must be a dog.
10. The = clue between R5C5 and R6C5 means they are the same. R5C5 is a dog, so R6C5 is a dog.
11. R5C3 and R7C3 are both dogs with one square between them, so R6C3 must be a cat.
12. R6C2 and R6C3 are both cats, so R6C1 must be a dog (no three in a row).
13. R6C2 and R6C3 are both cats, so R6C4 must be a dog (no three in a row).
14. R6C4 and R6C5 are both dogs, so R6C6 must be a cat (no three in a row).
15. R5C5 and R6C5 are both dogs, so R4C5 must be a cat (no three in a row).
16. R5C5 and R6C5 are both dogs, so R7C5 must be a cat (no three in a row).
17. R5C6 and R6C6 are both cats, so R4C6 must be a dog (no three in a row).
18. R4C6 and R4C8 are both dogs with one square between them, so R4C7 must be a cat.
19. R5C6 and R6C6 are both cats, so R7C6 must be a dog (no three in a row).
20. R3C7 and R4C7 are both cats, so R2C7 must be a dog (no three in a row).
21. R3C7 and R4C7 are both cats, so R5C7 must be a dog (no three in a row).
22. Imagine R1C6 were a cat: following the rules from there soon forces a contradiction, so R1C6 must be a dog.
23. The = clue between R1C6 and R2C6 means they are the same. R1C6 is a dog, so R2C6 is a dog.
24. R2C6 and R2C7 are both dogs, so R2C5 must be a cat (no three in a row).
25. R2C6 and R2C7 are both dogs, so R2C8 must be a cat (no three in a row).
26. R2C5 and R4C5 are both cats with one square between them, so R3C5 must be a dog.
27. R1C6 and R2C6 are both dogs, so R3C6 must be a cat (no three in a row).
28. R3C6 and R3C7 are both cats, so R3C8 must be a dog (no three in a row).
29. R3C8 and R4C8 are both dogs, so R5C8 must be a cat (no three in a row).
30. The × clue between R5C8 and R6C8 means they are different. R5C8 is a cat, so R6C8 is a dog.
31. Imagine R2C1 were a dog: following the rules from there soon forces a contradiction, so R2C1 must be a cat.
32. The = clue between R2C1 and R2C2 means they are the same. R2C1 is a cat, so R2C2 is a cat.
33. R2C1 and R2C2 are both cats, so R2C3 must be a dog (no three in a row).
34. R1C3 and R2C3 are both dogs, so R3C3 must be a cat (no three in a row).
35. Imagine R1C1 were a dog: following the rules from there soon forces a contradiction, so R1C1 must be a cat.
36. R1C1 and R2C1 are both cats, so R3C1 must be a dog (no three in a row).
37. Imagine R1C2 were a cat: following the rules from there soon forces a contradiction, so R1C2 must be a dog.
38. R1C2 and R1C3 are both dogs, so R1C4 must be a cat (no three in a row).
39. Imagine R3C4 were a cat: following the rules from there soon forces a contradiction, so R3C4 must be a dog.
40. The = clue between R3C4 and R4C4 means they are the same. R3C4 is a dog, so R4C4 is a dog.
41. R3C4 and R4C4 are both dogs, so R2C4 must be a cat (no three in a row).
42. Row 2 already has its 5 cats, so R2C9 and R2C10 must be dogs.
43. Imagine R1C9 were a dog: following the rules from there soon forces a contradiction, so R1C9 must be a cat.
44. Imagine R3C2 were a dog: following the rules from there soon forces a contradiction, so R3C2 must be a cat.
45. R2C2 and R3C2 are both cats, so R4C2 must be a dog (no three in a row).
46. The × clue between R4C2 and R4C1 means they are different. R4C2 is a dog, so R4C1 is a cat.
47. R4C2 and R4C4 are both dogs with one square between them, so R4C3 must be a cat.
48. Row 4 already has its 5 cats, so R4C10 must be dogs.
49. The = clue between R4C10 and R5C10 means they are the same. R4C10 is a dog, so R5C10 is a dog.
50. R2C10 and R4C10 are both dogs with one square between them, so R3C10 must be a cat.
51. R4C10 and R5C10 are both dogs, so R6C10 must be a cat (no three in a row).
52. R6C10 and R8C10 are both cats with one square between them, so R7C10 must be a dog.
53. Row 3 already has its 5 cats, so R3C9 must be dogs.
54. Row 5 already has its 5 dogs, so R5C9 must be cats.
55. R4C9 and R5C9 are both cats, so R6C9 must be a dog (no three in a row).
56. R6C8 and R6C9 are both dogs, so R6C7 must be a cat (no three in a row).
57. Column 1 already has its 5 cats, so R7C1, R9C1 and R10C1 must be dogs.
58. The = clue between R10C1 and R10C2 means they are the same. R10C1 is a dog, so R10C2 is a dog.
59. R10C1 and R10C2 are both dogs, so R10C3 must be a cat (no three in a row).
60. R8C2 and R10C2 are both dogs with one square between them, so R9C2 must be a cat.
61. Column 10 already has its 5 dogs, so R1C10 must be cats.
62. R1C9 and R1C10 are both cats, so R1C8 must be a dog (no three in a row).
63. R1C6 and R1C8 are both dogs with one square between them, so R1C7 must be a cat.
64. Row 1 already has its 5 cats, so R1C5 must be dogs.
65. Column 10 already has its 5 dogs, so R9C10 must be cats.
66. Imagine R7C4 were a dog: following the rules from there soon forces a contradiction, so R7C4 must be a cat.
67. Imagine R7C7 were a cat: following the rules from there soon forces a contradiction, so R7C7 must be a dog.
68. R7C6 and R7C7 are both dogs, so R7C8 must be a cat (no three in a row).
69. Row 7 already has its 5 dogs, so R7C9 must be cats.
70. Imagine R8C5 were a cat: following the rules from there soon forces a contradiction, so R8C5 must be a dog.
71. The = clue between R8C5 and R8C6 means they are the same. R8C5 is a dog, so R8C6 is a dog.
72. R8C5 and R8C6 are both dogs, so R8C4 must be a cat (no three in a row).
73. R8C5 and R8C6 are both dogs, so R8C7 must be a cat (no three in a row).
74. R7C4 and R8C4 are both cats, so R9C4 must be a dog (no three in a row).
75. R7C6 and R8C6 are both dogs, so R9C6 must be a cat (no three in a row).
76. Column 4 already has its 5 cats, so R10C4 must be dogs.
77. Column 5 already has its 5 dogs, so R9C5 must be cats.
78. R9C5 and R9C6 are both cats, so R9C7 must be a dog (no three in a row).
79. Column 5 already has its 5 dogs, so R10C5 must be cats.
80. R10C5 and R10C6 are both cats, so R10C7 must be a dog (no three in a row).
81. Row 10 already has its 5 dogs, so R10C8 and R10C9 must be cats.
82. Column 9 already has its 5 cats, so R8C9 and R9C9 must be dogs.
83. R9C7 and R9C9 are both dogs with one square between them, so R9C8 must be a cat.
84. R7C8 and R9C8 are both cats with one square between them, so R8C8 must be a dog.
85. Row 8 already has its 5 dogs, so R8C3 must be cats.
86. R8C3 and R10C3 are both cats with one square between them, so R9C3 must be a dog.