Cats & Dogs #287: 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 R1C2 and R2C2 means they are different. R1C2 is a dog, so R2C2 is a cat.
2. R1C2 and R1C4 are both dogs with one square between them, so R1C3 must be a cat.
3. R2C1 and R2C2 are both cats, so R2C3 must be a dog (no three in a row).
4. Imagine R1C7 were a cat: following the rules from there soon forces a contradiction, so R1C7 must be a dog.
5. The = clue between R1C7 and R2C7 means they are the same. R1C7 is a dog, so R2C7 is a dog.
6. R2C7 and R2C9 are both dogs with one square between them, so R2C8 must be a cat.
7. The = clue between R2C8 and R1C8 means they are the same. R2C8 is a cat, so R1C8 is a cat.
8. R1C7 and R2C7 are both dogs, so R3C7 must be a cat (no three in a row).
9. The = clue between R3C7 and R3C6 means they are the same. R3C7 is a cat, so R3C6 is a cat.
10. The × clue between R3C6 and R2C6 means they are different. R3C6 is a cat, so R2C6 is a dog.
11. R2C6 and R2C7 are both dogs, so R2C5 must be a cat (no three in a row).
12. R3C6 and R3C7 are both cats, so R3C5 must be a dog (no three in a row).
13. R3C6 and R3C7 are both cats, so R3C8 must be a dog (no three in a row).
14. Imagine R3C9 were a dog: following the rules from there soon forces a contradiction, so R3C9 must be a cat.
15. The = clue between R3C9 and R4C9 means they are the same. R3C9 is a cat, so R4C9 is a cat.
16. R3C9 and R4C9 are both cats, so R5C9 must be a dog (no three in a row).
17. R5C9 and R7C9 are both dogs with one square between them, so R6C9 must be a cat.
18. Imagine R7C5 were a cat: following the rules from there soon forces a contradiction, so R7C5 must be a dog.
19. The = clue between R7C5 and R7C6 means they are the same. R7C5 is a dog, so R7C6 is a dog.
20. R7C5 and R7C6 are both dogs, so R7C4 must be a cat (no three in a row).
21. R7C5 and R7C6 are both dogs, so R7C7 must be a cat (no three in a row).
22. The = clue between R7C7 and R7C8 means they are the same. R7C7 is a cat, so R7C8 is a cat.
23. R6C4 and R7C4 are both cats, so R5C4 must be a dog (no three in a row).
24. R6C4 and R7C4 are both cats, so R8C4 must be a dog (no three in a row).
25. Imagine R5C5 were a dog: following the rules from there soon forces a contradiction, so R5C5 must be a cat.
26. Imagine R5C7 were a cat: following the rules from there soon forces a contradiction, so R5C7 must be a dog.
27. R5C7 and R5C9 are both dogs with one square between them, so R5C8 must be a cat.
28. R5C8 and R7C8 are both cats with one square between them, so R6C8 must be a dog.
29. Imagine R4C8 were a cat: following the rules from there soon forces a contradiction, so R4C8 must be a dog.
30. Imagine R6C5 were a cat: following the rules from there soon forces a contradiction, so R6C5 must be a dog.
31. R6C5 and R7C5 are both dogs, so R8C5 must be a cat (no three in a row).
32. Imagine R6C6 were a dog: following the rules from there soon forces a contradiction, so R6C6 must be a cat.
33. The = clue between R6C6 and R6C7 means they are the same. R6C6 is a cat, so R6C7 is a cat.
34. R6C7 and R7C7 are both cats, so R8C7 must be a dog (no three in a row).
35. Imagine R6C10 were a cat: following the rules from there soon forces a contradiction, so R6C10 must be a dog.
36. Imagine R9C5 were a cat: following the rules from there soon forces a contradiction, so R9C5 must be a dog.
37. The = clue between R9C5 and R10C5 means they are the same. R9C5 is a dog, so R10C5 is a dog.
38. Column 5 already has its 5 dogs, so R1C5 and R4C5 must be cats.
39. Imagine R3C2 were a cat: following the rules from there soon forces a contradiction, so R3C2 must be a dog.
40. The = clue between R3C2 and R3C3 means they are the same. R3C2 is a dog, so R3C3 is a dog.
41. R3C2 and R3C3 are both dogs, so R3C1 must be a cat (no three in a row).
42. R3C2 and R3C3 are both dogs, so R3C4 must be a cat (no three in a row).
43. R2C1 and R3C1 are both cats, so R1C1 must be a dog (no three in a row).
44. R2C1 and R3C1 are both cats, so R4C1 must be a dog (no three in a row).
45. R2C3 and R3C3 are both dogs, so R4C3 must be a cat (no three in a row).
46. R4C3 and R4C5 are both cats with one square between them, so R4C4 must be a dog.
47. Row 3 already has its 5 cats, so R3C10 must be dogs.
48. Imagine R1C6 were a dog: following the rules from there soon forces a contradiction, so R1C6 must be a cat.
49. Imagine R1C9 were a cat: following the rules from there soon forces a contradiction, so R1C9 must be a dog.
50. Row 1 already has its 5 dogs, so R1C10 must be cats.
51. Imagine R2C4 were a dog: following the rules from there soon forces a contradiction, so R2C4 must be a cat.
52. Row 2 already has its 5 cats, so R2C10 must be dogs.
53. R2C10 and R3C10 are both dogs, so R4C10 must be a cat (no three in a row).
54. Imagine R4C2 were a cat: following the rules from there soon forces a contradiction, so R4C2 must be a dog.
55. R3C2 and R4C2 are both dogs, so R5C2 must be a cat (no three in a row).
56. Imagine R5C1 were a dog: following the rules from there soon forces a contradiction, so R5C1 must be a cat.
57. R5C1 and R5C2 are both cats, so R5C3 must be a dog (no three in a row).
58. Imagine R6C1 were a cat: following the rules from there soon forces a contradiction, so R6C1 must be a dog.
59. The = clue between R6C1 and R7C1 means they are the same. R6C1 is a dog, so R7C1 is a dog.
60. R6C1 and R7C1 are both dogs, so R8C1 must be a cat (no three in a row).
61. Imagine R6C2 were a dog: following the rules from there soon forces a contradiction, so R6C2 must be a cat.
62. R6C2 and R6C4 are both cats with one square between them, so R6C3 must be a dog.
63. R5C2 and R6C2 are both cats, so R7C2 must be a dog (no three in a row).
64. The × clue between R7C2 and R8C2 means they are different. R7C2 is a dog, so R8C2 is a cat.
65. R7C1 and R7C2 are both dogs, so R7C3 must be a cat (no three in a row).
66. R8C1 and R8C2 are both cats, so R8C3 must be a dog (no three in a row).
67. Row 7 already has its 5 dogs, so R7C10 must be cats.
68. Column 2 already has its 5 dogs, so R9C2 must be cats.
69. R9C2 and R9C3 are both cats, so R9C1 must be a dog (no three in a row).
70. R9C2 and R9C3 are both cats, so R9C4 must be a dog (no three in a row).
71. R9C4 and R9C5 are both dogs, so R9C6 must be a cat (no three in a row).
72. R8C4 and R9C4 are both dogs, so R10C4 must be a cat (no three in a row).
73. Column 1 already has its 5 dogs, so R10C1 must be cats.
74. Column 3 already has its 5 dogs, so R10C3 must be cats.
75. Imagine R4C6 were a dog: following the rules from there soon forces a contradiction, so R4C6 must be a cat.
76. The × clue between R4C6 and R5C6 means they are different. R4C6 is a cat, so R5C6 is a dog.
77. R4C5 and R4C6 are both cats, so R4C7 must be a dog (no three in a row).
78. Row 5 already has its 5 dogs, so R5C10 must be cats.
79. Column 6 already has its 5 cats, so R8C6 must be dogs.
80. R8C6 and R8C7 are both dogs, so R8C8 must be a cat (no three in a row).
81. The × clue between R8C8 and R8C9 means they are different. R8C8 is a cat, so R8C9 is a dog.
82. R7C8 and R8C8 are both cats, so R9C8 must be a dog (no three in a row).
83. R7C9 and R8C9 are both dogs, so R9C9 must be a cat (no three in a row).
84. Row 8 already has its 5 dogs, so R8C10 must be cats.
85. R7C10 and R8C10 are both cats, so R9C10 must be a dog (no three in a row).
86. Row 9 already has its 5 dogs, so R9C7 must be cats.
87. Column 6 already has its 5 cats, so R10C6 must be dogs.
88. R10C5 and R10C6 are both dogs, so R10C7 must be a cat (no three in a row).
89. Column 8 already has its 5 cats, so R10C8 must be dogs.
90. Column 9 already has its 5 dogs, so R10C9 must be cats.
91. Row 10 already has its 5 cats, so R10C10 must be dogs.