Cats & Dogs #283: 10x10 Grid Puzzle (Hard)

Step-by-step solution

Squares are written as R<row>C<column>, counting from the top-left.

1. R7C9 and R7C10 are both dogs, so R7C8 must be a cat (no three in a row).
2. R4C1 and R5C1 are both dogs, so R3C1 must be a cat (no three in a row).
3. R1C1 and R3C1 are both cats with one square between them, so R2C1 must be a dog.
4. R4C1 and R5C1 are both dogs, so R6C1 must be a cat (no three in a row).
5. The = clue between R6C1 and R6C2 means they are the same. R6C1 is a cat, so R6C2 is a cat.
6. R6C1 and R6C2 are both cats, so R6C3 must be a dog (no three in a row).
7. The × clue between R6C3 and R7C3 means they are different. R6C3 is a dog, so R7C3 is a cat.
8. Imagine R1C4 were a dog: following the rules from there soon forces a contradiction, so R1C4 must be a cat.
9. The = clue between R1C4 and R1C5 means they are the same. R1C4 is a cat, so R1C5 is a cat.
10. R1C4 and R1C5 are both cats, so R1C6 must be a dog (no three in a row).
11. Imagine R4C2 were a dog: following the rules from there soon forces a contradiction, so R4C2 must be a cat.
12. R4C2 and R6C2 are both cats with one square between them, so R5C2 must be a dog.
13. R5C1 and R5C2 are both dogs, so R5C3 must be a cat (no three in a row).
14. The × clue between R5C3 and R4C3 means they are different. R5C3 is a cat, so R4C3 is a dog.
15. The = clue between R5C3 and R5C4 means they are the same. R5C3 is a cat, so R5C4 is a cat.
16. Imagine R8C5 were a dog: following the rules from there soon forces a contradiction, so R8C5 must be a cat.
17. The = clue between R8C5 and R8C6 means they are the same. R8C5 is a cat, so R8C6 is a cat.
18. The = clue between R8C5 and R9C5 means they are the same. R8C5 is a cat, so R9C5 is a cat.
19. R8C5 and R8C6 are both cats, so R8C4 must be a dog (no three in a row).
20. The × clue between R8C4 and R9C4 means they are different. R8C4 is a dog, so R9C4 is a cat.
21. The × clue between R9C4 and R10C4 means they are different. R9C4 is a cat, so R10C4 is a dog.
22. R8C5 and R8C6 are both cats, so R8C7 must be a dog (no three in a row).
23. R9C4 and R9C5 are both cats, so R9C3 must be a dog (no three in a row).
24. R9C4 and R9C5 are both cats, so R9C6 must be a dog (no three in a row).
25. R8C5 and R9C5 are both cats, so R7C5 must be a dog (no three in a row).
26. R5C5 and R7C5 are both dogs with one square between them, so R6C5 must be a cat.
27. R8C5 and R9C5 are both cats, so R10C5 must be a dog (no three in a row).
28. R10C4 and R10C5 are both dogs, so R10C3 must be a cat (no three in a row).
29. R10C4 and R10C5 are both dogs, so R10C6 must be a cat (no three in a row).
30. Imagine R1C2 were a dog: following the rules from there soon forces a contradiction, so R1C2 must be a cat.
31. The = clue between R1C2 and R2C2 means they are the same. R1C2 is a cat, so R2C2 is a cat.
32. R1C2 and R2C2 are both cats, so R3C2 must be a dog (no three in a row).
33. Imagine R1C7 were a cat: following the rules from there soon forces a contradiction, so R1C7 must be a dog.
34. R1C6 and R1C7 are both dogs, so R1C8 must be a cat (no three in a row).
35. Row 1 already has its 5 cats, so R1C9 and R1C10 must be dogs.
36. Imagine R2C3 were a cat: following the rules from there soon forces a contradiction, so R2C3 must be a dog.
37. R1C3 and R2C3 are both dogs, so R3C3 must be a cat (no three in a row).
38. The × clue between R3C3 and R3C4 means they are different. R3C3 is a cat, so R3C4 is a dog.
39. The × clue between R3C4 and R2C4 means they are different. R3C4 is a dog, so R2C4 is a cat.
40. The × clue between R2C4 and R2C5 means they are different. R2C4 is a cat, so R2C5 is a dog.
41. Column 3 already has its 5 dogs, so R8C3 must be cats.
42. Imagine R2C9 were a dog: following the rules from there soon forces a contradiction, so R2C9 must be a cat.
43. The = clue between R2C9 and R3C9 means they are the same. R2C9 is a cat, so R3C9 is a cat.
44. R2C9 and R3C9 are both cats, so R4C9 must be a dog (no three in a row).
45. Imagine R2C8 were a cat: following the rules from there soon forces a contradiction, so R2C8 must be a dog.
46. Imagine R3C5 were a cat: following the rules from there soon forces a contradiction, so R3C5 must be a dog.
47. R3C4 and R3C5 are both dogs, so R3C6 must be a cat (no three in a row).
48. The = clue between R3C6 and R4C6 means they are the same. R3C6 is a cat, so R4C6 is a cat.
49. R2C5 and R3C5 are both dogs, so R4C5 must be a cat (no three in a row).
50. R4C5 and R4C6 are both cats, so R4C4 must be a dog (no three in a row).
51. R4C5 and R4C6 are both cats, so R4C7 must be a dog (no three in a row).
52. R4C7 and R4C9 are both dogs with one square between them, so R4C8 must be a cat.
53. The = clue between R4C8 and R5C8 means they are the same. R4C8 is a cat, so R5C8 is a cat.
54. R3C6 and R4C6 are both cats, so R2C6 must be a dog (no three in a row).
55. R2C5 and R2C6 are both dogs, so R2C7 must be a cat (no three in a row).
56. R3C6 and R4C6 are both cats, so R5C6 must be a dog (no three in a row).
57. R5C5 and R5C6 are both dogs, so R5C7 must be a cat (no three in a row).
58. R5C7 and R5C8 are both cats, so R5C9 must be a dog (no three in a row).
59. R4C8 and R5C8 are both cats, so R3C8 must be a dog (no three in a row).
60. R4C8 and R5C8 are both cats, so R6C8 must be a dog (no three in a row).
61. R4C9 and R5C9 are both dogs, so R6C9 must be a cat (no three in a row).
62. Row 2 already has its 5 dogs, so R2C10 must be cats.
63. Row 4 already has its 5 dogs, so R4C10 must be cats.
64. R2C10 and R4C10 are both cats with one square between them, so R3C10 must be a dog.
65. Row 3 already has its 5 dogs, so R3C7 must be cats.
66. Row 5 already has its 5 dogs, so R5C10 must be cats.
67. R4C10 and R5C10 are both cats, so R6C10 must be a dog (no three in a row).
68. R6C10 and R7C10 are both dogs, so R8C10 must be a cat (no three in a row).
69. Imagine R6C4 were a cat: following the rules from there soon forces a contradiction, so R6C4 must be a dog.
70. R6C4 and R8C4 are both dogs with one square between them, so R7C4 must be a cat.
71. R7C3 and R7C4 are both cats, so R7C2 must be a dog (no three in a row).
72. Imagine R7C1 were a dog: following the rules from there soon forces a contradiction, so R7C1 must be a cat.
73. R6C1 and R7C1 are both cats, so R8C1 must be a dog (no three in a row).
74. Imagine R8C2 were a cat: following the rules from there soon forces a contradiction, so R8C2 must be a dog.
75. R7C2 and R8C2 are both dogs, so R9C2 must be a cat (no three in a row).
76. Column 2 already has its 5 cats, so R10C2 must be dogs.
77. Imagine R8C8 were a cat: following the rules from there soon forces a contradiction, so R8C8 must be a dog.
78. The × clue between R8C8 and R9C8 means they are different. R8C8 is a dog, so R9C8 is a cat.
79. R8C7 and R8C8 are both dogs, so R8C9 must be a cat (no three in a row).
80. The × clue between R8C9 and R9C9 means they are different. R8C9 is a cat, so R9C9 is a dog.
81. Column 8 already has its 5 cats, so R10C8 must be dogs.
82. Column 9 already has its 5 dogs, so R10C9 must be cats.
83. The × clue between R10C9 and R10C10 means they are different. R10C9 is a cat, so R10C10 is a dog.
84. Row 10 already has its 5 dogs, so R10C1 and R10C7 must be cats.
85. Column 1 already has its 5 cats, so R9C1 must be dogs.
86. Column 10 already has its 5 dogs, so R9C10 must be cats.
87. Row 9 already has its 5 cats, so R9C7 must be dogs.
88. R8C7 and R9C7 are both dogs, so R7C7 must be a cat (no three in a row).
89. R7C7 and R7C8 are both cats, so R7C6 must be a dog (no three in a row).
90. R5C6 and R7C6 are both dogs with one square between them, so R6C6 must be a cat.
91. R6C5 and R6C6 are both cats, so R6C7 must be a dog (no three in a row).