Cats & Dogs #228: 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 R9C6 and R9C7 means they are different. R9C6 is a cat, so R9C7 is a dog.
2. The = clue between R10C1 and R10C2 means they are the same. R10C1 is a cat, so R10C2 is a cat.
3. The × clue between R10C2 and R9C2 means they are different. R10C2 is a cat, so R9C2 is a dog.
4. R10C1 and R10C2 are both cats, so R10C3 must be a dog (no three in a row).
5. The = clue between R10C3 and R10C4 means they are the same. R10C3 is a dog, so R10C4 is a dog.
6. R10C3 and R10C4 are both dogs, so R10C5 must be a cat (no three in a row).
7. R5C1 and R6C1 are both cats, so R4C1 must be a dog (no three in a row).
8. R5C1 and R6C1 are both cats, so R7C1 must be a dog (no three in a row).
9. Imagine R7C5 were a dog: following the rules from there soon forces a contradiction, so R7C5 must be a cat.
10. Imagine R7C6 were a cat: following the rules from there soon forces a contradiction, so R7C6 must be a dog.
11. The = clue between R7C6 and R7C7 means they are the same. R7C6 is a dog, so R7C7 is a dog.
12. R7C6 and R7C7 are both dogs, so R7C8 must be a cat (no three in a row).
13. R7C7 and R9C7 are both dogs with one square between them, so R8C7 must be a cat.
14. Imagine R7C2 were a dog: following the rules from there soon forces a contradiction, so R7C2 must be a cat.
15. Imagine R8C1 were a cat: following the rules from there soon forces a contradiction, so R8C1 must be a dog.
16. R7C1 and R8C1 are both dogs, so R9C1 must be a cat (no three in a row).
17. Imagine R1C1 were a cat: following the rules from there soon forces a contradiction, so R1C1 must be a dog.
18. Imagine R9C5 were a cat: following the rules from there soon forces a contradiction, so R9C5 must be a dog.
19. Imagine R10C6 were a cat: following the rules from there soon forces a contradiction, so R10C6 must be a dog.
20. The = clue between R10C6 and R10C7 means they are the same. R10C6 is a dog, so R10C7 is a dog.
21. R10C6 and R10C7 are both dogs, so R10C8 must be a cat (no three in a row).
22. Imagine R4C5 were a dog: following the rules from there soon forces a contradiction, so R4C5 must be a cat.
23. The × clue between R4C5 and R5C5 means they are different. R4C5 is a cat, so R5C5 is a dog.
24. The = clue between R5C5 and R5C6 means they are the same. R5C5 is a dog, so R5C6 is a dog.
25. R5C5 and R5C6 are both dogs, so R5C4 must be a cat (no three in a row).
26. R5C5 and R5C6 are both dogs, so R5C7 must be a cat (no three in a row).
27. Imagine R3C6 were a dog: following the rules from there soon forces a contradiction, so R3C6 must be a cat.
28. Imagine R3C7 were a cat: following the rules from there soon forces a contradiction, so R3C7 must be a dog.
29. The = clue between R3C7 and R4C7 means they are the same. R3C7 is a dog, so R4C7 is a dog.
30. R3C7 and R4C7 are both dogs, so R2C7 must be a cat (no three in a row).
31. Column 7 already has its 5 dogs, so R1C7 must be cats.
32. The × clue between R1C7 and R1C8 means they are different. R1C7 is a cat, so R1C8 is a dog.
33. The × clue between R1C8 and R2C8 means they are different. R1C8 is a dog, so R2C8 is a cat.
34. R1C8 and R1C9 are both dogs, so R1C10 must be a cat (no three in a row).
35. R2C7 and R2C8 are both cats, so R2C6 must be a dog (no three in a row).
36. R2C7 and R2C8 are both cats, so R2C9 must be a dog (no three in a row).
37. R1C9 and R2C9 are both dogs, so R3C9 must be a cat (no three in a row).
38. R1C10 and R2C10 are both cats, so R3C10 must be a dog (no three in a row).
39. Column 7 already has its 5 dogs, so R6C7 must be cats.
40. R6C6 and R6C7 are both cats, so R6C8 must be a dog (no three in a row).
41. The × clue between R6C8 and R5C8 means they are different. R6C8 is a dog, so R5C8 is a cat.
42. R5C7 and R5C8 are both cats, so R5C9 must be a dog (no three in a row).
43. Imagine R4C2 were a dog: following the rules from there soon forces a contradiction, so R4C2 must be a cat.
44. Imagine R4C4 were a cat: following the rules from there soon forces a contradiction, so R4C4 must be a dog.
45. Imagine R4C6 were a dog: following the rules from there soon forces a contradiction, so R4C6 must be a cat.
46. Imagine R6C2 were a cat: following the rules from there soon forces a contradiction, so R6C2 must be a dog.
47. Imagine R8C8 were a cat: following the rules from there soon forces a contradiction, so R8C8 must be a dog.
48. R8C8 and R8C9 are both dogs, so R8C10 must be a cat (no three in a row).
49. Imagine R9C8 were a cat: following the rules from there soon forces a contradiction, so R9C8 must be a dog.
50. R9C7 and R9C8 are both dogs, so R9C9 must be a cat (no three in a row).
51. Imagine R7C10 were a cat: following the rules from there soon forces a contradiction, so R7C10 must be a dog.
52. Imagine R5C3 were a cat: following the rules from there soon forces a contradiction, so R5C3 must be a dog.
53. Row 5 already has its 5 dogs, so R5C10 must be cats.
54. Imagine R4C10 were a cat: following the rules from there soon forces a contradiction, so R4C10 must be a dog.
55. Imagine R6C9 were a dog: following the rules from there soon forces a contradiction, so R6C9 must be a cat.
56. Imagine R6C10 were a cat: following the rules from there soon forces a contradiction, so R6C10 must be a dog.
57. Imagine R7C9 were a dog: following the rules from there soon forces a contradiction, so R7C9 must be a cat.
58. Imagine R3C8 were a cat: following the rules from there soon forces a contradiction, so R3C8 must be a dog.
59. The × clue between R3C8 and R4C8 means they are different. R3C8 is a dog, so R4C8 is a cat.
60. Imagine R2C4 were a dog: following the rules from there soon forces a contradiction, so R2C4 must be a cat.
61. Imagine R2C5 were a cat: following the rules from there soon forces a contradiction, so R2C5 must be a dog.
62. Imagine R1C5 were a cat: following the rules from there soon forces a contradiction, so R1C5 must be a dog.
63. R1C5 and R2C5 are both dogs, so R3C5 must be a cat (no three in a row).
64. R3C5 and R3C6 are both cats, so R3C4 must be a dog (no three in a row).
65. Column 5 already has its 5 dogs, so R8C5 must be cats.
66. The = clue between R8C5 and R8C4 means they are the same. R8C5 is a cat, so R8C4 is a cat.
67. R8C4 and R8C5 are both cats, so R8C3 must be a dog (no three in a row).
68. The × clue between R8C3 and R7C3 means they are different. R8C3 is a dog, so R7C3 is a cat.
69. R7C2 and R7C3 are both cats, so R7C4 must be a dog (no three in a row).
70. R8C1 and R8C3 are both dogs with one square between them, so R8C2 must be a cat.
71. R8C4 and R8C5 are both cats, so R8C6 must be a dog (no three in a row).
72. R8C3 and R10C3 are both dogs with one square between them, so R9C3 must be a cat.
73. The × clue between R9C3 and R9C4 means they are different. R9C3 is a cat, so R9C4 is a dog.
74. Row 9 already has its 5 dogs, so R9C10 must be cats.
75. R8C10 and R9C10 are both cats, so R10C10 must be a dog (no three in a row).
76. Row 10 already has its 5 dogs, so R10C9 must be cats.
77. Column 4 already has its 5 dogs, so R1C4 and R6C4 must be cats.
78. Row 6 already has its 5 cats, so R6C3 must be dogs.
79. R5C3 and R6C3 are both dogs, so R4C3 must be a cat (no three in a row).
80. Row 4 already has its 5 cats, so R4C9 must be dogs.
81. Column 6 already has its 5 dogs, so R1C6 must be cats.
82. Imagine R1C2 were a cat: following the rules from there soon forces a contradiction, so R1C2 must be a dog.
83. R1C1 and R1C2 are both dogs, so R1C3 must be a cat (no three in a row).
84. R1C2 and R2C2 are both dogs, so R3C2 must be a cat (no three in a row).
85. The × clue between R3C2 and R3C1 means they are different. R3C2 is a cat, so R3C1 is a dog.
86. R1C1 and R3C1 are both dogs with one square between them, so R2C1 must be a cat.
87. Row 2 already has its 5 cats, so R2C3 must be dogs.
88. Row 3 already has its 5 dogs, so R3C3 must be cats.