Cats & Dogs #298: 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 R7C4 and R6C4 means they are the same. R7C4 is a dog, so R6C4 is a dog.
2. The × clue between R10C3 and R9C3 means they are different. R10C3 is a cat, so R9C3 is a dog.
3. R6C4 and R7C4 are both dogs, so R5C4 must be a cat (no three in a row).
4. R5C3 and R5C4 are both cats, so R5C2 must be a dog (no three in a row).
5. R5C3 and R5C4 are both cats, so R5C5 must be a dog (no three in a row).
6. R6C4 and R7C4 are both dogs, so R8C4 must be a cat (no three in a row).
7. Imagine R1C1 were a dog: following the rules from there soon forces a contradiction, so R1C1 must be a cat.
8. The = clue between R1C1 and R1C2 means they are the same. R1C1 is a cat, so R1C2 is a cat.
9. Imagine R2C2 were a cat: following the rules from there soon forces a contradiction, so R2C2 must be a dog.
10. The = clue between R2C2 and R2C3 means they are the same. R2C2 is a dog, so R2C3 is a dog.
11. R2C2 and R2C3 are both dogs, so R2C1 must be a cat (no three in a row).
12. R2C2 and R2C3 are both dogs, so R2C4 must be a cat (no three in a row).
13. R1C1 and R2C1 are both cats, so R3C1 must be a dog (no three in a row).
14. R1C3 and R2C3 are both dogs, so R3C3 must be a cat (no three in a row).
15. R3C3 and R5C3 are both cats with one square between them, so R4C3 must be a dog.
16. R1C4 and R2C4 are both cats, so R3C4 must be a dog (no three in a row).
17. Imagine R3C2 were a dog: following the rules from there soon forces a contradiction, so R3C2 must be a cat.
18. The = clue between R3C2 and R4C2 means they are the same. R3C2 is a cat, so R4C2 is a cat.
19. Imagine R3C5 were a dog: following the rules from there soon forces a contradiction, so R3C5 must be a cat.
20. The = clue between R3C5 and R4C5 means they are the same. R3C5 is a cat, so R4C5 is a cat.
21. R3C5 and R4C5 are both cats, so R2C5 must be a dog (no three in a row).
22. Imagine R8C2 were a cat: following the rules from there soon forces a contradiction, so R8C2 must be a dog.
23. Imagine R8C3 were a dog: following the rules from there soon forces a contradiction, so R8C3 must be a cat.
24. R8C3 and R8C4 are both cats, so R8C5 must be a dog (no three in a row).
25. Imagine R8C6 were a dog: following the rules from there soon forces a contradiction, so R8C6 must be a cat.
26. The = clue between R8C6 and R8C7 means they are the same. R8C6 is a cat, so R8C7 is a cat.
27. R8C6 and R8C7 are both cats, so R8C8 must be a dog (no three in a row).
28. The = clue between R8C8 and R7C8 means they are the same. R8C8 is a dog, so R7C8 is a dog.
29. R7C8 and R8C8 are both dogs, so R6C8 must be a cat (no three in a row).
30. The × clue between R6C8 and R5C8 means they are different. R6C8 is a cat, so R5C8 is a dog.
31. R7C8 and R8C8 are both dogs, so R9C8 must be a cat (no three in a row).
32. The = clue between R9C8 and R10C8 means they are the same. R9C8 is a cat, so R10C8 is a cat.
33. R9C8 and R9C10 are both cats with one square between them, so R9C9 must be a dog.
34. Imagine R5C7 were a dog: following the rules from there soon forces a contradiction, so R5C7 must be a cat.
35. Imagine R6C5 were a dog: following the rules from there soon forces a contradiction, so R6C5 must be a cat.
36. Imagine R6C6 were a cat: following the rules from there soon forces a contradiction, so R6C6 must be a dog.
37. Imagine R6C7 were a cat: following the rules from there soon forces a contradiction, so R6C7 must be a dog.
38. Imagine R7C6 were a dog: following the rules from there soon forces a contradiction, so R7C6 must be a cat.
39. The = clue between R7C6 and R7C7 means they are the same. R7C6 is a cat, so R7C7 is a cat.
40. R7C6 and R7C7 are both cats, so R7C5 must be a dog (no three in a row).
41. R7C4 and R7C5 are both dogs, so R7C3 must be a cat (no three in a row).
42. R5C3 and R7C3 are both cats with one square between them, so R6C3 must be a dog.
43. R6C3 and R6C4 are both dogs, so R6C2 must be a cat (no three in a row).
44. R7C5 and R8C5 are both dogs, so R9C5 must be a cat (no three in a row).
45. R7C6 and R8C6 are both cats, so R9C6 must be a dog (no three in a row).
46. R7C7 and R8C7 are both cats, so R9C7 must be a dog (no three in a row).
47. Imagine R6C1 were a dog: following the rules from there soon forces a contradiction, so R6C1 must be a cat.
48. Imagine R7C1 were a cat: following the rules from there soon forces a contradiction, so R7C1 must be a dog.
49. Imagine R7C2 were a cat: following the rules from there soon forces a contradiction, so R7C2 must be a dog.
50. R7C2 and R8C2 are both dogs, so R9C2 must be a cat (no three in a row).
51. Row 7 already has its 5 dogs, so R7C9 and R7C10 must be cats.
52. R7C10 and R9C10 are both cats with one square between them, so R8C10 must be a dog.
53. R8C8 and R8C10 are both dogs with one square between them, so R8C9 must be a cat.
54. R7C9 and R8C9 are both cats, so R6C9 must be a dog (no three in a row).
55. Row 6 already has its 5 dogs, so R6C10 must be cats.
56. R6C10 and R7C10 are both cats, so R5C10 must be a dog (no three in a row).
57. R5C8 and R5C10 are both dogs with one square between them, so R5C9 must be a cat.
58. Row 8 already has its 5 cats, so R8C1 must be dogs.
59. R7C1 and R8C1 are both dogs, so R9C1 must be a cat (no three in a row).
60. Row 9 already has its 5 cats, so R9C4 must be dogs.
61. Column 2 already has its 5 cats, so R10C2 must be dogs.
62. Imagine R3C6 were a cat: following the rules from there soon forces a contradiction, so R3C6 must be a dog.
63. Imagine R2C6 were a dog: following the rules from there soon forces a contradiction, so R2C6 must be a cat.
64. Imagine R4C8 were a dog: following the rules from there soon forces a contradiction, so R4C8 must be a cat.
65. Imagine R1C8 were a cat: following the rules from there soon forces a contradiction, so R1C8 must be a dog.
66. Imagine R1C5 were a cat: following the rules from there soon forces a contradiction, so R1C5 must be a dog.
67. Column 5 already has its 5 dogs, so R10C5 must be cats.
68. The × clue between R10C5 and R10C6 means they are different. R10C5 is a cat, so R10C6 is a dog.
69. R10C3 and R10C5 are both cats with one square between them, so R10C4 must be a dog.
70. Column 4 already has its 5 dogs, so R4C4 must be cats.
71. R4C4 and R4C5 are both cats, so R4C6 must be a dog (no three in a row).
72. R3C6 and R4C6 are both dogs, so R5C6 must be a cat (no three in a row).
73. Row 5 already has its 5 cats, so R5C1 must be dogs.
74. R3C1 and R5C1 are both dogs with one square between them, so R4C1 must be a cat.
75. Row 4 already has its 5 cats, so R4C9 and R4C10 must be dogs.
76. R4C10 and R5C10 are both dogs, so R3C10 must be a cat (no three in a row).
77. Column 1 already has its 5 cats, so R10C1 must be dogs.
78. Column 6 already has its 5 dogs, so R1C6 must be cats.
79. Imagine R1C7 were a cat: following the rules from there soon forces a contradiction, so R1C7 must be a dog.
80. The × clue between R1C7 and R2C7 means they are different. R1C7 is a dog, so R2C7 is a cat.
81. R1C7 and R1C8 are both dogs, so R1C9 must be a cat (no three in a row).
82. R2C6 and R2C7 are both cats, so R2C8 must be a dog (no three in a row).
83. The × clue between R2C8 and R3C8 means they are different. R2C8 is a dog, so R3C8 is a cat.
84. R3C8 and R3C10 are both cats with one square between them, so R3C9 must be a dog.
85. R3C9 and R4C9 are both dogs, so R2C9 must be a cat (no three in a row).
86. Row 1 already has its 5 cats, so R1C10 must be dogs.
87. Row 2 already has its 5 cats, so R2C10 must be dogs.
88. Row 3 already has its 5 cats, so R3C7 must be dogs.
89. Column 7 already has its 5 dogs, so R10C7 must be cats.
90. R10C7 and R10C8 are both cats, so R10C9 must be a dog (no three in a row).
91. Row 10 already has its 5 dogs, so R10C10 must be cats.