Cats & Dogs #216: 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 R6C3 and R6C2 means they are the same. R6C3 is a cat, so R6C2 is a cat.
2. The × clue between R6C2 and R5C2 means they are different. R6C2 is a cat, so R5C2 is a dog.
3. R6C2 and R6C3 are both cats, so R6C1 must be a dog (no three in a row).
4. R6C2 and R6C3 are both cats, so R6C4 must be a dog (no three in a row).
5. The × clue between R6C4 and R5C4 means they are different. R6C4 is a dog, so R5C4 is a cat.
6. R10C8 and R10C10 are both dogs with one square between them, so R10C9 must be a cat.
7. Imagine R2C3 were a cat: following the rules from there soon forces a contradiction, so R2C3 must be a dog.
8. The = clue between R2C3 and R2C4 means they are the same. R2C3 is a dog, so R2C4 is a dog.
9. R2C3 and R2C4 are both dogs, so R2C2 must be a cat (no three in a row).
10. R1C4 and R2C4 are both dogs, so R3C4 must be a cat (no three in a row).
11. R3C4 and R5C4 are both cats with one square between them, so R4C4 must be a dog.
12. Imagine R6C5 were a dog: following the rules from there soon forces a contradiction, so R6C5 must be a cat.
13. Imagine R7C2 were a cat: following the rules from there soon forces a contradiction, so R7C2 must be a dog.
14. The = clue between R7C2 and R7C3 means they are the same. R7C2 is a dog, so R7C3 is a dog.
15. The × clue between R7C3 and R8C3 means they are different. R7C3 is a dog, so R8C3 is a cat.
16. R7C2 and R7C3 are both dogs, so R7C1 must be a cat (no three in a row).
17. R7C2 and R7C3 are both dogs, so R7C4 must be a cat (no three in a row).
18. R7C1 and R9C1 are both cats with one square between them, so R8C1 must be a dog.
19. Imagine R8C2 were a dog: following the rules from there soon forces a contradiction, so R8C2 must be a cat.
20. R8C2 and R8C3 are both cats, so R8C4 must be a dog (no three in a row).
21. Column 4 already has its 5 dogs, so R9C4 and R10C4 must be cats.
22. Imagine R8C5 were a dog: following the rules from there soon forces a contradiction, so R8C5 must be a cat.
23. The = clue between R8C5 and R8C6 means they are the same. R8C5 is a cat, so R8C6 is a cat.
24. R8C5 and R8C6 are both cats, so R8C7 must be a dog (no three in a row).
25. Imagine R8C10 were a cat: following the rules from there soon forces a contradiction, so R8C10 must be a dog.
26. R8C10 and R10C10 are both dogs with one square between them, so R9C10 must be a cat.
27. Imagine R9C2 were a cat: following the rules from there soon forces a contradiction, so R9C2 must be a dog.
28. Imagine R3C2 were a cat: following the rules from there soon forces a contradiction, so R3C2 must be a dog.
29. R3C1 and R3C2 are both dogs, so R3C3 must be a cat (no three in a row).
30. R3C3 and R3C4 are both cats, so R3C5 must be a dog (no three in a row).
31. R3C2 and R5C2 are both dogs with one square between them, so R4C2 must be a cat.
32. Imagine R1C2 were a dog: following the rules from there soon forces a contradiction, so R1C2 must be a cat.
33. Column 2 already has its 5 cats, so R10C2 must be dogs.
34. The = clue between R10C2 and R10C3 means they are the same. R10C2 is a dog, so R10C3 is a dog.
35. The × clue between R10C3 and R9C3 means they are different. R10C3 is a dog, so R9C3 is a cat.
36. R9C3 and R9C4 are both cats, so R9C5 must be a dog (no three in a row).
37. R10C2 and R10C3 are both dogs, so R10C1 must be a cat (no three in a row).
38. Imagine R6C8 were a cat: following the rules from there soon forces a contradiction, so R6C8 must be a dog.
39. The = clue between R6C8 and R7C8 means they are the same. R6C8 is a dog, so R7C8 is a dog.
40. R6C8 and R7C8 are both dogs, so R5C8 must be a cat (no three in a row).
41. R6C8 and R7C8 are both dogs, so R8C8 must be a cat (no three in a row).
42. Row 8 already has its 5 cats, so R8C9 must be dogs.
43. Imagine R5C6 were a cat: following the rules from there soon forces a contradiction, so R5C6 must be a dog.
44. The = clue between R5C6 and R6C6 means they are the same. R5C6 is a dog, so R6C6 is a dog.
45. R6C6 and R6C8 are both dogs with one square between them, so R6C7 must be a cat.
46. The × clue between R6C7 and R5C7 means they are different. R6C7 is a cat, so R5C7 is a dog.
47. R5C6 and R5C7 are both dogs, so R5C5 must be a cat (no three in a row).
48. R5C4 and R5C5 are both cats, so R5C3 must be a dog (no three in a row).
49. R5C2 and R5C3 are both dogs, so R5C1 must be a cat (no three in a row).
50. R5C5 and R6C5 are both cats, so R4C5 must be a dog (no three in a row).
51. R4C4 and R4C5 are both dogs, so R4C3 must be a cat (no three in a row).
52. R4C2 and R4C3 are both cats, so R4C1 must be a dog (no three in a row).
53. R4C4 and R4C5 are both dogs, so R4C6 must be a cat (no three in a row).
54. R3C1 and R4C1 are both dogs, so R2C1 must be a cat (no three in a row).
55. R5C6 and R6C6 are both dogs, so R7C6 must be a cat (no three in a row).
56. R7C6 and R8C6 are both cats, so R9C6 must be a dog (no three in a row).
57. R9C5 and R9C6 are both dogs, so R9C7 must be a cat (no three in a row).
58. Row 9 already has its 5 cats, so R9C8 and R9C9 must be dogs.
59. R8C9 and R9C9 are both dogs, so R7C9 must be a cat (no three in a row).
60. Column 1 already has its 5 cats, so R1C1 must be dogs.
61. Column 3 already has its 5 cats, so R1C3 must be dogs.
62. R1C3 and R1C4 are both dogs, so R1C5 must be a cat (no three in a row).
63. Column 5 already has its 5 cats, so R10C5 must be dogs.
64. Row 10 already has its 5 dogs, so R10C6 and R10C7 must be cats.
65. Imagine R1C8 were a dog: following the rules from there soon forces a contradiction, so R1C8 must be a cat.
66. Imagine R1C9 were a cat: following the rules from there soon forces a contradiction, so R1C9 must be a dog.
67. Imagine R1C10 were a dog: following the rules from there soon forces a contradiction, so R1C10 must be a cat.
68. Imagine R2C6 were a cat: following the rules from there soon forces a contradiction, so R2C6 must be a dog.
69. Imagine R1C6 were a dog: following the rules from there soon forces a contradiction, so R1C6 must be a cat.
70. R1C5 and R1C6 are both cats, so R1C7 must be a dog (no three in a row).
71. Column 6 already has its 5 cats, so R3C6 must be dogs.
72. The × clue between R3C6 and R3C7 means they are different. R3C6 is a dog, so R3C7 is a cat.
73. Imagine R2C7 were a cat: following the rules from there soon forces a contradiction, so R2C7 must be a dog.
74. R2C6 and R2C7 are both dogs, so R2C8 must be a cat (no three in a row).
75. R2C8 and R2C9 are both cats, so R2C10 must be a dog (no three in a row).
76. R1C8 and R2C8 are both cats, so R3C8 must be a dog (no three in a row).
77. Row 3 already has its 5 dogs, so R3C9 must be cats.
78. R2C9 and R3C9 are both cats, so R4C9 must be a dog (no three in a row).
79. Row 3 already has its 5 dogs, so R3C10 must be cats.
80. Column 8 already has its 5 dogs, so R4C8 must be cats.
81. R4C6 and R4C8 are both cats with one square between them, so R4C7 must be a dog.
82. Row 4 already has its 5 dogs, so R4C10 must be cats.
83. R3C10 and R4C10 are both cats, so R5C10 must be a dog (no three in a row).
84. Row 5 already has its 5 dogs, so R5C9 must be cats.
85. R5C9 and R7C9 are both cats with one square between them, so R6C9 must be a dog.
86. R6C8 and R6C9 are both dogs, so R6C10 must be a cat (no three in a row).
87. Column 7 already has its 5 dogs, so R7C7 must be cats.
88. Row 7 already has its 5 cats, so R7C10 must be dogs.