Cats & Dogs #233: 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 R3C4 and R4C4 means they are different. R3C4 is a cat, so R4C4 is a dog.
2. The × clue between R4C4 and R4C5 means they are different. R4C4 is a dog, so R4C5 is a cat.
3. The × clue between R4C5 and R4C6 means they are different. R4C5 is a cat, so R4C6 is a dog.
4. The × clue between R7C5 and R7C6 means they are different. R7C5 is a cat, so R7C6 is a dog.
5. The = clue between R10C10 and R10C9 means they are the same. R10C10 is a cat, so R10C9 is a cat.
6. The × clue between R10C9 and R9C9 means they are different. R10C9 is a cat, so R9C9 is a dog.
7. R3C4 and R3C5 are both cats, so R3C3 must be a dog (no three in a row).
8. R3C4 and R3C5 are both cats, so R3C6 must be a dog (no three in a row).
9. R4C2 and R4C4 are both dogs with one square between them, so R4C3 must be a cat.
10. R10C9 and R10C10 are both cats, so R10C8 must be a dog (no three in a row).
11. R4C3 and R5C3 are both cats, so R6C3 must be a dog (no three in a row).
12. R3C5 and R4C5 are both cats, so R2C5 must be a dog (no three in a row).
13. R3C5 and R4C5 are both cats, so R5C5 must be a dog (no three in a row).
14. R1C6 and R3C6 are both dogs with one square between them, so R2C6 must be a cat.
15. R3C6 and R4C6 are both dogs, so R5C6 must be a cat (no three in a row).
16. Imagine R5C7 were a cat: following the rules from there soon forces a contradiction, so R5C7 must be a dog.
17. The = clue between R5C7 and R5C8 means they are the same. R5C7 is a dog, so R5C8 is a dog.
18. R5C7 and R5C8 are both dogs, so R5C9 must be a cat (no three in a row).
19. Imagine R1C2 were a cat: following the rules from there soon forces a contradiction, so R1C2 must be a dog.
20. The = clue between R1C2 and R2C2 means they are the same. R1C2 is a dog, so R2C2 is a dog.
21. R1C2 and R2C2 are both dogs, so R3C2 must be a cat (no three in a row).
22. Imagine R4C1 were a cat: following the rules from there soon forces a contradiction, so R4C1 must be a dog.
23. Imagine R4C7 were a dog: following the rules from there soon forces a contradiction, so R4C7 must be a cat.
24. Imagine R4C8 were a dog: following the rules from there soon forces a contradiction, so R4C8 must be a cat.
25. R4C7 and R4C8 are both cats, so R4C9 must be a dog (no three in a row).
26. Row 4 already has its 5 dogs, so R4C10 must be cats.
27. Imagine R5C1 were a dog: following the rules from there soon forces a contradiction, so R5C1 must be a cat.
28. R5C1 and R5C3 are both cats with one square between them, so R5C2 must be a dog.
29. R5C1 and R6C1 are both cats, so R7C1 must be a dog (no three in a row).
30. R4C2 and R5C2 are both dogs, so R6C2 must be a cat (no three in a row).
31. Row 5 already has its 5 dogs, so R5C4 must be cats.
32. Imagine R6C6 were a dog: following the rules from there soon forces a contradiction, so R6C6 must be a cat.
33. Imagine R6C7 were a cat: following the rules from there soon forces a contradiction, so R6C7 must be a dog.
34. The = clue between R6C7 and R6C8 means they are the same. R6C7 is a dog, so R6C8 is a dog.
35. R6C7 and R6C8 are both dogs, so R6C9 must be a cat (no three in a row).
36. R5C7 and R6C7 are both dogs, so R7C7 must be a cat (no three in a row).
37. R5C8 and R6C8 are both dogs, so R7C8 must be a cat (no three in a row).
38. R7C7 and R7C8 are both cats, so R7C9 must be a dog (no three in a row).
39. R7C9 and R9C9 are both dogs with one square between them, so R8C9 must be a cat.
40. Imagine R1C8 were a dog: following the rules from there soon forces a contradiction, so R1C8 must be a cat.
41. The = clue between R1C8 and R2C8 means they are the same. R1C8 is a cat, so R2C8 is a cat.
42. R2C6 and R2C8 are both cats with one square between them, so R2C7 must be a dog.
43. R1C8 and R2C8 are both cats, so R3C8 must be a dog (no three in a row).
44. R3C6 and R3C8 are both dogs with one square between them, so R3C7 must be a cat.
45. Imagine R1C9 were a cat: following the rules from there soon forces a contradiction, so R1C9 must be a dog.
46. The × clue between R1C9 and R2C9 means they are different. R1C9 is a dog, so R2C9 is a cat.
47. R2C8 and R2C9 are both cats, so R2C10 must be a dog (no three in a row).
48. Column 9 already has its 5 cats, so R3C9 must be dogs.
49. R3C8 and R3C9 are both dogs, so R3C10 must be a cat (no three in a row).
50. Row 3 already has its 5 cats, so R3C1 must be dogs.
51. R3C1 and R4C1 are both dogs, so R2C1 must be a cat (no three in a row).
52. Imagine R6C10 were a cat: following the rules from there soon forces a contradiction, so R6C10 must be a dog.
53. R5C10 and R6C10 are both dogs, so R7C10 must be a cat (no three in a row).
54. The = clue between R7C10 and R8C10 means they are the same. R7C10 is a cat, so R8C10 is a cat.
55. R8C9 and R8C10 are both cats, so R8C8 must be a dog (no three in a row).
56. R8C8 and R10C8 are both dogs with one square between them, so R9C8 must be a cat.
57. R7C10 and R8C10 are both cats, so R9C10 must be a dog (no three in a row).
58. Column 10 already has its 5 cats, so R1C10 must be dogs.
59. Imagine R1C1 were a dog: following the rules from there soon forces a contradiction, so R1C1 must be a cat.
60. Imagine R1C7 were a dog: following the rules from there soon forces a contradiction, so R1C7 must be a cat.
61. Imagine R7C2 were a dog: following the rules from there soon forces a contradiction, so R7C2 must be a cat.
62. R6C2 and R7C2 are both cats, so R8C2 must be a dog (no three in a row).
63. Row 7 already has its 5 cats, so R7C3 must be dogs.
64. R6C3 and R7C3 are both dogs, so R8C3 must be a cat (no three in a row).
65. Row 7 already has its 5 cats, so R7C4 must be dogs.
66. Column 2 already has its 5 dogs, so R9C2 must be cats.
67. The × clue between R9C2 and R9C1 means they are different. R9C2 is a cat, so R9C1 is a dog.
68. R7C1 and R9C1 are both dogs with one square between them, so R8C1 must be a cat.
69. Column 1 already has its 5 cats, so R10C1 must be dogs.
70. Column 2 already has its 5 dogs, so R10C2 must be cats.
71. Imagine R6C4 were a dog: following the rules from there soon forces a contradiction, so R6C4 must be a cat.
72. R6C4 and R6C6 are both cats with one square between them, so R6C5 must be a dog.
73. Imagine R8C4 were a cat: following the rules from there soon forces a contradiction, so R8C4 must be a dog.
74. R7C4 and R8C4 are both dogs, so R9C4 must be a cat (no three in a row).
75. R9C2 and R9C4 are both cats with one square between them, so R9C3 must be a dog.
76. Imagine R8C5 were a cat: following the rules from there soon forces a contradiction, so R8C5 must be a dog.
77. R8C4 and R8C5 are both dogs, so R8C6 must be a cat (no three in a row).
78. Row 8 already has its 5 cats, so R8C7 must be dogs.
79. Imagine R9C5 were a dog: following the rules from there soon forces a contradiction, so R9C5 must be a cat.
80. R9C4 and R9C5 are both cats, so R9C6 must be a dog (no three in a row).
81. Row 9 already has its 5 dogs, so R9C7 must be cats.
82. Column 6 already has its 5 dogs, so R10C6 must be cats.
83. The = clue between R10C6 and R10C5 means they are the same. R10C6 is a cat, so R10C5 is a cat.
84. R10C5 and R10C6 are both cats, so R10C4 must be a dog (no three in a row).
85. R10C5 and R10C6 are both cats, so R10C7 must be a dog (no three in a row).
86. Row 10 already has its 5 cats, so R10C3 must be dogs.
87. Column 3 already has its 5 dogs, so R1C3 and R2C3 must be cats.
88. Row 2 already has its 5 cats, so R2C4 must be dogs.
89. Column 4 already has its 5 dogs, so R1C4 must be cats.
90. R1C3 and R1C4 are both cats, so R1C5 must be a dog (no three in a row).