Cats & Dogs #234: 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 R1C9 and R2C9 means they are different. R1C9 is a cat, so R2C9 is a dog.
2. The = clue between R3C8 and R3C9 means they are the same. R3C8 is a dog, so R3C9 is a dog.
3. The × clue between R5C4 and R5C5 means they are different. R5C4 is a dog, so R5C5 is a cat.
4. The = clue between R5C4 and R6C4 means they are the same. R5C4 is a dog, so R6C4 is a dog.
5. R1C7 and R1C9 are both cats with one square between them, so R1C8 must be a dog.
6. R3C8 and R3C9 are both dogs, so R3C7 must be a cat (no three in a row).
7. R3C8 and R3C9 are both dogs, so R3C10 must be a cat (no three in a row).
8. The × clue between R3C10 and R2C10 means they are different. R3C10 is a cat, so R2C10 is a dog.
9. R2C9 and R2C10 are both dogs, so R2C8 must be a cat (no three in a row).
10. R5C4 and R6C4 are both dogs, so R4C4 must be a cat (no three in a row).
11. R4C2 and R4C4 are both cats with one square between them, so R4C3 must be a dog.
12. R5C4 and R6C4 are both dogs, so R7C4 must be a cat (no three in a row).
13. R1C7 and R3C7 are both cats with one square between them, so R2C7 must be a dog.
14. R2C9 and R3C9 are both dogs, so R4C9 must be a cat (no three in a row).
15. Imagine R2C2 were a dog: following the rules from there soon forces a contradiction, so R2C2 must be a cat.
16. The = clue between R2C2 and R2C3 means they are the same. R2C2 is a cat, so R2C3 is a cat.
17. R2C2 and R2C3 are both cats, so R2C1 must be a dog (no three in a row).
18. R2C2 and R2C3 are both cats, so R2C4 must be a dog (no three in a row).
19. R2C2 and R4C2 are both cats with one square between them, so R3C2 must be a dog.
20. Row 2 already has its 5 dogs, so R2C5 and R2C6 must be cats.
21. Imagine R4C6 were a cat: following the rules from there soon forces a contradiction, so R4C6 must be a dog.
22. The = clue between R4C6 and R4C7 means they are the same. R4C6 is a dog, so R4C7 is a dog.
23. The = clue between R4C7 and R5C7 means they are the same. R4C7 is a dog, so R5C7 is a dog.
24. R4C6 and R4C7 are both dogs, so R4C5 must be a cat (no three in a row).
25. R4C6 and R4C7 are both dogs, so R4C8 must be a cat (no three in a row).
26. The × clue between R4C8 and R5C8 means they are different. R4C8 is a cat, so R5C8 is a dog.
27. R4C8 and R4C9 are both cats, so R4C10 must be a dog (no three in a row).
28. R5C7 and R5C8 are both dogs, so R5C6 must be a cat (no three in a row).
29. R5C7 and R5C8 are both dogs, so R5C9 must be a cat (no three in a row).
30. R2C5 and R4C5 are both cats with one square between them, so R3C5 must be a dog.
31. R4C5 and R5C5 are both cats, so R6C5 must be a dog (no three in a row).
32. R6C4 and R6C5 are both dogs, so R6C3 must be a cat (no three in a row).
33. R6C4 and R6C5 are both dogs, so R6C6 must be a cat (no three in a row).
34. R5C6 and R6C6 are both cats, so R7C6 must be a dog (no three in a row).
35. R4C7 and R5C7 are both dogs, so R6C7 must be a cat (no three in a row).
36. R6C6 and R6C7 are both cats, so R6C8 must be a dog (no three in a row).
37. R5C8 and R6C8 are both dogs, so R7C8 must be a cat (no three in a row).
38. R4C9 and R5C9 are both cats, so R6C9 must be a dog (no three in a row).
39. R6C8 and R6C9 are both dogs, so R6C10 must be a cat (no three in a row).
40. The × clue between R6C10 and R5C10 means they are different. R6C10 is a cat, so R5C10 is a dog.
41. Row 4 already has its 5 cats, so R4C1 must be dogs.
42. R2C1 and R4C1 are both dogs with one square between them, so R3C1 must be a cat.
43. Imagine R10C6 were a dog: following the rules from there soon forces a contradiction, so R10C6 must be a cat.
44. Imagine R1C1 were a dog: following the rules from there soon forces a contradiction, so R1C1 must be a cat.
45. The = clue between R1C1 and R1C2 means they are the same. R1C1 is a cat, so R1C2 is a cat.
46. R1C1 and R1C2 are both cats, so R1C3 must be a dog (no three in a row).
47. Imagine R1C6 were a cat: following the rules from there soon forces a contradiction, so R1C6 must be a dog.
48. Imagine R1C10 were a cat: following the rules from there soon forces a contradiction, so R1C10 must be a dog.
49. Imagine R3C3 were a dog: following the rules from there soon forces a contradiction, so R3C3 must be a cat.
50. Imagine R3C4 were a dog: following the rules from there soon forces a contradiction, so R3C4 must be a cat.
51. Row 3 already has its 5 cats, so R3C6 must be dogs.
52. Imagine R5C1 were a dog: following the rules from there soon forces a contradiction, so R5C1 must be a cat.
53. Imagine R6C1 were a dog: following the rules from there soon forces a contradiction, so R6C1 must be a cat.
54. R6C1 and R6C3 are both cats with one square between them, so R6C2 must be a dog.
55. R5C1 and R6C1 are both cats, so R7C1 must be a dog (no three in a row).
56. Imagine R7C9 were a cat: following the rules from there soon forces a contradiction, so R7C9 must be a dog.
57. R6C9 and R7C9 are both dogs, so R8C9 must be a cat (no three in a row).
58. Imagine R7C10 were a dog: following the rules from there soon forces a contradiction, so R7C10 must be a cat.
59. R6C10 and R7C10 are both cats, so R8C10 must be a dog (no three in a row).
60. Column 10 already has its 5 dogs, so R9C10 and R10C10 must be cats.
61. Imagine R8C7 were a cat: following the rules from there soon forces a contradiction, so R8C7 must be a dog.
62. Imagine R7C5 were a cat: following the rules from there soon forces a contradiction, so R7C5 must be a dog.
63. R7C5 and R7C6 are both dogs, so R7C7 must be a cat (no three in a row).
64. R6C5 and R7C5 are both dogs, so R8C5 must be a cat (no three in a row).
65. Imagine R8C4 were a cat: following the rules from there soon forces a contradiction, so R8C4 must be a dog.
66. Imagine R8C2 were a dog: following the rules from there soon forces a contradiction, so R8C2 must be a cat.
67. The × clue between R8C2 and R9C2 means they are different. R8C2 is a cat, so R9C2 is a dog.
68. Imagine R8C3 were a cat: following the rules from there soon forces a contradiction, so R8C3 must be a dog.
69. Imagine R5C2 were a dog: following the rules from there soon forces a contradiction, so R5C2 must be a cat.
70. R5C1 and R5C2 are both cats, so R5C3 must be a dog (no three in a row).
71. Column 2 already has its 5 cats, so R7C2 must be dogs.
72. The × clue between R7C2 and R7C3 means they are different. R7C2 is a dog, so R7C3 is a cat.
73. Column 2 already has its 5 cats, so R10C2 must be dogs.
74. Imagine R8C1 were a cat: following the rules from there soon forces a contradiction, so R8C1 must be a dog.
75. R7C1 and R8C1 are both dogs, so R9C1 must be a cat (no three in a row).
76. Row 8 already has its 5 dogs, so R8C6 must be cats.
77. R8C6 and R10C6 are both cats with one square between them, so R9C6 must be a dog.
78. Row 8 already has its 5 dogs, so R8C8 must be cats.
79. R7C8 and R8C8 are both cats, so R9C8 must be a dog (no three in a row).
80. R9C6 and R9C8 are both dogs with one square between them, so R9C7 must be a cat.
81. Column 1 already has its 5 cats, so R10C1 must be dogs.
82. R10C1 and R10C2 are both dogs, so R10C3 must be a cat (no three in a row).
83. Column 3 already has its 5 cats, so R9C3 must be dogs.
84. R9C2 and R9C3 are both dogs, so R9C4 must be a cat (no three in a row).
85. Column 7 already has its 5 cats, so R10C7 must be dogs.
86. The × clue between R10C7 and R10C8 means they are different. R10C7 is a dog, so R10C8 is a cat.
87. R10C8 and R10C10 are both cats with one square between them, so R10C9 must be a dog.
88. Row 10 already has its 5 dogs, so R10C4 must be cats.
89. Column 4 already has its 5 cats, so R1C4 must be dogs.
90. R1C3 and R1C4 are both dogs, so R1C5 must be a cat (no three in a row).
91. Column 5 already has its 5 cats, so R9C5 must be dogs.
92. Row 9 already has its 5 dogs, so R9C9 must be cats.