Cats & Dogs #238: 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 R7C9 and R7C10 means they are different. R7C9 is a cat, so R7C10 is a dog.
2. R1C8 and R2C8 are both dogs, so R3C8 must be a cat (no three in a row).
3. Imagine R1C7 were a dog: following the rules from there soon forces a contradiction, so R1C7 must be a cat.
4. The = clue between R1C7 and R2C7 means they are the same. R1C7 is a cat, so R2C7 is a cat.
5. R1C7 and R2C7 are both cats, so R3C7 must be a dog (no three in a row).
6. Imagine R8C2 were a cat: following the rules from there soon forces a contradiction, so R8C2 must be a dog.
7. The = clue between R8C2 and R8C3 means they are the same. R8C2 is a dog, so R8C3 is a dog.
8. The × clue between R8C3 and R9C3 means they are different. R8C3 is a dog, so R9C3 is a cat.
9. R8C2 and R8C3 are both dogs, so R8C1 must be a cat (no three in a row).
10. The × clue between R8C1 and R7C1 means they are different. R8C1 is a cat, so R7C1 is a dog.
11. The = clue between R7C1 and R7C2 means they are the same. R7C1 is a dog, so R7C2 is a dog.
12. R7C1 and R7C2 are both dogs, so R7C3 must be a cat (no three in a row).
13. R7C3 and R7C4 are both cats, so R7C5 must be a dog (no three in a row).
14. The × clue between R7C5 and R8C5 means they are different. R7C5 is a dog, so R8C5 is a cat.
15. R8C2 and R8C3 are both dogs, so R8C4 must be a cat (no three in a row).
16. R8C4 and R8C5 are both cats, so R8C6 must be a dog (no three in a row).
17. The × clue between R8C6 and R9C6 means they are different. R8C6 is a dog, so R9C6 is a cat.
18. R5C1 and R7C1 are both dogs with one square between them, so R6C1 must be a cat.
19. R7C2 and R8C2 are both dogs, so R6C2 must be a cat (no three in a row).
20. R6C1 and R6C2 are both cats, so R6C3 must be a dog (no three in a row).
21. R7C2 and R8C2 are both dogs, so R9C2 must be a cat (no three in a row).
22. The = clue between R9C2 and R10C2 means they are the same. R9C2 is a cat, so R10C2 is a cat.
23. R9C2 and R9C3 are both cats, so R9C1 must be a dog (no three in a row).
24. R9C2 and R9C3 are both cats, so R9C4 must be a dog (no three in a row).
25. The × clue between R9C4 and R10C4 means they are different. R9C4 is a dog, so R10C4 is a cat.
26. R7C4 and R8C4 are both cats, so R6C4 must be a dog (no three in a row).
27. R6C3 and R6C4 are both dogs, so R6C5 must be a cat (no three in a row).
28. Imagine R7C6 were a dog: following the rules from there soon forces a contradiction, so R7C6 must be a cat.
29. Imagine R6C6 were a cat: following the rules from there soon forces a contradiction, so R6C6 must be a dog.
30. Imagine R6C7 were a dog: following the rules from there soon forces a contradiction, so R6C7 must be a cat.
31. The = clue between R6C7 and R6C8 means they are the same. R6C7 is a cat, so R6C8 is a cat.
32. R6C7 and R6C8 are both cats, so R6C9 must be a dog (no three in a row).
33. Row 6 already has its 5 cats, so R6C10 must be dogs.
34. R6C10 and R7C10 are both dogs, so R5C10 must be a cat (no three in a row).
35. R6C10 and R7C10 are both dogs, so R8C10 must be a cat (no three in a row).
36. The = clue between R8C10 and R9C10 means they are the same. R8C10 is a cat, so R9C10 is a cat.
37. R8C10 and R9C10 are both cats, so R10C10 must be a dog (no three in a row).
38. Imagine R4C7 were a cat: following the rules from there soon forces a contradiction, so R4C7 must be a dog.
39. R3C7 and R4C7 are both dogs, so R5C7 must be a cat (no three in a row).
40. The = clue between R5C7 and R5C6 means they are the same. R5C7 is a cat, so R5C6 is a cat.
41. R5C6 and R5C7 are both cats, so R5C5 must be a dog (no three in a row).
42. R5C6 and R5C7 are both cats, so R5C8 must be a dog (no three in a row).
43. R5C7 and R6C7 are both cats, so R7C7 must be a dog (no three in a row).
44. Row 7 already has its 5 dogs, so R7C8 must be cats.
45. R6C8 and R7C8 are both cats, so R8C8 must be a dog (no three in a row).
46. R8C6 and R8C8 are both dogs with one square between them, so R8C7 must be a cat.
47. Row 8 already has its 5 cats, so R8C9 must be dogs.
48. R8C9 and R9C9 are both dogs, so R10C9 must be a cat (no three in a row).
49. Column 7 already has its 5 cats, so R9C7 must be dogs.
50. R9C7 and R9C9 are both dogs with one square between them, so R9C8 must be a cat.
51. Row 9 already has its 5 cats, so R9C5 must be dogs.
52. Column 7 already has its 5 cats, so R10C7 must be dogs.
53. Imagine R1C9 were a dog: following the rules from there soon forces a contradiction, so R1C9 must be a cat.
54. Imagine R2C9 were a dog: following the rules from there soon forces a contradiction, so R2C9 must be a cat.
55. The × clue between R2C9 and R2C10 means they are different. R2C9 is a cat, so R2C10 is a dog.
56. Imagine R1C10 were a dog: following the rules from there soon forces a contradiction, so R1C10 must be a cat.
57. Imagine R3C5 were a dog: following the rules from there soon forces a contradiction, so R3C5 must be a cat.
58. The = clue between R3C5 and R4C5 means they are the same. R3C5 is a cat, so R4C5 is a cat.
59. R3C5 and R4C5 are both cats, so R2C5 must be a dog (no three in a row).
60. Imagine R1C6 were a cat: following the rules from there soon forces a contradiction, so R1C6 must be a dog.
61. The × clue between R1C6 and R2C6 means they are different. R1C6 is a dog, so R2C6 is a cat.
62. Imagine R1C5 were a dog: following the rules from there soon forces a contradiction, so R1C5 must be a cat.
63. Column 5 already has its 5 cats, so R10C5 must be dogs.
64. R10C5 and R10C7 are both dogs with one square between them, so R10C6 must be a cat.
65. Column 6 already has its 5 cats, so R3C6 and R4C6 must be dogs.
66. R4C6 and R4C7 are both dogs, so R4C8 must be a cat (no three in a row).
67. The × clue between R4C8 and R4C9 means they are different. R4C8 is a cat, so R4C9 is a dog.
68. R3C9 and R4C9 are both dogs, so R5C9 must be a cat (no three in a row).
69. Column 8 already has its 5 cats, so R10C8 must be dogs.
70. Row 10 already has its 5 dogs, so R10C1 must be cats.
71. Imagine R1C1 were a cat: following the rules from there soon forces a contradiction, so R1C1 must be a dog.
72. The × clue between R1C1 and R1C2 means they are different. R1C1 is a dog, so R1C2 is a cat.
73. Row 1 already has its 5 cats, so R1C3 and R1C4 must be dogs.
74. Imagine R2C2 were a cat: following the rules from there soon forces a contradiction, so R2C2 must be a dog.
75. Imagine R2C3 were a dog: following the rules from there soon forces a contradiction, so R2C3 must be a cat.
76. Imagine R2C1 were a cat: following the rules from there soon forces a contradiction, so R2C1 must be a dog.
77. R1C1 and R2C1 are both dogs, so R3C1 must be a cat (no three in a row).
78. Row 2 already has its 5 dogs, so R2C4 must be cats.
79. Column 1 already has its 5 dogs, so R4C1 must be cats.
80. Imagine R3C2 were a cat: following the rules from there soon forces a contradiction, so R3C2 must be a dog.
81. R2C2 and R3C2 are both dogs, so R4C2 must be a cat (no three in a row).
82. R4C1 and R4C2 are both cats, so R4C3 must be a dog (no three in a row).
83. R4C2 and R6C2 are both cats with one square between them, so R5C2 must be a dog.
84. R5C1 and R5C2 are both dogs, so R5C3 must be a cat (no three in a row).
85. Row 5 already has its 5 cats, so R5C4 must be dogs.
86. R5C4 and R6C4 are both dogs, so R4C4 must be a cat (no three in a row).
87. R2C4 and R4C4 are both cats with one square between them, so R3C4 must be a dog.
88. R3C2 and R3C4 are both dogs with one square between them, so R3C3 must be a cat.
89. Row 3 already has its 5 dogs, so R3C10 must be cats.
90. R3C10 and R5C10 are both cats with one square between them, so R4C10 must be a dog.