Cats & Dogs #240: 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 R2C1 and R1C1 means they are different. R2C1 is a cat, so R1C1 is a dog.
2. The × clue between R3C7 and R2C7 means they are different. R3C7 is a cat, so R2C7 is a dog.
3. The × clue between R2C7 and R2C8 means they are different. R2C7 is a dog, so R2C8 is a cat.
4. The = clue between R3C9 and R4C9 means they are the same. R3C9 is a dog, so R4C9 is a dog.
5. The = clue between R8C3 and R9C3 means they are the same. R8C3 is a cat, so R9C3 is a cat.
6. The × clue between R10C9 and R10C8 means they are different. R10C9 is a dog, so R10C8 is a cat.
7. R1C1 and R1C2 are both dogs, so R1C3 must be a cat (no three in a row).
8. R8C7 and R8C8 are both dogs, so R8C6 must be a cat (no three in a row).
9. R8C7 and R8C8 are both dogs, so R8C9 must be a cat (no three in a row).
10. R8C3 and R9C3 are both cats, so R7C3 must be a dog (no three in a row).
11. R8C3 and R9C3 are both cats, so R10C3 must be a dog (no three in a row).
12. R3C9 and R4C9 are both dogs, so R2C9 must be a cat (no three in a row).
13. R2C8 and R2C9 are both cats, so R2C10 must be a dog (no three in a row).
14. The = clue between R2C10 and R1C10 means they are the same. R2C10 is a dog, so R1C10 is a dog.
15. R3C9 and R4C9 are both dogs, so R5C9 must be a cat (no three in a row).
16. The × clue between R5C9 and R6C9 means they are different. R5C9 is a cat, so R6C9 is a dog.
17. R1C10 and R2C10 are both dogs, so R3C10 must be a cat (no three in a row).
18. Imagine R1C9 were a dog: following the rules from there soon forces a contradiction, so R1C9 must be a cat.
19. Imagine R2C2 were a cat: following the rules from there soon forces a contradiction, so R2C2 must be a dog.
20. R1C2 and R2C2 are both dogs, so R3C2 must be a cat (no three in a row).
21. Imagine R2C3 were a cat: following the rules from there soon forces a contradiction, so R2C3 must be a dog.
22. Imagine R5C10 were a cat: following the rules from there soon forces a contradiction, so R5C10 must be a dog.
23. Imagine R6C7 were a dog: following the rules from there soon forces a contradiction, so R6C7 must be a cat.
24. The = clue between R6C7 and R6C8 means they are the same. R6C7 is a cat, so R6C8 is a cat.
25. R6C7 and R6C8 are both cats, so R6C6 must be a dog (no three in a row).
26. Imagine R3C8 were a cat: following the rules from there soon forces a contradiction, so R3C8 must be a dog.
27. Imagine R4C10 were a dog: following the rules from there soon forces a contradiction, so R4C10 must be a cat.
28. Imagine R7C8 were a cat: following the rules from there soon forces a contradiction, so R7C8 must be a dog.
29. R7C8 and R8C8 are both dogs, so R9C8 must be a cat (no three in a row).
30. Imagine R1C8 were a cat: following the rules from there soon forces a contradiction, so R1C8 must be a dog.
31. Imagine R1C4 were a dog: following the rules from there soon forces a contradiction, so R1C4 must be a cat.
32. R1C3 and R1C4 are both cats, so R1C5 must be a dog (no three in a row).
33. R1C4 and R2C4 are both cats, so R3C4 must be a dog (no three in a row).
34. The × clue between R3C4 and R3C5 means they are different. R3C4 is a dog, so R3C5 is a cat.
35. R3C5 and R3C7 are both cats with one square between them, so R3C6 must be a dog.
36. The × clue between R3C6 and R4C6 means they are different. R3C6 is a dog, so R4C6 is a cat.
37. The = clue between R4C6 and R4C7 means they are the same. R4C6 is a cat, so R4C7 is a cat.
38. R4C6 and R4C7 are both cats, so R4C5 must be a dog (no three in a row).
39. R4C6 and R4C7 are both cats, so R4C8 must be a dog (no three in a row).
40. R3C7 and R4C7 are both cats, so R5C7 must be a dog (no three in a row).
41. The × clue between R5C7 and R5C8 means they are different. R5C7 is a dog, so R5C8 is a cat.
42. Row 1 already has its 5 dogs, so R1C6 and R1C7 must be cats.
43. Imagine R7C6 were a dog: following the rules from there soon forces a contradiction, so R7C6 must be a cat.
44. R7C6 and R8C6 are both cats, so R9C6 must be a dog (no three in a row).
45. Imagine R7C7 were a cat: following the rules from there soon forces a contradiction, so R7C7 must be a dog.
46. R7C7 and R7C8 are both dogs, so R7C9 must be a cat (no three in a row).
47. R7C7 and R8C7 are both dogs, so R9C7 must be a cat (no three in a row).
48. R9C7 and R9C8 are both cats, so R9C9 must be a dog (no three in a row).
49. The × clue between R9C9 and R9C10 means they are different. R9C9 is a dog, so R9C10 is a cat.
50. Column 7 already has its 5 cats, so R10C7 must be dogs.
51. Imagine R8C1 were a cat: following the rules from there soon forces a contradiction, so R8C1 must be a dog.
52. Imagine R6C1 were a dog: following the rules from there soon forces a contradiction, so R6C1 must be a cat.
53. Imagine R7C1 were a dog: following the rules from there soon forces a contradiction, so R7C1 must be a cat.
54. Imagine R8C2 were a dog: following the rules from there soon forces a contradiction, so R8C2 must be a cat.
55. The × clue between R8C2 and R9C2 means they are different. R8C2 is a cat, so R9C2 is a dog.
56. R8C2 and R8C3 are both cats, so R8C4 must be a dog (no three in a row).
57. Imagine R7C4 were a dog: following the rules from there soon forces a contradiction, so R7C4 must be a cat.
58. R7C4 and R7C6 are both cats with one square between them, so R7C5 must be a dog.
59. Imagine R5C2 were a cat: following the rules from there soon forces a contradiction, so R5C2 must be a dog.
60. The × clue between R5C2 and R6C2 means they are different. R5C2 is a dog, so R6C2 is a cat.
61. The × clue between R6C2 and R6C3 means they are different. R6C2 is a cat, so R6C3 is a dog.
62. R5C1 and R5C2 are both dogs, so R5C3 must be a cat (no three in a row).
63. R6C2 and R8C2 are both cats with one square between them, so R7C2 must be a dog.
64. Row 7 already has its 5 dogs, so R7C10 must be cats.
65. R7C10 and R9C10 are both cats with one square between them, so R8C10 must be a dog.
66. Row 8 already has its 5 dogs, so R8C5 must be cats.
67. Column 2 already has its 5 dogs, so R4C2 and R10C2 must be cats.
68. Imagine R2C5 were a dog: following the rules from there soon forces a contradiction, so R2C5 must be a cat.
69. R2C4 and R2C5 are both cats, so R2C6 must be a dog (no three in a row).
70. Imagine R3C1 were a dog: following the rules from there soon forces a contradiction, so R3C1 must be a cat.
71. R3C1 and R3C2 are both cats, so R3C3 must be a dog (no three in a row).
72. R2C1 and R3C1 are both cats, so R4C1 must be a dog (no three in a row).
73. R2C3 and R3C3 are both dogs, so R4C3 must be a cat (no three in a row).
74. R4C2 and R4C3 are both cats, so R4C4 must be a dog (no three in a row).
75. R3C4 and R4C4 are both dogs, so R5C4 must be a cat (no three in a row).
76. R5C3 and R5C4 are both cats, so R5C5 must be a dog (no three in a row).
77. R5C5 and R5C7 are both dogs with one square between them, so R5C6 must be a cat.
78. R5C4 and R7C4 are both cats with one square between them, so R6C4 must be a dog.
79. R6C3 and R6C4 are both dogs, so R6C5 must be a cat (no three in a row).
80. Row 6 already has its 5 cats, so R6C10 must be dogs.
81. Column 6 already has its 5 cats, so R10C6 must be dogs.
82. R10C6 and R10C7 are both dogs, so R10C5 must be a cat (no three in a row).
83. R8C5 and R10C5 are both cats with one square between them, so R9C5 must be a dog.
84. R9C5 and R9C6 are both dogs, so R9C4 must be a cat (no three in a row).
85. Row 9 already has its 5 cats, so R9C1 must be dogs.
86. R8C1 and R9C1 are both dogs, so R10C1 must be a cat (no three in a row).
87. Column 4 already has its 5 cats, so R10C4 must be dogs.
88. Row 10 already has its 5 dogs, so R10C10 must be cats.