Cats & Dogs #213: 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 R7C3 and R7C4 means they are different. R7C3 is a cat, so R7C4 is a dog.
2. The = clue between R8C8 and R7C8 means they are the same. R8C8 is a dog, so R7C8 is a dog.
3. R7C8 and R7C9 are both dogs, so R7C7 must be a cat (no three in a row).
4. R7C8 and R7C9 are both dogs, so R7C10 must be a cat (no three in a row).
5. R7C8 and R8C8 are both dogs, so R6C8 must be a cat (no three in a row).
6. R7C8 and R8C8 are both dogs, so R9C8 must be a cat (no three in a row).
7. The × clue between R9C8 and R10C8 means they are different. R9C8 is a cat, so R10C8 is a dog.
8. Imagine R3C4 were a cat: following the rules from there soon forces a contradiction, so R3C4 must be a dog.
9. The = clue between R3C4 and R4C4 means they are the same. R3C4 is a dog, so R4C4 is a dog.
10. R3C4 and R4C4 are both dogs, so R2C4 must be a cat (no three in a row).
11. R2C3 and R2C4 are both cats, so R2C2 must be a dog (no three in a row).
12. The × clue between R2C2 and R1C2 means they are different. R2C2 is a dog, so R1C2 is a cat.
13. The × clue between R2C2 and R3C2 means they are different. R2C2 is a dog, so R3C2 is a cat.
14. R2C3 and R2C4 are both cats, so R2C5 must be a dog (no three in a row).
15. The × clue between R2C5 and R1C5 means they are different. R2C5 is a dog, so R1C5 is a cat.
16. The × clue between R1C5 and R1C6 means they are different. R1C5 is a cat, so R1C6 is a dog.
17. R1C6 and R1C7 are both dogs, so R1C8 must be a cat (no three in a row).
18. R2C5 and R2C6 are both dogs, so R2C7 must be a cat (no three in a row).
19. R3C4 and R4C4 are both dogs, so R5C4 must be a cat (no three in a row).
20. The = clue between R5C4 and R5C3 means they are the same. R5C4 is a cat, so R5C3 is a cat.
21. R5C3 and R5C4 are both cats, so R5C2 must be a dog (no three in a row).
22. R5C3 and R5C4 are both cats, so R5C5 must be a dog (no three in a row).
23. R5C5 and R5C7 are both dogs with one square between them, so R5C6 must be a cat.
24. R5C3 and R7C3 are both cats with one square between them, so R6C3 must be a dog.
25. R1C6 and R2C6 are both dogs, so R3C6 must be a cat (no three in a row).
26. R3C6 and R5C6 are both cats with one square between them, so R4C6 must be a dog.
27. Imagine R3C7 were a cat: following the rules from there soon forces a contradiction, so R3C7 must be a dog.
28. R3C7 and R5C7 are both dogs with one square between them, so R4C7 must be a cat.
29. Imagine R6C5 were a dog: following the rules from there soon forces a contradiction, so R6C5 must be a cat.
30. Imagine R7C5 were a cat: following the rules from there soon forces a contradiction, so R7C5 must be a dog.
31. R7C4 and R7C5 are both dogs, so R7C6 must be a cat (no three in a row).
32. Imagine R10C6 were a dog: following the rules from there soon forces a contradiction, so R10C6 must be a cat.
33. Imagine R10C9 were a dog: following the rules from there soon forces a contradiction, so R10C9 must be a cat.
34. The = clue between R10C9 and R10C10 means they are the same. R10C9 is a cat, so R10C10 is a cat.
35. Imagine R8C6 were a dog: following the rules from there soon forces a contradiction, so R8C6 must be a cat.
36. R7C6 and R8C6 are both cats, so R9C6 must be a dog (no three in a row).
37. Imagine R8C5 were a cat: following the rules from there soon forces a contradiction, so R8C5 must be a dog.
38. R7C5 and R8C5 are both dogs, so R9C5 must be a cat (no three in a row).
39. Imagine R8C7 were a cat: following the rules from there soon forces a contradiction, so R8C7 must be a dog.
40. R8C7 and R8C8 are both dogs, so R8C9 must be a cat (no three in a row).
41. The × clue between R8C9 and R8C10 means they are different. R8C9 is a cat, so R8C10 is a dog.
42. R8C9 and R10C9 are both cats with one square between them, so R9C9 must be a dog.
43. Imagine R1C3 were a cat: following the rules from there soon forces a contradiction, so R1C3 must be a dog.
44. Imagine R4C2 were a dog: following the rules from there soon forces a contradiction, so R4C2 must be a cat.
45. Imagine R4C3 were a cat: following the rules from there soon forces a contradiction, so R4C3 must be a dog.
46. Imagine R4C1 were a dog: following the rules from there soon forces a contradiction, so R4C1 must be a cat.
47. R4C1 and R6C1 are both cats with one square between them, so R5C1 must be a dog.
48. Imagine R5C9 were a dog: following the rules from there soon forces a contradiction, so R5C9 must be a cat.
49. Imagine R1C9 were a dog: following the rules from there soon forces a contradiction, so R1C9 must be a cat.
50. The = clue between R1C9 and R2C9 means they are the same. R1C9 is a cat, so R2C9 is a cat.
51. R1C8 and R1C9 are both cats, so R1C10 must be a dog (no three in a row).
52. The × clue between R1C10 and R2C10 means they are different. R1C10 is a dog, so R2C10 is a cat.
53. R2C7 and R2C9 are both cats with one square between them, so R2C8 must be a dog.
54. R1C9 and R2C9 are both cats, so R3C9 must be a dog (no three in a row).
55. R3C7 and R3C9 are both dogs with one square between them, so R3C8 must be a cat.
56. Row 2 already has its 5 cats, so R2C1 must be dogs.
57. Column 9 already has its 5 cats, so R4C9 must be dogs.
58. R4C9 and R4C10 are both dogs, so R4C8 must be a cat (no three in a row).
59. R3C8 and R4C8 are both cats, so R5C8 must be a dog (no three in a row).
60. Row 5 already has its 5 dogs, so R5C10 must be cats.
61. R5C10 and R7C10 are both cats with one square between them, so R6C10 must be a dog.
62. Column 9 already has its 5 cats, so R6C9 must be dogs.
63. Imagine R1C1 were a dog: following the rules from there soon forces a contradiction, so R1C1 must be a cat.
64. Row 1 already has its 5 cats, so R1C4 must be dogs.
65. Imagine R3C5 were a dog: following the rules from there soon forces a contradiction, so R3C5 must be a cat.
66. Column 5 already has its 5 cats, so R10C5 must be dogs.
67. The × clue between R10C5 and R10C4 means they are different. R10C5 is a dog, so R10C4 is a cat.
68. The × clue between R10C4 and R9C4 means they are different. R10C4 is a cat, so R9C4 is a dog.
69. R7C4 and R9C4 are both dogs with one square between them, so R8C4 must be a cat.
70. The × clue between R8C4 and R8C3 means they are different. R8C4 is a cat, so R8C3 is a dog.
71. Row 8 already has its 5 dogs, so R8C1 must be cats.
72. R6C1 and R8C1 are both cats with one square between them, so R7C1 must be a dog.
73. Row 7 already has its 5 dogs, so R7C2 must be cats.
74. Row 8 already has its 5 dogs, so R8C2 must be cats.
75. R7C2 and R8C2 are both cats, so R6C2 must be a dog (no three in a row).
76. R6C2 and R6C3 are both dogs, so R6C4 must be a cat (no three in a row).
77. R7C2 and R8C2 are both cats, so R9C2 must be a dog (no three in a row).
78. The = clue between R9C2 and R9C1 means they are the same. R9C2 is a dog, so R9C1 is a dog.
79. R9C1 and R9C2 are both dogs, so R9C3 must be a cat (no three in a row).
80. Row 6 already has its 5 dogs, so R6C7 must be cats.
81. Row 9 already has its 5 dogs, so R9C7 and R9C10 must be cats.
82. Column 2 already has its 5 cats, so R10C2 must be dogs.
83. The × clue between R10C2 and R10C3 means they are different. R10C2 is a dog, so R10C3 is a cat.
84. Row 10 already has its 5 cats, so R10C1 and R10C7 must be dogs.
85. Column 1 already has its 5 dogs, so R3C1 must be cats.
86. R3C1 and R3C2 are both cats, so R3C3 must be a dog (no three in a row).
87. Row 3 already has its 5 cats, so R3C10 must be dogs.