Cats & Dogs #215: 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 R4C5 and R3C5 means they are the same. R4C5 is a cat, so R3C5 is a cat.
2. The = clue between R3C5 and R3C6 means they are the same. R3C5 is a cat, so R3C6 is a cat.
3. The = clue between R10C10 and R9C10 means they are the same. R10C10 is a dog, so R9C10 is a dog.
4. R3C3 and R3C5 are both cats with one square between them, so R3C4 must be a dog.
5. R3C5 and R3C6 are both cats, so R3C7 must be a dog (no three in a row).
6. The = clue between R3C7 and R2C7 means they are the same. R3C7 is a dog, so R2C7 is a dog.
7. R4C3 and R4C5 are both cats with one square between them, so R4C4 must be a dog.
8. R3C3 and R4C3 are both cats, so R2C3 must be a dog (no three in a row).
9. The × clue between R2C3 and R1C3 means they are different. R2C3 is a dog, so R1C3 is a cat.
10. R3C3 and R4C3 are both cats, so R5C3 must be a dog (no three in a row).
11. R3C4 and R4C4 are both dogs, so R2C4 must be a cat (no three in a row).
12. R3C4 and R4C4 are both dogs, so R5C4 must be a cat (no three in a row).
13. R3C5 and R4C5 are both cats, so R2C5 must be a dog (no three in a row).
14. R2C5 and R2C7 are both dogs with one square between them, so R2C6 must be a cat.
15. R3C5 and R4C5 are both cats, so R5C5 must be a dog (no three in a row).
16. R5C5 and R5C6 are both dogs, so R5C7 must be a cat (no three in a row).
17. R2C6 and R3C6 are both cats, so R1C6 must be a dog (no three in a row).
18. R2C6 and R3C6 are both cats, so R4C6 must be a dog (no three in a row).
19. R4C6 and R5C6 are both dogs, so R6C6 must be a cat (no three in a row).
20. R2C7 and R3C7 are both dogs, so R1C7 must be a cat (no three in a row).
21. R2C7 and R3C7 are both dogs, so R4C7 must be a cat (no three in a row).
22. R4C7 and R5C7 are both cats, so R6C7 must be a dog (no three in a row).
23. R9C10 and R10C10 are both dogs, so R8C10 must be a cat (no three in a row).
24. Imagine R6C4 were a cat: following the rules from there soon forces a contradiction, so R6C4 must be a dog.
25. Imagine R6C10 were a cat: following the rules from there soon forces a contradiction, so R6C10 must be a dog.
26. The = clue between R6C10 and R7C10 means they are the same. R6C10 is a dog, so R7C10 is a dog.
27. R6C10 and R7C10 are both dogs, so R5C10 must be a cat (no three in a row).
28. The = clue between R5C10 and R5C9 means they are the same. R5C10 is a cat, so R5C9 is a cat.
29. R5C7 and R5C9 are both cats with one square between them, so R5C8 must be a dog.
30. The = clue between R5C8 and R4C8 means they are the same. R5C8 is a dog, so R4C8 is a dog.
31. R4C8 and R5C8 are both dogs, so R3C8 must be a cat (no three in a row).
32. R4C8 and R5C8 are both dogs, so R6C8 must be a cat (no three in a row).
33. Imagine R1C8 were a cat: following the rules from there soon forces a contradiction, so R1C8 must be a dog.
34. Imagine R1C10 were a dog: following the rules from there soon forces a contradiction, so R1C10 must be a cat.
35. Imagine R2C10 were a dog: following the rules from there soon forces a contradiction, so R2C10 must be a cat.
36. R1C10 and R2C10 are both cats, so R3C10 must be a dog (no three in a row).
37. Column 10 already has its 5 dogs, so R4C10 must be cats.
38. Imagine R6C9 were a cat: following the rules from there soon forces a contradiction, so R6C9 must be a dog.
39. The = clue between R6C9 and R7C9 means they are the same. R6C9 is a dog, so R7C9 is a dog.
40. R7C9 and R7C10 are both dogs, so R7C8 must be a cat (no three in a row).
41. R6C8 and R7C8 are both cats, so R8C8 must be a dog (no three in a row).
42. R6C9 and R7C9 are both dogs, so R8C9 must be a cat (no three in a row).
43. Imagine R6C5 were a dog: following the rules from there soon forces a contradiction, so R6C5 must be a cat.
44. Imagine R7C4 were a dog: following the rules from there soon forces a contradiction, so R7C4 must be a cat.
45. The = clue between R7C4 and R7C5 means they are the same. R7C4 is a cat, so R7C5 is a cat.
46. R7C4 and R7C5 are both cats, so R7C3 must be a dog (no three in a row).
47. R7C4 and R7C5 are both cats, so R7C6 must be a dog (no three in a row).
48. R5C3 and R7C3 are both dogs with one square between them, so R6C3 must be a cat.
49. R6C5 and R7C5 are both cats, so R8C5 must be a dog (no three in a row).
50. Imagine R1C2 were a cat: following the rules from there soon forces a contradiction, so R1C2 must be a dog.
51. Imagine R1C4 were a dog: following the rules from there soon forces a contradiction, so R1C4 must be a cat.
52. R1C3 and R1C4 are both cats, so R1C5 must be a dog (no three in a row).
53. Row 1 already has its 5 dogs, so R1C9 must be cats.
54. Imagine R2C8 were a dog: following the rules from there soon forces a contradiction, so R2C8 must be a cat.
55. R2C8 and R2C10 are both cats with one square between them, so R2C9 must be a dog.
56. The = clue between R2C9 and R3C9 means they are the same. R2C9 is a dog, so R3C9 is a dog.
57. R2C9 and R3C9 are both dogs, so R4C9 must be a cat (no three in a row).
58. Row 4 already has its 5 cats, so R4C1 and R4C2 must be dogs.
59. Imagine R7C1 were a dog: following the rules from there soon forces a contradiction, so R7C1 must be a cat.
60. Imagine R8C2 were a dog: following the rules from there soon forces a contradiction, so R8C2 must be a cat.
61. Imagine R2C1 were a cat: following the rules from there soon forces a contradiction, so R2C1 must be a dog.
62. R2C1 and R2C3 are both dogs with one square between them, so R2C2 must be a cat.
63. R1C1 and R2C1 are both dogs, so R3C1 must be a cat (no three in a row).
64. R3C1 and R3C3 are both cats with one square between them, so R3C2 must be a dog.
65. R3C2 and R4C2 are both dogs, so R5C2 must be a cat (no three in a row).
66. Row 5 already has its 5 cats, so R5C1 must be dogs.
67. R4C1 and R5C1 are both dogs, so R6C1 must be a cat (no three in a row).
68. R6C1 and R6C3 are both cats with one square between them, so R6C2 must be a dog.
69. Column 1 already has its 5 dogs, so R9C1 and R10C1 must be cats.
70. Imagine R7C2 were a dog: following the rules from there soon forces a contradiction, so R7C2 must be a cat.
71. R7C2 and R8C2 are both cats, so R9C2 must be a dog (no three in a row).
72. Row 7 already has its 5 cats, so R7C7 must be dogs.
73. R6C7 and R7C7 are both dogs, so R8C7 must be a cat (no three in a row).
74. Column 2 already has its 5 dogs, so R10C2 must be cats.
75. R10C1 and R10C2 are both cats, so R10C3 must be a dog (no three in a row).
76. The × clue between R10C3 and R9C3 means they are different. R10C3 is a dog, so R9C3 is a cat.
77. Column 3 already has its 5 cats, so R8C3 must be dogs.
78. R8C3 and R8C5 are both dogs with one square between them, so R8C4 must be a cat.
79. R7C4 and R8C4 are both cats, so R9C4 must be a dog (no three in a row).
80. Row 8 already has its 5 cats, so R8C6 must be dogs.
81. R7C6 and R8C6 are both dogs, so R9C6 must be a cat (no three in a row).
82. Column 4 already has its 5 cats, so R10C4 must be dogs.
83. R10C3 and R10C4 are both dogs, so R10C5 must be a cat (no three in a row).
84. Column 5 already has its 5 cats, so R9C5 must be dogs.
85. Column 6 already has its 5 dogs, so R10C6 must be cats.
86. R10C5 and R10C6 are both cats, so R10C7 must be a dog (no three in a row).
87. Column 7 already has its 5 dogs, so R9C7 must be cats.
88. R9C6 and R9C7 are both cats, so R9C8 must be a dog (no three in a row).
89. R9C8 and R9C10 are both dogs with one square between them, so R9C9 must be a cat.
90. R8C8 and R9C8 are both dogs, so R10C8 must be a cat (no three in a row).
91. R8C9 and R9C9 are both cats, so R10C9 must be a dog (no three in a row).