Cats & Dogs #250: 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 R6C5 and R5C5 means they are the same. R6C5 is a cat, so R5C5 is a cat.
2. The = clue between R5C5 and R5C6 means they are the same. R5C5 is a cat, so R5C6 is a cat.
3. R5C5 and R5C6 are both cats, so R5C4 must be a dog (no three in a row).
4. R5C5 and R5C6 are both cats, so R5C7 must be a dog (no three in a row).
5. The = clue between R5C7 and R6C7 means they are the same. R5C7 is a dog, so R6C7 is a dog.
6. R8C3 and R8C5 are both cats with one square between them, so R8C4 must be a dog.
7. R5C5 and R6C5 are both cats, so R4C5 must be a dog (no three in a row).
8. R5C5 and R6C5 are both cats, so R7C5 must be a dog (no three in a row).
9. R5C7 and R6C7 are both dogs, so R4C7 must be a cat (no three in a row).
10. R5C7 and R6C7 are both dogs, so R7C7 must be a cat (no three in a row).
11. R7C8 and R8C8 are both dogs, so R6C8 must be a cat (no three in a row).
12. R5C8 and R6C8 are both cats, so R4C8 must be a dog (no three in a row).
13. The × clue between R4C8 and R3C8 means they are different. R4C8 is a dog, so R3C8 is a cat.
14. The × clue between R4C8 and R4C9 means they are different. R4C8 is a dog, so R4C9 is a cat.
15. R7C8 and R8C8 are both dogs, so R9C8 must be a cat (no three in a row).
16. Imagine R1C8 were a cat: following the rules from there soon forces a contradiction, so R1C8 must be a dog.
17. Imagine R2C8 were a cat: following the rules from there soon forces a contradiction, so R2C8 must be a dog.
18. R2C8 and R2C10 are both dogs with one square between them, so R2C9 must be a cat.
19. R2C9 and R4C9 are both cats with one square between them, so R3C9 must be a dog.
20. Column 8 already has its 5 dogs, so R10C8 must be cats.
21. The = clue between R10C8 and R10C9 means they are the same. R10C8 is a cat, so R10C9 is a cat.
22. R10C8 and R10C9 are both cats, so R10C7 must be a dog (no three in a row).
23. Imagine R3C1 were a dog: following the rules from there soon forces a contradiction, so R3C1 must be a cat.
24. The = clue between R3C1 and R4C1 means they are the same. R3C1 is a cat, so R4C1 is a cat.
25. The = clue between R4C1 and R4C2 means they are the same. R4C1 is a cat, so R4C2 is a cat.
26. R4C1 and R4C2 are both cats, so R4C3 must be a dog (no three in a row).
27. R4C3 and R4C5 are both dogs with one square between them, so R4C4 must be a cat.
28. R3C1 and R4C1 are both cats, so R2C1 must be a dog (no three in a row).
29. R3C1 and R4C1 are both cats, so R5C1 must be a dog (no three in a row).
30. R3C3 and R4C3 are both dogs, so R2C3 must be a cat (no three in a row).
31. R3C3 and R4C3 are both dogs, so R5C3 must be a cat (no three in a row).
32. Row 4 already has its 5 cats, so R4C6 and R4C10 must be dogs.
33. R2C10 and R4C10 are both dogs with one square between them, so R3C10 must be a cat.
34. R4C10 and R6C10 are both dogs with one square between them, so R5C10 must be a cat.
35. R5C8 and R5C10 are both cats with one square between them, so R5C9 must be a dog.
36. Row 5 already has its 5 cats, so R5C2 must be dogs.
37. Imagine R1C10 were a dog: following the rules from there soon forces a contradiction, so R1C10 must be a cat.
38. Imagine R6C1 were a dog: following the rules from there soon forces a contradiction, so R6C1 must be a cat.
39. The = clue between R6C1 and R6C2 means they are the same. R6C1 is a cat, so R6C2 is a cat.
40. R6C1 and R6C2 are both cats, so R6C3 must be a dog (no three in a row).
41. R6C1 and R7C1 are both cats, so R8C1 must be a dog (no three in a row).
42. Imagine R1C1 were a cat: following the rules from there soon forces a contradiction, so R1C1 must be a dog.
43. Imagine R7C2 were a cat: following the rules from there soon forces a contradiction, so R7C2 must be a dog.
44. Imagine R7C3 were a dog: following the rules from there soon forces a contradiction, so R7C3 must be a cat.
45. The = clue between R7C3 and R7C4 means they are the same. R7C3 is a cat, so R7C4 is a cat.
46. R7C3 and R8C3 are both cats, so R9C3 must be a dog (no three in a row).
47. Imagine R1C3 were a dog: following the rules from there soon forces a contradiction, so R1C3 must be a cat.
48. Column 3 already has its 5 cats, so R10C3 must be dogs.
49. Imagine R6C4 were a cat: following the rules from there soon forces a contradiction, so R6C4 must be a dog.
50. Imagine R7C6 were a cat: following the rules from there soon forces a contradiction, so R7C6 must be a dog.
51. Imagine R8C2 were a cat: following the rules from there soon forces a contradiction, so R8C2 must be a dog.
52. R7C2 and R8C2 are both dogs, so R9C2 must be a cat (no three in a row).
53. The = clue between R9C2 and R9C1 means they are the same. R9C2 is a cat, so R9C1 is a cat.
54. Column 1 already has its 5 cats, so R10C1 must be dogs.
55. Imagine R1C2 were a cat: following the rules from there soon forces a contradiction, so R1C2 must be a dog.
56. Imagine R8C6 were a dog: following the rules from there soon forces a contradiction, so R8C6 must be a cat.
57. R8C5 and R8C6 are both cats, so R8C7 must be a dog (no three in a row).
58. R8C7 and R8C8 are both dogs, so R8C9 must be a cat (no three in a row).
59. R8C7 and R10C7 are both dogs with one square between them, so R9C7 must be a cat.
60. R9C7 and R9C8 are both cats, so R9C6 must be a dog (no three in a row).
61. R9C7 and R9C8 are both cats, so R9C9 must be a dog (no three in a row).
62. Row 8 already has its 5 dogs, so R8C10 must be cats.
63. Imagine R1C5 were a cat: following the rules from there soon forces a contradiction, so R1C5 must be a dog.
64. The = clue between R1C5 and R2C5 means they are the same. R1C5 is a dog, so R2C5 is a dog.
65. The × clue between R2C5 and R2C4 means they are different. R2C5 is a dog, so R2C4 is a cat.
66. R2C3 and R2C4 are both cats, so R2C2 must be a dog (no three in a row).
67. R1C2 and R2C2 are both dogs, so R3C2 must be a cat (no three in a row).
68. R2C4 and R4C4 are both cats with one square between them, so R3C4 must be a dog.
69. R3C3 and R3C4 are both dogs, so R3C5 must be a cat (no three in a row).
70. Row 2 already has its 5 dogs, so R2C6 and R2C7 must be cats.
71. R2C7 and R4C7 are both cats with one square between them, so R3C7 must be a dog.
72. Row 3 already has its 5 cats, so R3C6 must be dogs.
73. Column 7 already has its 5 dogs, so R1C7 must be cats.
74. Imagine R1C4 were a dog: following the rules from there soon forces a contradiction, so R1C4 must be a cat.
75. Imagine R1C6 were a dog: following the rules from there soon forces a contradiction, so R1C6 must be a cat.
76. Row 1 already has its 5 cats, so R1C9 must be dogs.
77. Imagine R6C6 were a cat: following the rules from there soon forces a contradiction, so R6C6 must be a dog.
78. Row 6 already has its 5 dogs, so R6C9 must be cats.
79. R6C9 and R8C9 are both cats with one square between them, so R7C9 must be a dog.
80. R7C8 and R7C9 are both dogs, so R7C10 must be a cat (no three in a row).
81. R7C10 and R8C10 are both cats, so R9C10 must be a dog (no three in a row).
82. Column 6 already has its 5 dogs, so R10C6 must be cats.
83. The × clue between R10C6 and R10C5 means they are different. R10C6 is a cat, so R10C5 is a dog.
84. R10C3 and R10C5 are both dogs with one square between them, so R10C4 must be a cat.
85. Column 4 already has its 5 cats, so R9C4 must be dogs.
86. R9C3 and R9C4 are both dogs, so R9C5 must be a cat (no three in a row).