Cats & Dogs #276: 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 R1C2 and R1C3 means they are different. R1C2 is a cat, so R1C3 is a dog.
2. The = clue between R10C7 and R9C7 means they are the same. R10C7 is a cat, so R9C7 is a cat.
3. R2C1 and R2C2 are both cats, so R2C3 must be a dog (no three in a row).
4. The × clue between R2C3 and R2C4 means they are different. R2C3 is a dog, so R2C4 is a cat.
5. R1C2 and R2C2 are both cats, so R3C2 must be a dog (no three in a row).
6. R1C3 and R2C3 are both dogs, so R3C3 must be a cat (no three in a row).
7. R9C7 and R10C7 are both cats, so R8C7 must be a dog (no three in a row).
8. Imagine R2C6 were a cat: following the rules from there soon forces a contradiction, so R2C6 must be a dog.
9. The = clue between R2C6 and R2C7 means they are the same. R2C6 is a dog, so R2C7 is a dog.
10. R2C6 and R2C7 are both dogs, so R2C5 must be a cat (no three in a row).
11. R2C6 and R2C7 are both dogs, so R2C8 must be a cat (no three in a row).
12. Row 2 already has its 5 cats, so R2C9 must be dogs.
13. The = clue between R2C9 and R1C9 means they are the same. R2C9 is a dog, so R1C9 is a dog.
14. R1C9 and R2C9 are both dogs, so R3C9 must be a cat (no three in a row).
15. Row 2 already has its 5 cats, so R2C10 must be dogs.
16. The × clue between R2C10 and R3C10 means they are different. R2C10 is a dog, so R3C10 is a cat.
17. R3C9 and R3C10 are both cats, so R3C8 must be a dog (no three in a row).
18. Imagine R3C5 were a cat: following the rules from there soon forces a contradiction, so R3C5 must be a dog.
19. Imagine R3C7 were a dog: following the rules from there soon forces a contradiction, so R3C7 must be a cat.
20. Imagine R3C1 were a cat: following the rules from there soon forces a contradiction, so R3C1 must be a dog.
21. Imagine R4C5 were a dog: following the rules from there soon forces a contradiction, so R4C5 must be a cat.
22. The = clue between R4C5 and R4C6 means they are the same. R4C5 is a cat, so R4C6 is a cat.
23. The × clue between R4C5 and R5C5 means they are different. R4C5 is a cat, so R5C5 is a dog.
24. R4C5 and R4C6 are both cats, so R4C4 must be a dog (no three in a row).
25. R4C5 and R4C6 are both cats, so R4C7 must be a dog (no three in a row).
26. The = clue between R4C7 and R5C7 means they are the same. R4C7 is a dog, so R5C7 is a dog.
27. R5C5 and R5C7 are both dogs with one square between them, so R5C6 must be a cat.
28. R4C6 and R5C6 are both cats, so R3C6 must be a dog (no three in a row).
29. R3C5 and R3C6 are both dogs, so R3C4 must be a cat (no three in a row).
30. R2C4 and R3C4 are both cats, so R1C4 must be a dog (no three in a row).
31. R1C3 and R1C4 are both dogs, so R1C5 must be a cat (no three in a row).
32. R2C6 and R3C6 are both dogs, so R1C6 must be a cat (no three in a row).
33. R1C5 and R1C6 are both cats, so R1C7 must be a dog (no three in a row).
34. R1C7 and R1C9 are both dogs with one square between them, so R1C8 must be a cat.
35. R4C6 and R5C6 are both cats, so R6C6 must be a dog (no three in a row).
36. The × clue between R6C6 and R6C5 means they are different. R6C6 is a dog, so R6C5 is a cat.
37. R6C6 and R6C8 are both dogs with one square between them, so R6C7 must be a cat.
38. Column 7 already has its 5 dogs, so R7C7 must be cats.
39. The × clue between R7C7 and R7C8 means they are different. R7C7 is a cat, so R7C8 is a dog.
40. R6C8 and R7C8 are both dogs, so R5C8 must be a cat (no three in a row).
41. The × clue between R5C8 and R4C8 means they are different. R5C8 is a cat, so R4C8 is a dog.
42. R4C7 and R4C8 are both dogs, so R4C9 must be a cat (no three in a row).
43. R6C8 and R7C8 are both dogs, so R8C8 must be a cat (no three in a row).
44. R3C9 and R4C9 are both cats, so R5C9 must be a dog (no three in a row).
45. The = clue between R5C9 and R6C9 means they are the same. R5C9 is a dog, so R6C9 is a dog.
46. R6C8 and R6C9 are both dogs, so R6C10 must be a cat (no three in a row).
47. R5C9 and R6C9 are both dogs, so R7C9 must be a cat (no three in a row).
48. Imagine R7C3 were a dog: following the rules from there soon forces a contradiction, so R7C3 must be a cat.
49. Imagine R7C5 were a cat: following the rules from there soon forces a contradiction, so R7C5 must be a dog.
50. Imagine R8C9 were a dog: following the rules from there soon forces a contradiction, so R8C9 must be a cat.
51. R8C8 and R8C9 are both cats, so R8C10 must be a dog (no three in a row).
52. R7C9 and R8C9 are both cats, so R9C9 must be a dog (no three in a row).
53. Column 9 already has its 5 dogs, so R10C9 must be cats.
54. R10C7 and R10C9 are both cats with one square between them, so R10C8 must be a dog.
55. Column 8 already has its 5 dogs, so R9C8 must be cats.
56. R9C7 and R9C8 are both cats, so R9C6 must be a dog (no three in a row).
57. Imagine R9C2 were a dog: following the rules from there soon forces a contradiction, so R9C2 must be a cat.
58. Imagine R5C2 were a dog: following the rules from there soon forces a contradiction, so R5C2 must be a cat.
59. The = clue between R5C2 and R6C2 means they are the same. R5C2 is a cat, so R6C2 is a cat.
60. R5C2 and R6C2 are both cats, so R4C2 must be a dog (no three in a row).
61. R4C2 and R4C4 are both dogs with one square between them, so R4C3 must be a cat.
62. R5C2 and R6C2 are both cats, so R7C2 must be a dog (no three in a row).
63. R3C3 and R4C3 are both cats, so R5C3 must be a dog (no three in a row).
64. R5C3 and R5C5 are both dogs with one square between them, so R5C4 must be a cat.
65. Column 2 already has its 5 cats, so R8C2 must be dogs.
66. The = clue between R8C2 and R8C3 means they are the same. R8C2 is a dog, so R8C3 is a dog.
67. R8C2 and R8C3 are both dogs, so R8C1 must be a cat (no three in a row).
68. R8C2 and R8C3 are both dogs, so R8C4 must be a cat (no three in a row).
69. Column 3 already has its 5 dogs, so R9C3 must be cats.
70. R9C2 and R9C3 are both cats, so R9C4 must be a dog (no three in a row).
71. R9C4 and R9C6 are both dogs with one square between them, so R9C5 must be a cat.
72. Row 9 already has its 5 cats, so R9C10 must be dogs.
73. R8C10 and R9C10 are both dogs, so R7C10 must be a cat (no three in a row).
74. R6C10 and R7C10 are both cats, so R5C10 must be a dog (no three in a row).
75. R8C10 and R9C10 are both dogs, so R10C10 must be a cat (no three in a row).
76. Row 5 already has its 5 dogs, so R5C1 must be cats.
77. Column 3 already has its 5 dogs, so R10C3 must be cats.
78. Column 5 already has its 5 cats, so R8C5 must be dogs.
79. R8C5 and R8C7 are both dogs with one square between them, so R8C6 must be a cat.
80. The × clue between R8C6 and R7C6 means they are different. R8C6 is a cat, so R7C6 is a dog.
81. R7C5 and R7C6 are both dogs, so R7C4 must be a cat (no three in a row).
82. R5C4 and R7C4 are both cats with one square between them, so R6C4 must be a dog.
83. Row 6 already has its 5 dogs, so R6C1 must be cats.
84. R5C1 and R6C1 are both cats, so R4C1 must be a dog (no three in a row).
85. R5C1 and R6C1 are both cats, so R7C1 must be a dog (no three in a row).
86. Row 4 already has its 5 dogs, so R4C10 must be cats.
87. Column 4 already has its 5 cats, so R10C4 must be dogs.
88. Column 5 already has its 5 cats, so R10C5 must be dogs.
89. R10C4 and R10C5 are both dogs, so R10C6 must be a cat (no three in a row).
90. Row 10 already has its 5 cats, so R10C1 must be dogs.
91. Column 1 already has its 5 dogs, so R1C1 must be cats.
92. Row 1 already has its 5 cats, so R1C10 must be dogs.