Cats & Dogs #280: 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 R3C9 and R2C9 means they are the same. R3C9 is a dog, so R2C9 is a dog.
2. The = clue between R4C6 and R3C6 means they are the same. R4C6 is a dog, so R3C6 is a dog.
3. The × clue between R3C9 and R3C10 means they are different. R3C9 is a dog, so R3C10 is a cat.
4. The × clue between R6C8 and R5C8 means they are different. R6C8 is a cat, so R5C8 is a dog.
5. R3C6 and R4C6 are both dogs, so R2C6 must be a cat (no three in a row).
6. R3C6 and R4C6 are both dogs, so R5C6 must be a cat (no three in a row).
7. The = clue between R5C6 and R5C5 means they are the same. R5C6 is a cat, so R5C5 is a cat.
8. The × clue between R5C5 and R4C5 means they are different. R5C5 is a cat, so R4C5 is a dog.
9. R4C5 and R4C6 are both dogs, so R4C4 must be a cat (no three in a row).
10. R4C5 and R4C6 are both dogs, so R4C7 must be a cat (no three in a row).
11. R5C5 and R5C6 are both cats, so R5C4 must be a dog (no three in a row).
12. R5C5 and R5C6 are both cats, so R5C7 must be a dog (no three in a row).
13. R5C7 and R5C8 are both dogs, so R5C9 must be a cat (no three in a row).
14. R2C9 and R3C9 are both dogs, so R1C9 must be a cat (no three in a row).
15. R2C9 and R3C9 are both dogs, so R4C9 must be a cat (no three in a row).
16. R4C7 and R4C9 are both cats with one square between them, so R4C8 must be a dog.
17. R4C8 and R5C8 are both dogs, so R3C8 must be a cat (no three in a row).
18. R4C9 and R5C9 are both cats, so R6C9 must be a dog (no three in a row).
19. Imagine R2C4 were a cat: following the rules from there soon forces a contradiction, so R2C4 must be a dog.
20. The = clue between R2C4 and R3C4 means they are the same. R2C4 is a dog, so R3C4 is a dog.
21. R3C4 and R3C6 are both dogs with one square between them, so R3C5 must be a cat.
22. R2C4 and R3C4 are both dogs, so R1C4 must be a cat (no three in a row).
23. Imagine R3C3 were a dog: following the rules from there soon forces a contradiction, so R3C3 must be a cat.
24. The × clue between R3C3 and R4C3 means they are different. R3C3 is a cat, so R4C3 is a dog.
25. The = clue between R4C3 and R4C2 means they are the same. R4C3 is a dog, so R4C2 is a dog.
26. R4C2 and R4C3 are both dogs, so R4C1 must be a cat (no three in a row).
27. Row 4 already has its 5 dogs, so R4C10 must be cats.
28. R3C10 and R4C10 are both cats, so R2C10 must be a dog (no three in a row).
29. R2C9 and R2C10 are both dogs, so R2C8 must be a cat (no three in a row).
30. R2C6 and R2C8 are both cats with one square between them, so R2C7 must be a dog.
31. The × clue between R2C7 and R3C7 means they are different. R2C7 is a dog, so R3C7 is a cat.
32. R2C8 and R3C8 are both cats, so R1C8 must be a dog (no three in a row).
33. R3C10 and R4C10 are both cats, so R5C10 must be a dog (no three in a row).
34. Row 3 already has its 5 cats, so R3C1 and R3C2 must be dogs.
35. R3C2 and R4C2 are both dogs, so R2C2 must be a cat (no three in a row).
36. R3C2 and R4C2 are both dogs, so R5C2 must be a cat (no three in a row).
37. The × clue between R5C2 and R5C3 means they are different. R5C2 is a cat, so R5C3 is a dog.
38. R4C3 and R5C3 are both dogs, so R6C3 must be a cat (no three in a row).
39. Row 5 already has its 5 dogs, so R5C1 must be cats.
40. R4C1 and R5C1 are both cats, so R6C1 must be a dog (no three in a row).
41. R6C1 and R7C1 are both dogs, so R8C1 must be a cat (no three in a row).
42. Imagine R1C5 were a cat: following the rules from there soon forces a contradiction, so R1C5 must be a dog.
43. Imagine R2C5 were a dog: following the rules from there soon forces a contradiction, so R2C5 must be a cat.
44. Imagine R9C1 were a cat: following the rules from there soon forces a contradiction, so R9C1 must be a dog.
45. The = clue between R9C1 and R10C1 means they are the same. R9C1 is a dog, so R10C1 is a dog.
46. Column 1 already has its 5 dogs, so R1C1 and R2C1 must be cats.
47. R2C1 and R2C2 are both cats, so R2C3 must be a dog (no three in a row).
48. Imagine R7C4 were a dog: following the rules from there soon forces a contradiction, so R7C4 must be a cat.
49. The = clue between R7C4 and R8C4 means they are the same. R7C4 is a cat, so R8C4 is a cat.
50. R7C4 and R8C4 are both cats, so R6C4 must be a dog (no three in a row).
51. R6C4 and R6C5 are both dogs, so R6C6 must be a cat (no three in a row).
52. R6C6 and R6C8 are both cats with one square between them, so R6C7 must be a dog.
53. R7C4 and R8C4 are both cats, so R9C4 must be a dog (no three in a row).
54. The = clue between R9C4 and R9C5 means they are the same. R9C4 is a dog, so R9C5 is a dog.
55. R9C4 and R9C5 are both dogs, so R9C3 must be a cat (no three in a row).
56. R9C4 and R9C5 are both dogs, so R9C6 must be a cat (no three in a row).
57. R9C6 and R9C8 are both cats with one square between them, so R9C7 must be a dog.
58. R5C6 and R6C6 are both cats, so R7C6 must be a dog (no three in a row).
59. R5C7 and R6C7 are both dogs, so R7C7 must be a cat (no three in a row).
60. Row 6 already has its 5 dogs, so R6C2 must be cats.
61. The × clue between R6C2 and R7C2 means they are different. R6C2 is a cat, so R7C2 is a dog.
62. R7C1 and R7C2 are both dogs, so R7C3 must be a cat (no three in a row).
63. R7C3 and R7C4 are both cats, so R7C5 must be a dog (no three in a row).
64. R6C3 and R7C3 are both cats, so R8C3 must be a dog (no three in a row).
65. R6C5 and R7C5 are both dogs, so R8C5 must be a cat (no three in a row).
66. R8C4 and R8C5 are both cats, so R8C6 must be a dog (no three in a row).
67. Row 6 already has its 5 dogs, so R6C10 must be cats.
68. Column 4 already has its 5 dogs, so R10C4 must be cats.
69. Column 5 already has its 5 dogs, so R10C5 must be cats.
70. R10C4 and R10C5 are both cats, so R10C3 must be a dog (no three in a row).
71. R10C1 and R10C3 are both dogs with one square between them, so R10C2 must be a cat.
72. R10C4 and R10C5 are both cats, so R10C6 must be a dog (no three in a row).
73. Column 3 already has its 5 dogs, so R1C3 must be cats.
74. R1C1 and R1C3 are both cats with one square between them, so R1C2 must be a dog.
75. Column 6 already has its 5 dogs, so R1C6 must be cats.
76. Row 1 already has its 5 cats, so R1C7 and R1C10 must be dogs.
77. Column 7 already has its 5 dogs, so R8C7 and R10C7 must be cats.
78. Imagine R7C10 were a dog: following the rules from there soon forces a contradiction, so R7C10 must be a cat.
79. R6C10 and R7C10 are both cats, so R8C10 must be a dog (no three in a row).
80. Imagine R8C2 were a cat: following the rules from there soon forces a contradiction, so R8C2 must be a dog.
81. R7C2 and R8C2 are both dogs, so R9C2 must be a cat (no three in a row).
82. Imagine R9C9 were a cat: following the rules from there soon forces a contradiction, so R9C9 must be a dog.
83. Row 9 already has its 5 dogs, so R9C10 must be cats.
84. Column 10 already has its 5 cats, so R10C10 must be dogs.
85. The = clue between R10C10 and R10C9 means they are the same. R10C10 is a dog, so R10C9 is a dog.
86. R10C9 and R10C10 are both dogs, so R10C8 must be a cat (no three in a row).
87. R9C8 and R10C8 are both cats, so R8C8 must be a dog (no three in a row).
88. R8C8 and R8C10 are both dogs with one square between them, so R8C9 must be a cat.
89. Column 8 already has its 5 cats, so R7C8 must be dogs.
90. Row 7 already has its 5 dogs, so R7C9 must be cats.