Cats & Dogs #239: 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 R1C4 and R1C3 means they are different. R1C4 is a cat, so R1C3 is a dog.
2. Imagine R2C3 were a dog: following the rules from there soon forces a contradiction, so R2C3 must be a cat.
3. The = clue between R2C3 and R3C3 means they are the same. R2C3 is a cat, so R3C3 is a cat.
4. R3C3 and R3C5 are both cats with one square between them, so R3C4 must be a dog.
5. R2C3 and R3C3 are both cats, so R4C3 must be a dog (no three in a row).
6. Imagine R4C4 were a dog: following the rules from there soon forces a contradiction, so R4C4 must be a cat.
7. Imagine R5C4 were a cat: following the rules from there soon forces a contradiction, so R5C4 must be a dog.
8. The = clue between R5C4 and R5C5 means they are the same. R5C4 is a dog, so R5C5 is a dog.
9. R5C4 and R5C5 are both dogs, so R5C3 must be a cat (no three in a row).
10. R5C4 and R5C5 are both dogs, so R5C6 must be a cat (no three in a row).
11. Imagine R6C3 were a cat: following the rules from there soon forces a contradiction, so R6C3 must be a dog.
12. The × clue between R6C3 and R7C3 means they are different. R6C3 is a dog, so R7C3 is a cat.
13. The × clue between R7C3 and R8C3 means they are different. R7C3 is a cat, so R8C3 is a dog.
14. Column 3 already has its 5 cats, so R9C3 must be dogs.
15. The = clue between R9C3 and R9C2 means they are the same. R9C3 is a dog, so R9C2 is a dog.
16. R9C2 and R9C3 are both dogs, so R9C1 must be a cat (no three in a row).
17. R9C2 and R9C3 are both dogs, so R9C4 must be a cat (no three in a row).
18. The = clue between R9C4 and R10C4 means they are the same. R9C4 is a cat, so R10C4 is a cat.
19. R10C3 and R10C4 are both cats, so R10C2 must be a dog (no three in a row).
20. R10C3 and R10C4 are both cats, so R10C5 must be a dog (no three in a row).
21. R9C2 and R10C2 are both dogs, so R8C2 must be a cat (no three in a row).
22. R9C4 and R10C4 are both cats, so R8C4 must be a dog (no three in a row).
23. R8C3 and R8C4 are both dogs, so R8C5 must be a cat (no three in a row).
24. Imagine R1C5 were a cat: following the rules from there soon forces a contradiction, so R1C5 must be a dog.
25. Imagine R1C6 were a dog: following the rules from there soon forces a contradiction, so R1C6 must be a cat.
26. Imagine R2C4 were a cat: following the rules from there soon forces a contradiction, so R2C4 must be a dog.
27. R2C4 and R2C6 are both dogs with one square between them, so R2C5 must be a cat.
28. R2C5 and R3C5 are both cats, so R4C5 must be a dog (no three in a row).
29. The × clue between R4C5 and R4C6 means they are different. R4C5 is a dog, so R4C6 is a cat.
30. R4C5 and R5C5 are both dogs, so R6C5 must be a cat (no three in a row).
31. R6C5 and R8C5 are both cats with one square between them, so R7C5 must be a dog.
32. R4C6 and R5C6 are both cats, so R3C6 must be a dog (no three in a row).
33. R4C6 and R5C6 are both cats, so R6C6 must be a dog (no three in a row).
34. The × clue between R6C6 and R6C7 means they are different. R6C6 is a dog, so R6C7 is a cat.
35. The × clue between R6C7 and R6C8 means they are different. R6C7 is a cat, so R6C8 is a dog.
36. The = clue between R6C7 and R7C7 means they are the same. R6C7 is a cat, so R7C7 is a cat.
37. The × clue between R7C7 and R7C6 means they are different. R7C7 is a cat, so R7C6 is a dog.
38. R7C5 and R7C6 are both dogs, so R7C4 must be a cat (no three in a row).
39. R7C3 and R7C4 are both cats, so R7C2 must be a dog (no three in a row).
40. R6C6 and R7C6 are both dogs, so R8C6 must be a cat (no three in a row).
41. R8C5 and R8C6 are both cats, so R8C7 must be a dog (no three in a row).
42. R6C7 and R7C7 are both cats, so R5C7 must be a dog (no three in a row).
43. Column 4 already has its 5 cats, so R6C4 must be dogs.
44. R6C3 and R6C4 are both dogs, so R6C2 must be a cat (no three in a row).
45. Column 5 already has its 5 dogs, so R9C5 must be cats.
46. R9C4 and R9C5 are both cats, so R9C6 must be a dog (no three in a row).
47. Column 6 already has its 5 dogs, so R10C6 must be cats.
48. Imagine R2C7 were a cat: following the rules from there soon forces a contradiction, so R2C7 must be a dog.
49. The × clue between R2C7 and R3C7 means they are different. R2C7 is a dog, so R3C7 is a cat.
50. R2C6 and R2C7 are both dogs, so R2C8 must be a cat (no three in a row).
51. Imagine R4C7 were a cat: following the rules from there soon forces a contradiction, so R4C7 must be a dog.
52. The = clue between R4C7 and R4C8 means they are the same. R4C7 is a dog, so R4C8 is a dog.
53. R4C7 and R4C8 are both dogs, so R4C9 must be a cat (no three in a row).
54. The = clue between R4C9 and R5C9 means they are the same. R4C9 is a cat, so R5C9 is a cat.
55. R4C8 and R6C8 are both dogs with one square between them, so R5C8 must be a cat.
56. R5C8 and R5C9 are both cats, so R5C10 must be a dog (no three in a row).
57. R4C9 and R5C9 are both cats, so R3C9 must be a dog (no three in a row).
58. R4C9 and R5C9 are both cats, so R6C9 must be a dog (no three in a row).
59. R6C8 and R6C9 are both dogs, so R6C10 must be a cat (no three in a row).
60. The × clue between R6C10 and R7C10 means they are different. R6C10 is a cat, so R7C10 is a dog.
61. Row 6 already has its 5 dogs, so R6C1 must be cats.
62. Imagine R4C1 were a dog: following the rules from there soon forces a contradiction, so R4C1 must be a cat.
63. R4C1 and R6C1 are both cats with one square between them, so R5C1 must be a dog.
64. Row 5 already has its 5 dogs, so R5C2 must be cats.
65. R5C2 and R6C2 are both cats, so R4C2 must be a dog (no three in a row).
66. Row 4 already has its 5 dogs, so R4C10 must be cats.
67. Imagine R1C2 were a dog: following the rules from there soon forces a contradiction, so R1C2 must be a cat.
68. Imagine R1C7 were a cat: following the rules from there soon forces a contradiction, so R1C7 must be a dog.
69. Column 7 already has its 5 dogs, so R9C7 and R10C7 must be cats.
70. R10C6 and R10C7 are both cats, so R10C8 must be a dog (no three in a row).
71. Imagine R1C10 were a cat: following the rules from there soon forces a contradiction, so R1C10 must be a dog.
72. Imagine R2C1 were a cat: following the rules from there soon forces a contradiction, so R2C1 must be a dog.
73. Imagine R1C8 were a cat: following the rules from there soon forces a contradiction, so R1C8 must be a dog.
74. R1C7 and R1C8 are both dogs, so R1C9 must be a cat (no three in a row).
75. Imagine R2C2 were a dog: following the rules from there soon forces a contradiction, so R2C2 must be a cat.
76. The × clue between R2C2 and R3C2 means they are different. R2C2 is a cat, so R3C2 is a dog.
77. Imagine R2C9 were a dog: following the rules from there soon forces a contradiction, so R2C9 must be a cat.
78. R2C8 and R2C9 are both cats, so R2C10 must be a dog (no three in a row).
79. R1C10 and R2C10 are both dogs, so R3C10 must be a cat (no three in a row).
80. Imagine R3C1 were a cat: following the rules from there soon forces a contradiction, so R3C1 must be a dog.
81. Row 3 already has its 5 dogs, so R3C8 must be cats.
82. Imagine R7C1 were a dog: following the rules from there soon forces a contradiction, so R7C1 must be a cat.
83. R6C1 and R7C1 are both cats, so R8C1 must be a dog (no three in a row).
84. Column 1 already has its 5 cats, so R10C1 must be dogs.
85. Imagine R7C8 were a dog: following the rules from there soon forces a contradiction, so R7C8 must be a cat.
86. The × clue between R7C8 and R8C8 means they are different. R7C8 is a cat, so R8C8 is a dog.
87. R7C7 and R7C8 are both cats, so R7C9 must be a dog (no three in a row).
88. R8C7 and R8C8 are both dogs, so R8C9 must be a cat (no three in a row).
89. R8C8 and R10C8 are both dogs with one square between them, so R9C8 must be a cat.
90. R9C7 and R9C8 are both cats, so R9C9 must be a dog (no three in a row).
91. Row 8 already has its 5 dogs, so R8C10 must be cats.
92. Row 9 already has its 5 cats, so R9C10 must be dogs.
93. Column 9 already has its 5 cats, so R10C9 must be dogs.
94. R10C8 and R10C9 are both dogs, so R10C10 must be a cat (no three in a row).