Cats & Dogs #244: 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 R3C2 and R2C2 means they are different. R3C2 is a cat, so R2C2 is a dog.
2. R4C6 and R4C7 are both cats, so R4C5 must be a dog (no three in a row).
3. R4C6 and R4C7 are both cats, so R4C8 must be a dog (no three in a row).
4. Imagine R5C5 were a dog: following the rules from there soon forces a contradiction, so R5C5 must be a cat.
5. The × clue between R5C5 and R5C6 means they are different. R5C5 is a cat, so R5C6 is a dog.
6. The × clue between R5C5 and R6C5 means they are different. R5C5 is a cat, so R6C5 is a dog.
7. The = clue between R6C5 and R6C6 means they are the same. R6C5 is a dog, so R6C6 is a dog.
8. R6C5 and R6C6 are both dogs, so R6C4 must be a cat (no three in a row).
9. R6C5 and R6C6 are both dogs, so R6C7 must be a cat (no three in a row).
10. R5C6 and R6C6 are both dogs, so R7C6 must be a cat (no three in a row).
11. R4C7 and R6C7 are both cats with one square between them, so R5C7 must be a dog.
12. R5C6 and R5C7 are both dogs, so R5C8 must be a cat (no three in a row).
13. Imagine R4C9 were a dog: following the rules from there soon forces a contradiction, so R4C9 must be a cat.
14. Imagine R5C9 were a cat: following the rules from there soon forces a contradiction, so R5C9 must be a dog.
15. The = clue between R5C9 and R5C10 means they are the same. R5C9 is a dog, so R5C10 is a dog.
16. R5C9 and R6C9 are both dogs, so R7C9 must be a cat (no three in a row).
17. R7C9 and R8C9 are both cats, so R9C9 must be a dog (no three in a row).
18. Imagine R4C2 were a cat: following the rules from there soon forces a contradiction, so R4C2 must be a dog.
19. Imagine R4C3 were a dog: following the rules from there soon forces a contradiction, so R4C3 must be a cat.
20. Imagine R4C4 were a cat: following the rules from there soon forces a contradiction, so R4C4 must be a dog.
21. Imagine R5C1 were a dog: following the rules from there soon forces a contradiction, so R5C1 must be a cat.
22. R5C1 and R7C1 are both cats with one square between them, so R6C1 must be a dog.
23. Imagine R5C2 were a dog: following the rules from there soon forces a contradiction, so R5C2 must be a cat.
24. R5C1 and R5C2 are both cats, so R5C3 must be a dog (no three in a row).
25. Row 5 already has its 5 dogs, so R5C4 must be cats.
26. R5C4 and R6C4 are both cats, so R7C4 must be a dog (no three in a row).
27. Imagine R6C8 were a dog: following the rules from there soon forces a contradiction, so R6C8 must be a cat.
28. R5C8 and R6C8 are both cats, so R7C8 must be a dog (no three in a row).
29. Imagine R6C10 were a dog: following the rules from there soon forces a contradiction, so R6C10 must be a cat.
30. Imagine R7C5 were a dog: following the rules from there soon forces a contradiction, so R7C5 must be a cat.
31. The = clue between R7C5 and R8C5 means they are the same. R7C5 is a cat, so R8C5 is a cat.
32. R7C5 and R7C6 are both cats, so R7C7 must be a dog (no three in a row).
33. R7C5 and R8C5 are both cats, so R9C5 must be a dog (no three in a row).
34. Imagine R1C5 were a cat: following the rules from there soon forces a contradiction, so R1C5 must be a dog.
35. The × clue between R1C5 and R2C5 means they are different. R1C5 is a dog, so R2C5 is a cat.
36. Imagine R1C6 were a dog: following the rules from there soon forces a contradiction, so R1C6 must be a cat.
37. Imagine R3C5 were a cat: following the rules from there soon forces a contradiction, so R3C5 must be a dog.
38. Column 5 already has its 5 dogs, so R10C5 must be cats.
39. Imagine R6C2 were a cat: following the rules from there soon forces a contradiction, so R6C2 must be a dog.
40. R6C1 and R6C2 are both dogs, so R6C3 must be a cat (no three in a row).
41. Imagine R7C2 were a dog: following the rules from there soon forces a contradiction, so R7C2 must be a cat.
42. The = clue between R7C2 and R8C2 means they are the same. R7C2 is a cat, so R8C2 is a cat.
43. R7C1 and R7C2 are both cats, so R7C3 must be a dog (no three in a row).
44. The = clue between R7C3 and R8C3 means they are the same. R7C3 is a dog, so R8C3 is a dog.
45. R7C2 and R8C2 are both cats, so R9C2 must be a dog (no three in a row).
46. The = clue between R9C2 and R10C2 means they are the same. R9C2 is a dog, so R10C2 is a dog.
47. R7C3 and R8C3 are both dogs, so R9C3 must be a cat (no three in a row).
48. Row 7 already has its 5 cats, so R7C10 must be dogs.
49. Column 2 already has its 5 dogs, so R1C2 must be cats.
50. The = clue between R1C2 and R1C1 means they are the same. R1C2 is a cat, so R1C1 is a cat.
51. R1C1 and R1C2 are both cats, so R1C3 must be a dog (no three in a row).
52. R1C3 and R1C5 are both dogs with one square between them, so R1C4 must be a cat.
53. The = clue between R1C4 and R2C4 means they are the same. R1C4 is a cat, so R2C4 is a cat.
54. R2C4 and R2C5 are both cats, so R2C3 must be a dog (no three in a row).
55. R2C2 and R2C3 are both dogs, so R2C1 must be a cat (no three in a row).
56. R2C4 and R2C5 are both cats, so R2C6 must be a dog (no three in a row).
57. R1C1 and R2C1 are both cats, so R3C1 must be a dog (no three in a row).
58. R1C3 and R2C3 are both dogs, so R3C3 must be a cat (no three in a row).
59. R3C2 and R3C3 are both cats, so R3C4 must be a dog (no three in a row).
60. R3C4 and R3C5 are both dogs, so R3C6 must be a cat (no three in a row).
61. Column 3 already has its 5 dogs, so R10C3 must be cats.
62. The × clue between R10C3 and R10C4 means they are different. R10C3 is a cat, so R10C4 is a dog.
63. The × clue between R10C4 and R9C4 means they are different. R10C4 is a dog, so R9C4 is a cat.
64. Column 4 already has its 5 cats, so R8C4 must be dogs.
65. Imagine R1C7 were a cat: following the rules from there soon forces a contradiction, so R1C7 must be a dog.
66. The × clue between R1C7 and R1C8 means they are different. R1C7 is a dog, so R1C8 is a cat.
67. Row 1 already has its 5 cats, so R1C9 and R1C10 must be dogs.
68. Imagine R2C7 were a dog: following the rules from there soon forces a contradiction, so R2C7 must be a cat.
69. The = clue between R2C7 and R2C8 means they are the same. R2C7 is a cat, so R2C8 is a cat.
70. R2C7 and R2C8 are both cats, so R2C9 must be a dog (no three in a row).
71. R2C7 and R4C7 are both cats with one square between them, so R3C7 must be a dog.
72. R1C8 and R2C8 are both cats, so R3C8 must be a dog (no three in a row).
73. R3C7 and R3C8 are both dogs, so R3C9 must be a cat (no three in a row).
74. Row 2 already has its 5 cats, so R2C10 must be dogs.
75. R1C10 and R2C10 are both dogs, so R3C10 must be a cat (no three in a row).
76. Column 9 already has its 5 dogs, so R10C9 must be cats.
77. Imagine R4C1 were a cat: following the rules from there soon forces a contradiction, so R4C1 must be a dog.
78. Row 4 already has its 5 dogs, so R4C10 must be cats.
79. Imagine R8C6 were a dog: following the rules from there soon forces a contradiction, so R8C6 must be a cat.
80. The × clue between R8C6 and R8C7 means they are different. R8C6 is a cat, so R8C7 is a dog.
81. R7C6 and R8C6 are both cats, so R9C6 must be a dog (no three in a row).
82. R9C5 and R9C6 are both dogs, so R9C7 must be a cat (no three in a row).
83. Column 7 already has its 5 dogs, so R10C7 must be cats.
84. R10C7 and R10C9 are both cats with one square between them, so R10C8 must be a dog.
85. The = clue between R10C8 and R9C8 means they are the same. R10C8 is a dog, so R9C8 is a dog.
86. R9C8 and R9C9 are both dogs, so R9C10 must be a cat (no three in a row).
87. R7C8 and R9C8 are both dogs with one square between them, so R8C8 must be a cat.
88. R8C8 and R8C9 are both cats, so R8C10 must be a dog (no three in a row).
89. Row 8 already has its 5 cats, so R8C1 must be dogs.
90. Row 9 already has its 5 dogs, so R9C1 must be cats.
91. Column 1 already has its 5 cats, so R10C1 must be dogs.
92. Row 10 already has its 5 dogs, so R10C10 must be cats.