Cats & Dogs #263: 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 R4C6 and R4C7 means they are different. R4C6 is a cat, so R4C7 is a dog.
2. The = clue between R7C5 and R8C5 means they are the same. R7C5 is a dog, so R8C5 is a dog.
3. R10C1 and R10C2 are both dogs, so R10C3 must be a cat (no three in a row).
4. The = clue between R10C3 and R9C3 means they are the same. R10C3 is a cat, so R9C3 is a cat.
5. R9C3 and R10C3 are both cats, so R8C3 must be a dog (no three in a row).
6. R8C3 and R8C5 are both dogs with one square between them, so R8C4 must be a cat.
7. R7C5 and R8C5 are both dogs, so R6C5 must be a cat (no three in a row).
8. R7C5 and R8C5 are both dogs, so R9C5 must be a cat (no three in a row).
9. R9C3 and R9C5 are both cats with one square between them, so R9C4 must be a dog.
10. Imagine R2C6 were a cat: following the rules from there soon forces a contradiction, so R2C6 must be a dog.
11. The = clue between R2C6 and R2C7 means they are the same. R2C6 is a dog, so R2C7 is a dog.
12. The × clue between R2C7 and R3C7 means they are different. R2C7 is a dog, so R3C7 is a cat.
13. The × clue between R3C7 and R3C6 means they are different. R3C7 is a cat, so R3C6 is a dog.
14. The × clue between R3C7 and R3C8 means they are different. R3C7 is a cat, so R3C8 is a dog.
15. R2C6 and R2C7 are both dogs, so R2C5 must be a cat (no three in a row).
16. The = clue between R2C5 and R1C5 means they are the same. R2C5 is a cat, so R1C5 is a cat.
17. R2C6 and R2C7 are both dogs, so R2C8 must be a cat (no three in a row).
18. R1C5 and R2C5 are both cats, so R3C5 must be a dog (no three in a row).
19. The = clue between R3C5 and R4C5 means they are the same. R3C5 is a dog, so R4C5 is a dog.
20. R3C5 and R3C6 are both dogs, so R3C4 must be a cat (no three in a row).
21. R3C5 and R4C5 are both dogs, so R5C5 must be a cat (no three in a row).
22. R2C6 and R3C6 are both dogs, so R1C6 must be a cat (no three in a row).
23. R1C5 and R1C6 are both cats, so R1C4 must be a dog (no three in a row).
24. R1C5 and R1C6 are both cats, so R1C7 must be a dog (no three in a row).
25. Column 5 already has its 5 cats, so R10C5 must be dogs.
26. Imagine R2C1 were a dog: following the rules from there soon forces a contradiction, so R2C1 must be a cat.
27. The = clue between R2C1 and R2C2 means they are the same. R2C1 is a cat, so R2C2 is a cat.
28. R2C1 and R2C2 are both cats, so R2C3 must be a dog (no three in a row).
29. Imagine R5C8 were a dog: following the rules from there soon forces a contradiction, so R5C8 must be a cat.
30. The = clue between R5C8 and R5C9 means they are the same. R5C8 is a cat, so R5C9 is a cat.
31. R5C8 and R5C9 are both cats, so R5C7 must be a dog (no three in a row).
32. R4C7 and R5C7 are both dogs, so R6C7 must be a cat (no three in a row).
33. R6C5 and R6C7 are both cats with one square between them, so R6C6 must be a dog.
34. Imagine R7C7 were a dog: following the rules from there soon forces a contradiction, so R7C7 must be a cat.
35. R6C7 and R7C7 are both cats, so R8C7 must be a dog (no three in a row).
36. R8C5 and R8C7 are both dogs with one square between them, so R8C6 must be a cat.
37. Column 7 already has its 5 dogs, so R9C7 must be cats.
38. R9C5 and R9C7 are both cats with one square between them, so R9C6 must be a dog.
39. Column 7 already has its 5 dogs, so R10C7 must be cats.
40. Imagine R7C8 were a cat: following the rules from there soon forces a contradiction, so R7C8 must be a dog.
41. Imagine R8C8 were a dog: following the rules from there soon forces a contradiction, so R8C8 must be a cat.
42. Imagine R8C9 were a cat: following the rules from there soon forces a contradiction, so R8C9 must be a dog.
43. The = clue between R8C9 and R8C10 means they are the same. R8C9 is a dog, so R8C10 is a dog.
44. R8C10 and R10C10 are both dogs with one square between them, so R9C10 must be a cat.
45. Row 8 already has its 5 dogs, so R8C1 must be cats.
46. R7C1 and R8C1 are both cats, so R6C1 must be a dog (no three in a row).
47. R7C1 and R8C1 are both cats, so R9C1 must be a dog (no three in a row).
48. Row 8 already has its 5 dogs, so R8C2 must be cats.
49. Imagine R2C4 were a cat: following the rules from there soon forces a contradiction, so R2C4 must be a dog.
50. Imagine R6C2 were a dog: following the rules from there soon forces a contradiction, so R6C2 must be a cat.
51. The = clue between R6C2 and R6C3 means they are the same. R6C2 is a cat, so R6C3 is a cat.
52. R6C2 and R6C3 are both cats, so R6C4 must be a dog (no three in a row).
53. R6C2 and R8C2 are both cats with one square between them, so R7C2 must be a dog.
54. Imagine R6C8 were a cat: following the rules from there soon forces a contradiction, so R6C8 must be a dog.
55. Imagine R6C9 were a cat: following the rules from there soon forces a contradiction, so R6C9 must be a dog.
56. R6C8 and R6C9 are both dogs, so R6C10 must be a cat (no three in a row).
57. R6C9 and R8C9 are both dogs with one square between them, so R7C9 must be a cat.
58. Imagine R7C3 were a cat: following the rules from there soon forces a contradiction, so R7C3 must be a dog.
59. R7C2 and R7C3 are both dogs, so R7C4 must be a cat (no three in a row).
60. Imagine R2C9 were a cat: following the rules from there soon forces a contradiction, so R2C9 must be a dog.
61. Row 2 already has its 5 dogs, so R2C10 must be cats.
62. The = clue between R2C10 and R3C10 means they are the same. R2C10 is a cat, so R3C10 is a cat.
63. R2C10 and R3C10 are both cats, so R1C10 must be a dog (no three in a row).
64. R2C10 and R3C10 are both cats, so R4C10 must be a dog (no three in a row).
65. Column 10 already has its 5 dogs, so R7C10 must be cats.
66. Row 7 already has its 5 cats, so R7C6 must be dogs.
67. R6C6 and R7C6 are both dogs, so R5C6 must be a cat (no three in a row).
68. R5C5 and R5C6 are both cats, so R5C4 must be a dog (no three in a row).
69. The × clue between R5C4 and R5C3 means they are different. R5C4 is a dog, so R5C3 is a cat.
70. The × clue between R5C3 and R4C3 means they are different. R5C3 is a cat, so R4C3 is a dog.
71. R4C3 and R4C5 are both dogs with one square between them, so R4C4 must be a cat.
72. R2C3 and R4C3 are both dogs with one square between them, so R3C3 must be a cat.
73. R3C3 and R3C4 are both cats, so R3C2 must be a dog (no three in a row).
74. Row 5 already has its 5 cats, so R5C1 must be dogs.
75. The × clue between R5C1 and R4C1 means they are different. R5C1 is a dog, so R4C1 is a cat.
76. R2C1 and R4C1 are both cats with one square between them, so R3C1 must be a dog.
77. Row 3 already has its 5 dogs, so R3C9 must be cats.
78. R3C9 and R5C9 are both cats with one square between them, so R4C9 must be a dog.
79. R4C7 and R4C9 are both dogs with one square between them, so R4C8 must be a cat.
80. Row 4 already has its 5 dogs, so R4C2 must be cats.
81. R4C2 and R6C2 are both cats with one square between them, so R5C2 must be a dog.
82. Column 1 already has its 5 dogs, so R1C1 must be cats.
83. Column 3 already has its 5 cats, so R1C3 must be dogs.
84. R1C3 and R1C4 are both dogs, so R1C2 must be a cat (no three in a row).
85. Column 2 already has its 5 cats, so R9C2 must be dogs.
86. Column 4 already has its 5 dogs, so R10C4 must be cats.
87. Column 6 already has its 5 dogs, so R10C6 must be cats.
88. R10C6 and R10C7 are both cats, so R10C8 must be a dog (no three in a row).
89. R10C8 and R10C10 are both dogs with one square between them, so R10C9 must be a cat.
90. The × clue between R10C9 and R9C9 means they are different. R10C9 is a cat, so R9C9 is a dog.
91. Row 9 already has its 5 dogs, so R9C8 must be cats.
92. Column 8 already has its 5 cats, so R1C8 must be dogs.
93. R1C7 and R1C8 are both dogs, so R1C9 must be a cat (no three in a row).