Cats & Dogs #272: 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 R3C7 and R2C7 means they are the same. R3C7 is a cat, so R2C7 is a cat.
2. R2C7 and R2C8 are both cats, so R2C6 must be a dog (no three in a row).
3. R2C7 and R2C8 are both cats, so R2C9 must be a dog (no three in a row).
4. R4C3 and R4C4 are both cats, so R4C2 must be a dog (no three in a row).
5. The × clue between R4C2 and R3C2 means they are different. R4C2 is a dog, so R3C2 is a cat.
6. The = clue between R3C2 and R3C1 means they are the same. R3C2 is a cat, so R3C1 is a cat.
7. The × clue between R4C2 and R4C1 means they are different. R4C2 is a dog, so R4C1 is a cat.
8. R3C1 and R3C2 are both cats, so R3C3 must be a dog (no three in a row).
9. R4C3 and R4C4 are both cats, so R4C5 must be a dog (no three in a row).
10. R3C1 and R4C1 are both cats, so R2C1 must be a dog (no three in a row).
11. The = clue between R2C1 and R2C2 means they are the same. R2C1 is a dog, so R2C2 is a dog.
12. R2C1 and R2C2 are both dogs, so R2C3 must be a cat (no three in a row).
13. R3C1 and R4C1 are both cats, so R5C1 must be a dog (no three in a row).
14. R4C5 and R6C5 are both dogs with one square between them, so R5C5 must be a cat.
15. R2C7 and R3C7 are both cats, so R1C7 must be a dog (no three in a row).
16. R2C7 and R3C7 are both cats, so R4C7 must be a dog (no three in a row).
17. The = clue between R4C7 and R5C7 means they are the same. R4C7 is a dog, so R5C7 is a dog.
18. R4C5 and R4C7 are both dogs with one square between them, so R4C6 must be a cat.
19. R4C7 and R5C7 are both dogs, so R6C7 must be a cat (no three in a row).
20. Imagine R1C6 were a dog: following the rules from there soon forces a contradiction, so R1C6 must be a cat.
21. Imagine R2C10 were a dog: following the rules from there soon forces a contradiction, so R2C10 must be a cat.
22. Imagine R3C6 were a cat: following the rules from there soon forces a contradiction, so R3C6 must be a dog.
23. Imagine R4C10 were a cat: following the rules from there soon forces a contradiction, so R4C10 must be a dog.
24. Imagine R5C2 were a cat: following the rules from there soon forces a contradiction, so R5C2 must be a dog.
25. R5C1 and R5C2 are both dogs, so R5C3 must be a cat (no three in a row).
26. R5C3 and R5C5 are both cats with one square between them, so R5C4 must be a dog.
27. R4C3 and R5C3 are both cats, so R6C3 must be a dog (no three in a row).
28. R6C3 and R6C5 are both dogs with one square between them, so R6C4 must be a cat.
29. R6C4 and R8C4 are both cats with one square between them, so R7C4 must be a dog.
30. Imagine R5C6 were a dog: following the rules from there soon forces a contradiction, so R5C6 must be a cat.
31. R4C6 and R5C6 are both cats, so R6C6 must be a dog (no three in a row).
32. Imagine R5C8 were a dog: following the rules from there soon forces a contradiction, so R5C8 must be a cat.
33. Imagine R6C1 were a dog: following the rules from there soon forces a contradiction, so R6C1 must be a cat.
34. The = clue between R6C1 and R7C1 means they are the same. R6C1 is a cat, so R7C1 is a cat.
35. The = clue between R7C1 and R7C2 means they are the same. R7C1 is a cat, so R7C2 is a cat.
36. R7C1 and R7C2 are both cats, so R7C3 must be a dog (no three in a row).
37. R7C3 and R7C4 are both dogs, so R7C5 must be a cat (no three in a row).
38. The = clue between R7C5 and R7C6 means they are the same. R7C5 is a cat, so R7C6 is a cat.
39. R7C5 and R7C6 are both cats, so R7C7 must be a dog (no three in a row).
40. R6C1 and R7C1 are both cats, so R8C1 must be a dog (no three in a row).
41. R6C2 and R7C2 are both cats, so R8C2 must be a dog (no three in a row).
42. R8C1 and R8C2 are both dogs, so R8C3 must be a cat (no three in a row).
43. The = clue between R8C3 and R9C3 means they are the same. R8C3 is a cat, so R9C3 is a cat.
44. R8C3 and R8C4 are both cats, so R8C5 must be a dog (no three in a row).
45. R8C3 and R9C3 are both cats, so R10C3 must be a dog (no three in a row).
46. Column 3 already has its 5 cats, so R1C3 must be dogs.
47. The × clue between R1C3 and R1C4 means they are different. R1C3 is a dog, so R1C4 is a cat.
48. R1C4 and R1C6 are both cats with one square between them, so R1C5 must be a dog.
49. The × clue between R1C5 and R2C5 means they are different. R1C5 is a dog, so R2C5 is a cat.
50. The × clue between R2C5 and R3C5 means they are different. R2C5 is a cat, so R3C5 is a dog.
51. R2C3 and R2C5 are both cats with one square between them, so R2C4 must be a dog.
52. R3C3 and R3C5 are both dogs with one square between them, so R3C4 must be a cat.
53. Column 4 already has its 5 cats, so R9C4 and R10C4 must be dogs.
54. R10C3 and R10C4 are both dogs, so R10C2 must be a cat (no three in a row).
55. R10C3 and R10C4 are both dogs, so R10C5 must be a cat (no three in a row).
56. The = clue between R10C5 and R10C6 means they are the same. R10C5 is a cat, so R10C6 is a cat.
57. R10C5 and R10C6 are both cats, so R10C7 must be a dog (no three in a row).
58. Column 5 already has its 5 dogs, so R9C5 must be cats.
59. Column 6 already has its 5 cats, so R8C6 must be dogs.
60. R8C5 and R8C6 are both dogs, so R8C7 must be a cat (no three in a row).
61. Column 6 already has its 5 cats, so R9C6 must be dogs.
62. Column 7 already has its 5 dogs, so R9C7 must be cats.
63. Imagine R1C1 were a cat: following the rules from there soon forces a contradiction, so R1C1 must be a dog.
64. R1C1 and R1C3 are both dogs with one square between them, so R1C2 must be a cat.
65. Column 2 already has its 5 cats, so R9C2 must be dogs.
66. Imagine R6C8 were a cat: following the rules from there soon forces a contradiction, so R6C8 must be a dog.
67. Imagine R7C10 were a cat: following the rules from there soon forces a contradiction, so R7C10 must be a dog.
68. Imagine R8C10 were a dog: following the rules from there soon forces a contradiction, so R8C10 must be a cat.
69. Imagine R9C8 were a cat: following the rules from there soon forces a contradiction, so R9C8 must be a dog.
70. Imagine R9C9 were a dog: following the rules from there soon forces a contradiction, so R9C9 must be a cat.
71. The = clue between R9C9 and R10C9 means they are the same. R9C9 is a cat, so R10C9 is a cat.
72. The × clue between R10C9 and R10C10 means they are different. R10C9 is a cat, so R10C10 is a dog.
73. R9C9 and R10C9 are both cats, so R8C9 must be a dog (no three in a row).
74. Row 8 already has its 5 dogs, so R8C8 must be cats.
75. Imagine R5C9 were a cat: following the rules from there soon forces a contradiction, so R5C9 must be a dog.
76. The × clue between R5C9 and R5C10 means they are different. R5C9 is a dog, so R5C10 is a cat.
77. Imagine R6C9 were a dog: following the rules from there soon forces a contradiction, so R6C9 must be a cat.
78. The = clue between R6C9 and R7C9 means they are the same. R6C9 is a cat, so R7C9 is a cat.
79. Row 6 already has its 5 cats, so R6C10 must be dogs.
80. Row 7 already has its 5 cats, so R7C8 must be dogs.
81. Imagine R1C8 were a dog: following the rules from there soon forces a contradiction, so R1C8 must be a cat.
82. R1C8 and R2C8 are both cats, so R3C8 must be a dog (no three in a row).
83. Imagine R1C9 were a cat: following the rules from there soon forces a contradiction, so R1C9 must be a dog.
84. R1C9 and R2C9 are both dogs, so R3C9 must be a cat (no three in a row).
85. Row 1 already has its 5 dogs, so R1C10 must be cats.
86. R1C10 and R2C10 are both cats, so R3C10 must be a dog (no three in a row).
87. Column 9 already has its 5 cats, so R4C9 must be dogs.
88. R4C7 and R4C9 are both dogs with one square between them, so R4C8 must be a cat.
89. Column 8 already has its 5 cats, so R10C8 must be dogs.
90. Row 10 already has its 5 dogs, so R10C1 must be cats.
91. Column 1 already has its 5 cats, so R9C1 must be dogs.
92. Row 9 already has its 5 dogs, so R9C10 must be cats.