Cats & Dogs #237: 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 R4C2 and R5C2 means they are the same. R4C2 is a dog, so R5C2 is a dog.
2. The = clue between R9C4 and R9C5 means they are the same. R9C4 is a dog, so R9C5 is a dog.
3. R9C4 and R9C5 are both dogs, so R9C3 must be a cat (no three in a row).
4. R9C4 and R9C5 are both dogs, so R9C6 must be a cat (no three in a row).
5. The = clue between R9C6 and R9C7 means they are the same. R9C6 is a cat, so R9C7 is a cat.
6. The = clue between R9C7 and R10C7 means they are the same. R9C7 is a cat, so R10C7 is a cat.
7. R9C6 and R9C7 are both cats, so R9C8 must be a dog (no three in a row).
8. R4C2 and R5C2 are both dogs, so R3C2 must be a cat (no three in a row).
9. R4C2 and R5C2 are both dogs, so R6C2 must be a cat (no three in a row).
10. R9C7 and R10C7 are both cats, so R8C7 must be a dog (no three in a row).
11. The × clue between R8C7 and R7C7 means they are different. R8C7 is a dog, so R7C7 is a cat.
12. Imagine R1C7 were a cat: following the rules from there soon forces a contradiction, so R1C7 must be a dog.
13. Imagine R1C8 were a dog: following the rules from there soon forces a contradiction, so R1C8 must be a cat.
14. Imagine R1C9 were a cat: following the rules from there soon forces a contradiction, so R1C9 must be a dog.
15. The = clue between R1C9 and R2C9 means they are the same. R1C9 is a dog, so R2C9 is a dog.
16. R1C9 and R2C9 are both dogs, so R3C9 must be a cat (no three in a row).
17. The = clue between R3C9 and R3C8 means they are the same. R3C9 is a cat, so R3C8 is a cat.
18. R3C8 and R3C9 are both cats, so R3C7 must be a dog (no three in a row).
19. The = clue between R3C7 and R4C7 means they are the same. R3C7 is a dog, so R4C7 is a dog.
20. R3C8 and R3C9 are both cats, so R3C10 must be a dog (no three in a row).
21. R3C7 and R4C7 are both dogs, so R5C7 must be a cat (no three in a row).
22. R5C7 and R7C7 are both cats with one square between them, so R6C7 must be a dog.
23. R1C8 and R3C8 are both cats with one square between them, so R2C8 must be a dog.
24. R2C8 and R2C9 are both dogs, so R2C10 must be a cat (no three in a row).
25. Imagine R4C8 were a dog: following the rules from there soon forces a contradiction, so R4C8 must be a cat.
26. R3C8 and R4C8 are both cats, so R5C8 must be a dog (no three in a row).
27. Imagine R4C9 were a cat: following the rules from there soon forces a contradiction, so R4C9 must be a dog.
28. Imagine R5C9 were a dog: following the rules from there soon forces a contradiction, so R5C9 must be a cat.
29. The = clue between R5C9 and R5C10 means they are the same. R5C9 is a cat, so R5C10 is a cat.
30. Imagine R7C6 were a cat: following the rules from there soon forces a contradiction, so R7C6 must be a dog.
31. Imagine R7C8 were a dog: following the rules from there soon forces a contradiction, so R7C8 must be a cat.
32. R7C7 and R7C8 are both cats, so R7C9 must be a dog (no three in a row).
33. Imagine R4C5 were a dog: following the rules from there soon forces a contradiction, so R4C5 must be a cat.
34. Imagine R6C4 were a cat: following the rules from there soon forces a contradiction, so R6C4 must be a dog.
35. The = clue between R6C4 and R6C5 means they are the same. R6C4 is a dog, so R6C5 is a dog.
36. R6C4 and R6C5 are both dogs, so R6C3 must be a cat (no three in a row).
37. R6C2 and R6C3 are both cats, so R6C1 must be a dog (no three in a row).
38. R6C4 and R6C5 are both dogs, so R6C6 must be a cat (no three in a row).
39. R5C5 and R6C5 are both dogs, so R7C5 must be a cat (no three in a row).
40. Imagine R4C1 were a dog: following the rules from there soon forces a contradiction, so R4C1 must be a cat.
41. Imagine R3C1 were a cat: following the rules from there soon forces a contradiction, so R3C1 must be a dog.
42. Imagine R4C3 were a dog: following the rules from there soon forces a contradiction, so R4C3 must be a cat.
43. R4C3 and R4C5 are both cats with one square between them, so R4C4 must be a dog.
44. R4C3 and R6C3 are both cats with one square between them, so R5C3 must be a dog.
45. The × clue between R5C3 and R5C4 means they are different. R5C3 is a dog, so R5C4 is a cat.
46. R5C2 and R5C3 are both dogs, so R5C1 must be a cat (no three in a row).
47. Row 5 already has its 5 cats, so R5C6 must be dogs.
48. Imagine R4C6 were a dog: following the rules from there soon forces a contradiction, so R4C6 must be a cat.
49. Row 4 already has its 5 cats, so R4C10 must be dogs.
50. Imagine R6C8 were a cat: following the rules from there soon forces a contradiction, so R6C8 must be a dog.
51. R6C7 and R6C8 are both dogs, so R6C9 must be a cat (no three in a row).
52. Row 6 already has its 5 dogs, so R6C10 must be cats.
53. R5C10 and R6C10 are both cats, so R7C10 must be a dog (no three in a row).
54. Imagine R8C6 were a dog: following the rules from there soon forces a contradiction, so R8C6 must be a cat.
55. R8C6 and R9C6 are both cats, so R10C6 must be a dog (no three in a row).
56. Imagine R1C5 were a dog: following the rules from there soon forces a contradiction, so R1C5 must be a cat.
57. Imagine R1C4 were a cat: following the rules from there soon forces a contradiction, so R1C4 must be a dog.
58. The × clue between R1C4 and R2C4 means they are different. R1C4 is a dog, so R2C4 is a cat.
59. Imagine R2C1 were a dog: following the rules from there soon forces a contradiction, so R2C1 must be a cat.
60. The × clue between R2C1 and R2C2 means they are different. R2C1 is a cat, so R2C2 is a dog.
61. Imagine R2C5 were a cat: following the rules from there soon forces a contradiction, so R2C5 must be a dog.
62. Imagine R1C2 were a cat: following the rules from there soon forces a contradiction, so R1C2 must be a dog.
63. The × clue between R1C2 and R1C3 means they are different. R1C2 is a dog, so R1C3 is a cat.
64. The = clue between R1C3 and R2C3 means they are the same. R1C3 is a cat, so R2C3 is a cat.
65. R1C3 and R2C3 are both cats, so R3C3 must be a dog (no three in a row).
66. Row 2 already has its 5 cats, so R2C6 must be dogs.
67. Column 3 already has its 5 cats, so R7C3, R8C3 and R10C3 must be dogs.
68. Imagine R3C5 were a dog: following the rules from there soon forces a contradiction, so R3C5 must be a cat.
69. Imagine R7C2 were a dog: following the rules from there soon forces a contradiction, so R7C2 must be a cat.
70. R6C2 and R7C2 are both cats, so R8C2 must be a dog (no three in a row).
71. R8C2 and R8C3 are both dogs, so R8C1 must be a cat (no three in a row).
72. R8C2 and R8C3 are both dogs, so R8C4 must be a cat (no three in a row).
73. R8C4 and R8C6 are both cats with one square between them, so R8C5 must be a dog.
74. R8C5 and R9C5 are both dogs, so R10C5 must be a cat (no three in a row).
75. Column 2 already has its 5 dogs, so R9C2 must be cats.
76. R9C2 and R9C3 are both cats, so R9C1 must be a dog (no three in a row).
77. The × clue between R9C1 and R10C1 means they are different. R9C1 is a dog, so R10C1 is a cat.
78. Column 1 already has its 5 cats, so R1C1 must be dogs.
79. Row 1 already has its 5 dogs, so R1C6 and R1C10 must be cats.
80. Column 1 already has its 5 cats, so R7C1 must be dogs.
81. Row 7 already has its 5 dogs, so R7C4 must be cats.
82. Column 2 already has its 5 dogs, so R10C2 must be cats.
83. Column 6 already has its 5 cats, so R3C6 must be dogs.
84. Row 3 already has its 5 dogs, so R3C4 must be cats.
85. Column 4 already has its 5 cats, so R10C4 must be dogs.
86. Column 10 already has its 5 cats, so R9C10 must be dogs.
87. R9C8 and R9C10 are both dogs with one square between them, so R9C9 must be a cat.
88. The = clue between R9C9 and R8C9 means they are the same. R9C9 is a cat, so R8C9 is a cat.
89. R8C9 and R8C10 are both cats, so R8C8 must be a dog (no three in a row).
90. R8C8 and R9C8 are both dogs, so R10C8 must be a cat (no three in a row).
91. R10C7 and R10C8 are both cats, so R10C9 must be a dog (no three in a row).
92. Row 10 already has its 5 cats, so R10C10 must be dogs.