Cats & Dogs #242: 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 R3C5 and R3C4 means they are the same. R3C5 is a dog, so R3C4 is a dog.
2. The × clue between R7C10 and R7C9 means they are different. R7C10 is a dog, so R7C9 is a cat.
3. The = clue between R7C9 and R6C9 means they are the same. R7C9 is a cat, so R6C9 is a cat.
4. R3C4 and R3C5 are both dogs, so R3C3 must be a cat (no three in a row).
5. R3C4 and R3C5 are both dogs, so R3C6 must be a cat (no three in a row).
6. R8C2 and R8C4 are both dogs with one square between them, so R8C3 must be a cat.
7. The × clue between R8C3 and R9C3 means they are different. R8C3 is a cat, so R9C3 is a dog.
8. R6C9 and R7C9 are both cats, so R5C9 must be a dog (no three in a row).
9. R5C7 and R5C9 are both dogs with one square between them, so R5C8 must be a cat.
10. The × clue between R5C8 and R4C8 means they are different. R5C8 is a cat, so R4C8 is a dog.
11. R6C9 and R7C9 are both cats, so R8C9 must be a dog (no three in a row).
12. The × clue between R8C9 and R9C9 means they are different. R8C9 is a dog, so R9C9 is a cat.
13. R8C9 and R8C10 are both dogs, so R8C8 must be a cat (no three in a row).
14. The × clue between R8C8 and R7C8 means they are different. R8C8 is a cat, so R7C8 is a dog.
15. The × clue between R7C8 and R7C7 means they are different. R7C8 is a dog, so R7C7 is a cat.
16. R7C10 and R8C10 are both dogs, so R6C10 must be a cat (no three in a row).
17. R6C9 and R6C10 are both cats, so R6C8 must be a dog (no three in a row).
18. R7C10 and R8C10 are both dogs, so R9C10 must be a cat (no three in a row).
19. R9C9 and R9C10 are both cats, so R9C8 must be a dog (no three in a row).
20. Column 8 already has its 5 dogs, so R2C8 and R3C8 must be cats.
21. R3C6 and R3C8 are both cats with one square between them, so R3C7 must be a dog.
22. R3C7 and R5C7 are both dogs with one square between them, so R4C7 must be a cat.
23. Column 8 already has its 5 dogs, so R10C8 must be cats.
24. R10C8 and R10C10 are both cats with one square between them, so R10C9 must be a dog.
25. Imagine R3C9 were a cat: following the rules from there soon forces a contradiction, so R3C9 must be a dog.
26. R3C9 and R5C9 are both dogs with one square between them, so R4C9 must be a cat.
27. Imagine R3C10 were a dog: following the rules from there soon forces a contradiction, so R3C10 must be a cat.
28. The = clue between R3C10 and R4C10 means they are the same. R3C10 is a cat, so R4C10 is a cat.
29. R3C10 and R4C10 are both cats, so R2C10 must be a dog (no three in a row).
30. R3C10 and R4C10 are both cats, so R5C10 must be a dog (no three in a row).
31. Column 10 already has its 5 cats, so R1C10 must be dogs.
32. R1C8 and R1C10 are both dogs with one square between them, so R1C9 must be a cat.
33. Column 9 already has its 5 cats, so R2C9 must be dogs.
34. Imagine R4C6 were a cat: following the rules from there soon forces a contradiction, so R4C6 must be a dog.
35. Imagine R5C5 were a dog: following the rules from there soon forces a contradiction, so R5C5 must be a cat.
36. Imagine R5C6 were a cat: following the rules from there soon forces a contradiction, so R5C6 must be a dog.
37. The × clue between R5C6 and R6C6 means they are different. R5C6 is a dog, so R6C6 is a cat.
38. Imagine R5C1 were a dog: following the rules from there soon forces a contradiction, so R5C1 must be a cat.
39. Imagine R5C2 were a dog: following the rules from there soon forces a contradiction, so R5C2 must be a cat.
40. R5C1 and R5C2 are both cats, so R5C3 must be a dog (no three in a row).
41. Row 5 already has its 5 dogs, so R5C4 must be cats.
42. Imagine R6C1 were a cat: following the rules from there soon forces a contradiction, so R6C1 must be a dog.
43. The = clue between R6C1 and R6C2 means they are the same. R6C1 is a dog, so R6C2 is a dog.
44. R6C1 and R6C2 are both dogs, so R6C3 must be a cat (no three in a row).
45. R6C2 and R8C2 are both dogs with one square between them, so R7C2 must be a cat.
46. R6C3 and R8C3 are both cats with one square between them, so R7C3 must be a dog.
47. Imagine R6C7 were a cat: following the rules from there soon forces a contradiction, so R6C7 must be a dog.
48. Imagine R8C1 were a dog: following the rules from there soon forces a contradiction, so R8C1 must be a cat.
49. Imagine R8C5 were a dog: following the rules from there soon forces a contradiction, so R8C5 must be a cat.
50. The × clue between R8C5 and R8C6 means they are different. R8C5 is a cat, so R8C6 is a dog.
51. Row 8 already has its 5 dogs, so R8C7 must be cats.
52. R7C7 and R8C7 are both cats, so R9C7 must be a dog (no three in a row).
53. R9C7 and R9C8 are both dogs, so R9C6 must be a cat (no three in a row).
54. Imagine R1C6 were a cat: following the rules from there soon forces a contradiction, so R1C6 must be a dog.
55. R1C6 and R1C8 are both dogs with one square between them, so R1C7 must be a cat.
56. Imagine R2C5 were a dog: following the rules from there soon forces a contradiction, so R2C5 must be a cat.
57. The = clue between R2C5 and R2C6 means they are the same. R2C5 is a cat, so R2C6 is a cat.
58. R2C5 and R2C6 are both cats, so R2C4 must be a dog (no three in a row).
59. R2C5 and R2C6 are both cats, so R2C7 must be a dog (no three in a row).
60. R2C4 and R3C4 are both dogs, so R1C4 must be a cat (no three in a row).
61. R2C4 and R3C4 are both dogs, so R4C4 must be a cat (no three in a row).
62. R4C4 and R5C4 are both cats, so R6C4 must be a dog (no three in a row).
63. R6C4 and R8C4 are both dogs with one square between them, so R7C4 must be a cat.
64. Row 6 already has its 5 dogs, so R6C5 must be cats.
65. R5C5 and R6C5 are both cats, so R4C5 must be a dog (no three in a row).
66. R5C5 and R6C5 are both cats, so R7C5 must be a dog (no three in a row).
67. Column 7 already has its 5 dogs, so R10C7 must be cats.
68. R10C7 and R10C8 are both cats, so R10C6 must be a dog (no three in a row).
69. Column 6 already has its 5 dogs, so R7C6 must be cats.
70. Row 7 already has its 5 cats, so R7C1 must be dogs.
71. Imagine R1C5 were a cat: following the rules from there soon forces a contradiction, so R1C5 must be a dog.
72. Imagine R1C1 were a dog: following the rules from there soon forces a contradiction, so R1C1 must be a cat.
73. Imagine R2C1 were a dog: following the rules from there soon forces a contradiction, so R2C1 must be a cat.
74. R1C1 and R2C1 are both cats, so R3C1 must be a dog (no three in a row).
75. Row 3 already has its 5 dogs, so R3C2 must be cats.
76. R3C2 and R5C2 are both cats with one square between them, so R4C2 must be a dog.
77. R4C1 and R4C2 are both dogs, so R4C3 must be a cat (no three in a row).
78. R3C3 and R4C3 are both cats, so R2C3 must be a dog (no three in a row).
79. R2C3 and R2C4 are both dogs, so R2C2 must be a cat (no three in a row).
80. R2C2 and R3C2 are both cats, so R1C2 must be a dog (no three in a row).
81. Row 1 already has its 5 dogs, so R1C3 must be cats.
82. Column 2 already has its 5 cats, so R10C2 must be dogs.
83. Column 3 already has its 5 cats, so R10C3 must be dogs.
84. R10C2 and R10C3 are both dogs, so R10C1 must be a cat (no three in a row).
85. R10C2 and R10C3 are both dogs, so R10C4 must be a cat (no three in a row).
86. R8C1 and R10C1 are both cats with one square between them, so R9C1 must be a dog.
87. Row 10 already has its 5 cats, so R10C5 must be dogs.
88. Column 4 already has its 5 cats, so R9C4 must be dogs.
89. R9C3 and R9C4 are both dogs, so R9C5 must be a cat (no three in a row).