Cats & Dogs #246: 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 R10C2 and R10C1 means they are the same. R10C2 is a dog, so R10C1 is a dog.
2. R3C9 and R3C10 are both cats, so R3C8 must be a dog (no three in a row).
3. R10C1 and R10C2 are both dogs, so R10C3 must be a cat (no three in a row).
4. Imagine R4C10 were a cat: following the rules from there soon forces a contradiction, so R4C10 must be a dog.
5. The = clue between R4C10 and R5C10 means they are the same. R4C10 is a dog, so R5C10 is a dog.
6. R5C9 and R5C10 are both dogs, so R5C8 must be a cat (no three in a row).
7. R4C10 and R5C10 are both dogs, so R6C10 must be a cat (no three in a row).
8. Imagine R7C1 were a dog: following the rules from there soon forces a contradiction, so R7C1 must be a cat.
9. The = clue between R7C1 and R8C1 means they are the same. R7C1 is a cat, so R8C1 is a cat.
10. R7C1 and R8C1 are both cats, so R6C1 must be a dog (no three in a row).
11. The × clue between R6C1 and R5C1 means they are different. R6C1 is a dog, so R5C1 is a cat.
12. R7C1 and R8C1 are both cats, so R9C1 must be a dog (no three in a row).
13. The = clue between R9C1 and R9C2 means they are the same. R9C1 is a dog, so R9C2 is a dog.
14. R9C1 and R9C2 are both dogs, so R9C3 must be a cat (no three in a row).
15. R9C2 and R10C2 are both dogs, so R8C2 must be a cat (no three in a row).
16. R8C1 and R8C2 are both cats, so R8C3 must be a dog (no three in a row).
17. The × clue between R8C3 and R7C3 means they are different. R8C3 is a dog, so R7C3 is a cat.
18. R7C1 and R7C3 are both cats with one square between them, so R7C2 must be a dog.
19. Imagine R2C8 were a dog: following the rules from there soon forces a contradiction, so R2C8 must be a cat.
20. Imagine R2C9 were a cat: following the rules from there soon forces a contradiction, so R2C9 must be a dog.
21. Imagine R4C8 were a cat: following the rules from there soon forces a contradiction, so R4C8 must be a dog.
22. R4C8 and R4C10 are both dogs with one square between them, so R4C9 must be a cat.
23. Imagine R6C2 were a dog: following the rules from there soon forces a contradiction, so R6C2 must be a cat.
24. Imagine R6C3 were a cat: following the rules from there soon forces a contradiction, so R6C3 must be a dog.
25. Imagine R6C8 were a dog: following the rules from there soon forces a contradiction, so R6C8 must be a cat.
26. R6C8 and R6C10 are both cats with one square between them, so R6C9 must be a dog.
27. R5C9 and R6C9 are both dogs, so R7C9 must be a cat (no three in a row).
28. R7C9 and R8C9 are both cats, so R9C9 must be a dog (no three in a row).
29. Imagine R7C4 were a cat: following the rules from there soon forces a contradiction, 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. The × clue between R5C6 and R6C6 means they are different. R5C6 is a cat, so R6C6 is a dog.
32. R5C6 and R5C8 are both cats with one square between them, so R5C7 must be a dog.
33. Imagine R7C5 were a cat: following the rules from there soon forces a contradiction, so R7C5 must be a dog.
34. The = clue between R7C5 and R8C5 means they are the same. R7C5 is a dog, so R8C5 is a dog.
35. R7C4 and R7C5 are both dogs, so R7C6 must be a cat (no three in a row).
36. R8C3 and R8C5 are both dogs with one square between them, so R8C4 must be a cat.
37. R7C5 and R8C5 are both dogs, so R6C5 must be a cat (no three in a row).
38. R7C5 and R8C5 are both dogs, so R9C5 must be a cat (no three in a row).
39. R9C3 and R9C5 are both cats with one square between them, so R9C4 must be a dog.
40. R7C6 and R8C6 are both cats, so R9C6 must be a dog (no three in a row).
41. Row 8 already has its 5 cats, so R8C7 and R8C8 must be dogs.
42. R7C8 and R8C8 are both dogs, so R9C8 must be a cat (no three in a row).
43. The × clue between R9C8 and R10C8 means they are different. R9C8 is a cat, so R10C8 is a dog.
44. Row 8 already has its 5 cats, so R8C10 must be dogs.
45. The × clue between R8C10 and R7C10 means they are different. R8C10 is a dog, so R7C10 is a cat.
46. Row 7 already has its 5 cats, so R7C7 must be dogs.
47. R5C7 and R7C7 are both dogs with one square between them, so R6C7 must be a cat.
48. R7C7 and R8C7 are both dogs, so R9C7 must be a cat (no three in a row).
49. Row 6 already has its 5 cats, so R6C4 must be dogs.
50. R6C4 and R7C4 are both dogs, so R5C4 must be a cat (no three in a row).
51. R5C4 and R5C6 are both cats with one square between them, so R5C5 must be a dog.
52. Row 9 already has its 5 dogs, so R9C10 must be cats.
53. Column 8 already has its 5 dogs, so R1C8 must be cats.
54. Imagine R2C5 were a dog: following the rules from there soon forces a contradiction, so R2C5 must be a cat.
55. The = clue between R2C5 and R3C5 means they are the same. R2C5 is a cat, so R3C5 is a cat.
56. R2C5 and R3C5 are both cats, so R1C5 must be a dog (no three in a row).
57. R2C5 and R3C5 are both cats, so R4C5 must be a dog (no three in a row).
58. Column 5 already has its 5 dogs, so R10C5 must be cats.
59. R10C3 and R10C5 are both cats with one square between them, so R10C4 must be a dog.
60. Imagine R1C3 were a dog: following the rules from there soon forces a contradiction, so R1C3 must be a cat.
61. Imagine R1C2 were a cat: following the rules from there soon forces a contradiction, so R1C2 must be a dog.
62. Imagine R1C4 were a dog: following the rules from there soon forces a contradiction, so R1C4 must be a cat.
63. Imagine R1C9 were a cat: following the rules from there soon forces a contradiction, so R1C9 must be a dog.
64. Column 9 already has its 5 dogs, so R10C9 must be cats.
65. Imagine R1C10 were a cat: following the rules from there soon forces a contradiction, so R1C10 must be a dog.
66. Imagine R1C1 were a dog: following the rules from there soon forces a contradiction, so R1C1 must be a cat.
67. Imagine R2C2 were a dog: following the rules from there soon forces a contradiction, so R2C2 must be a cat.
68. Imagine R2C3 were a cat: following the rules from there soon forces a contradiction, so R2C3 must be a dog.
69. R2C3 and R3C3 are both dogs, so R4C3 must be a cat (no three in a row).
70. Column 3 already has its 5 cats, so R5C3 must be dogs.
71. Row 5 already has its 5 dogs, so R5C2 must be cats.
72. R5C2 and R6C2 are both cats, so R4C2 must be a dog (no three in a row).
73. Row 4 already has its 5 dogs, so R4C4 must be cats.
74. R4C4 and R5C4 are both cats, so R3C4 must be a dog (no three in a row).
75. R3C3 and R3C4 are both dogs, so R3C2 must be a cat (no three in a row).
76. Row 4 already has its 5 dogs, so R4C6 must be cats.
77. R4C6 and R5C6 are both cats, so R3C6 must be a dog (no three in a row).
78. R3C6 and R3C8 are both dogs with one square between them, so R3C7 must be a cat.
79. Row 3 already has its 5 cats, so R3C1 must be dogs.
80. R3C1 and R4C1 are both dogs, so R2C1 must be a cat (no three in a row).
81. Row 4 already has its 5 dogs, so R4C7 must be cats.
82. R3C7 and R4C7 are both cats, so R2C7 must be a dog (no three in a row).
83. Column 4 already has its 5 dogs, so R2C4 must be cats.
84. R2C4 and R2C5 are both cats, so R2C6 must be a dog (no three in a row).
85. R2C6 and R3C6 are both dogs, so R1C6 must be a cat (no three in a row).
86. R1C6 and R1C8 are both cats with one square between them, so R1C7 must be a dog.
87. Row 2 already has its 5 cats, so R2C10 must be dogs.
88. Column 6 already has its 5 cats, so R10C6 must be dogs.
89. R10C6 and R10C8 are both dogs with one square between them, so R10C7 must be a cat.
90. Row 10 already has its 5 dogs, so R10C10 must be cats.