Cats & Dogs #300: 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 R6C2 and R7C2 means they are the same. R6C2 is a dog, so R7C2 is a dog.
2. R3C1 and R4C1 are both dogs, so R2C1 must be a cat (no three in a row).
3. R3C1 and R4C1 are both dogs, so R5C1 must be a cat (no three in a row).
4. R6C2 and R7C2 are both dogs, so R5C2 must be a cat (no three in a row).
5. R5C1 and R5C2 are both cats, so R5C3 must be a dog (no three in a row).
6. R6C2 and R7C2 are both dogs, so R8C2 must be a cat (no three in a row).
7. Imagine R6C1 were a cat: following the rules from there soon forces a contradiction, so R6C1 must be a dog.
8. The = clue between R6C1 and R7C1 means they are the same. R6C1 is a dog, so R7C1 is a dog.
9. R6C1 and R6C2 are both dogs, so R6C3 must be a cat (no three in a row).
10. R7C1 and R7C2 are both dogs, so R7C3 must be a cat (no three in a row).
11. R6C1 and R7C1 are both dogs, so R8C1 must be a cat (no three in a row).
12. The × clue between R8C1 and R9C1 means they are different. R8C1 is a cat, so R9C1 is a dog.
13. R8C1 and R8C2 are both cats, so R8C3 must be a dog (no three in a row).
14. The = clue between R8C3 and R8C4 means they are the same. R8C3 is a dog, so R8C4 is a dog.
15. R8C3 and R8C4 are both dogs, so R8C5 must be a cat (no three in a row).
16. R8C5 and R8C6 are both cats, so R8C7 must be a dog (no three in a row).
17. Column 1 already has its 5 dogs, so R1C1 and R10C1 must be cats.
18. Imagine R6C10 were a dog: following the rules from there soon forces a contradiction, so R6C10 must be a cat.
19. Imagine R7C5 were a cat: following the rules from there soon forces a contradiction, so R7C5 must be a dog.
20. Imagine R5C6 were a cat: following the rules from there soon forces a contradiction, so R5C6 must be a dog.
21. The = clue between R5C6 and R6C6 means they are the same. R5C6 is a dog, so R6C6 is a dog.
22. R5C6 and R6C6 are both dogs, so R4C6 must be a cat (no three in a row).
23. R5C6 and R6C6 are both dogs, so R7C6 must be a cat (no three in a row).
24. R7C6 and R8C6 are both cats, so R9C6 must be a dog (no three in a row).
25. The × clue between R9C6 and R9C5 means they are different. R9C6 is a dog, so R9C5 is a cat.
26. R8C5 and R9C5 are both cats, so R10C5 must be a dog (no three in a row).
27. R10C5 and R10C6 are both dogs, so R10C4 must be a cat (no three in a row).
28. R10C5 and R10C6 are both dogs, so R10C7 must be a cat (no three in a row).
29. Imagine R1C6 were a dog: following the rules from there soon forces a contradiction, so R1C6 must be a cat.
30. Imagine R6C7 were a dog: following the rules from there soon forces a contradiction, so R6C7 must be a cat.
31. Imagine R7C4 were a dog: following the rules from there soon forces a contradiction, so R7C4 must be a cat.
32. Imagine R7C9 were a dog: following the rules from there soon forces a contradiction, so R7C9 must be a cat.
33. Imagine R8C10 were a cat: following the rules from there soon forces a contradiction, so R8C10 must be a dog.
34. R7C10 and R8C10 are both dogs, so R9C10 must be a cat (no three in a row).
35. Imagine R9C2 were a cat: following the rules from there soon forces a contradiction, so R9C2 must be a dog.
36. The = clue between R9C2 and R10C2 means they are the same. R9C2 is a dog, so R10C2 is a dog.
37. R9C1 and R9C2 are both dogs, so R9C3 must be a cat (no three in a row).
38. R9C3 and R9C5 are both cats with one square between them, so R9C4 must be a dog.
39. Imagine R1C2 were a dog: following the rules from there soon forces a contradiction, so R1C2 must be a cat.
40. R1C1 and R1C2 are both cats, so R1C3 must be a dog (no three in a row).
41. Imagine R1C7 were a cat: following the rules from there soon forces a contradiction, so R1C7 must be a dog.
42. Imagine R2C2 were a dog: following the rules from there soon forces a contradiction, so R2C2 must be a cat.
43. R2C1 and R2C2 are both cats, so R2C3 must be a dog (no three in a row).
44. R1C2 and R2C2 are both cats, so R3C2 must be a dog (no three in a row).
45. R3C1 and R3C2 are both dogs, so R3C3 must be a cat (no three in a row).
46. The × clue between R3C3 and R3C4 means they are different. R3C3 is a cat, so R3C4 is a dog.
47. Column 2 already has its 5 dogs, so R4C2 must be cats.
48. Imagine R8C8 were a dog: following the rules from there soon forces a contradiction, so R8C8 must be a cat.
49. The = clue between R8C8 and R9C8 means they are the same. R8C8 is a cat, so R9C8 is a cat.
50. R9C8 and R9C10 are both cats with one square between them, so R9C9 must be a dog.
51. R8C8 and R9C8 are both cats, so R7C8 must be a dog (no three in a row).
52. R8C8 and R9C8 are both cats, so R10C8 must be a dog (no three in a row).
53. Row 7 already has its 5 dogs, so R7C7 must be cats.
54. R6C7 and R7C7 are both cats, so R5C7 must be a dog (no three in a row).
55. R5C6 and R5C7 are both dogs, so R5C5 must be a cat (no three in a row).
56. R5C6 and R5C7 are both dogs, so R5C8 must be a cat (no three in a row).
57. Row 8 already has its 5 cats, so R8C9 must be dogs.
58. R8C9 and R9C9 are both dogs, so R10C9 must be a cat (no three in a row).
59. Row 9 already has its 5 dogs, so R9C7 must be cats.
60. Imagine R2C7 were a cat: following the rules from there soon forces a contradiction, so R2C7 must be a dog.
61. R1C7 and R2C7 are both dogs, so R3C7 must be a cat (no three in a row).
62. Column 7 already has its 5 cats, so R4C7 must be dogs.
63. The × clue between R4C7 and R4C8 means they are different. R4C7 is a dog, so R4C8 is a cat.
64. R4C8 and R5C8 are both cats, so R3C8 must be a dog (no three in a row).
65. The = clue between R3C8 and R2C8 means they are the same. R3C8 is a dog, so R2C8 is a dog.
66. R2C7 and R2C8 are both dogs, so R2C6 must be a cat (no three in a row).
67. R2C7 and R2C8 are both dogs, so R2C9 must be a cat (no three in a row).
68. R1C6 and R2C6 are both cats, so R3C6 must be a dog (no three in a row).
69. R3C4 and R3C6 are both dogs with one square between them, so R3C5 must be a cat.
70. R3C5 and R5C5 are both cats with one square between them, so R4C5 must be a dog.
71. R2C8 and R3C8 are both dogs, so R1C8 must be a cat (no three in a row).
72. R4C8 and R5C8 are both cats, so R6C8 must be a dog (no three in a row).
73. Row 3 already has its 5 dogs, so R3C9 must be cats.
74. R2C9 and R3C9 are both cats, so R1C9 must be a dog (no three in a row).
75. R2C9 and R3C9 are both cats, so R4C9 must be a dog (no three in a row).
76. Row 3 already has its 5 dogs, so R3C10 must be cats.
77. Imagine R1C4 were a dog: following the rules from there soon forces a contradiction, so R1C4 must be a cat.
78. R1C4 and R1C6 are both cats with one square between them, so R1C5 must be a dog.
79. Row 1 already has its 5 cats, so R1C10 must be dogs.
80. Imagine R2C4 were a dog: following the rules from there soon forces a contradiction, so R2C4 must be a cat.
81. R2C4 and R2C6 are both cats with one square between them, so R2C5 must be a dog.
82. Row 2 already has its 5 cats, so R2C10 must be dogs.
83. Column 5 already has its 5 dogs, so R6C5 must be cats.
84. R6C3 and R6C5 are both cats with one square between them, so R6C4 must be a dog.
85. Row 6 already has its 5 dogs, so R6C9 must be cats.
86. R6C9 and R7C9 are both cats, so R5C9 must be a dog (no three in a row).
87. Imagine R4C3 were a dog: following the rules from there soon forces a contradiction, so R4C3 must be a cat.
88. R4C2 and R4C3 are both cats, so R4C4 must be a dog (no three in a row).
89. R3C4 and R4C4 are both dogs, so R5C4 must be a cat (no three in a row).
90. Row 4 already has its 5 dogs, so R4C10 must be cats.
91. R3C10 and R4C10 are both cats, so R5C10 must be a dog (no three in a row).
92. Column 3 already has its 5 cats, so R10C3 must be dogs.
93. Row 10 already has its 5 dogs, so R10C10 must be cats.