Cats & Dogs #278: 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 R3C8 means they are different. R3C7 is a dog, so R3C8 is a cat.
2. The × clue between R3C8 and R2C8 means they are different. R3C8 is a cat, so R2C8 is a dog.
3. The × clue between R2C8 and R1C8 means they are different. R2C8 is a dog, so R1C8 is a cat.
4. R1C1 and R1C3 are both dogs with one square between them, so R1C2 must be a cat.
5. R5C4 and R5C5 are both dogs, so R5C3 must be a cat (no three in a row).
6. R5C4 and R5C5 are both dogs, so R5C6 must be a cat (no three in a row).
7. The = clue between R5C6 and R6C6 means they are the same. R5C6 is a cat, so R6C6 is a cat.
8. R5C6 and R6C6 are both cats, so R4C6 must be a dog (no three in a row).
9. R5C6 and R6C6 are both cats, so R7C6 must be a dog (no three in a row).
10. Imagine R1C6 were a cat: following the rules from there soon forces a contradiction, so R1C6 must be a dog.
11. The = clue between R1C6 and R1C7 means they are the same. R1C6 is a dog, so R1C7 is a dog.
12. R1C6 and R1C7 are both dogs, so R1C5 must be a cat (no three in a row).
13. R1C7 and R3C7 are both dogs with one square between them, so R2C7 must be a cat.
14. The × clue between R2C7 and R2C6 means they are different. R2C7 is a cat, so R2C6 is a dog.
15. R1C6 and R2C6 are both dogs, so R3C6 must be a cat (no three in a row).
16. Imagine R1C4 were a dog: following the rules from there soon forces a contradiction, so R1C4 must be a cat.
17. Imagine R2C1 were a cat: following the rules from there soon forces a contradiction, so R2C1 must be a dog.
18. The = clue between R2C1 and R2C2 means they are the same. R2C1 is a dog, so R2C2 is a dog.
19. R2C1 and R2C2 are both dogs, so R2C3 must be a cat (no three in a row).
20. R1C1 and R2C1 are both dogs, so R3C1 must be a cat (no three in a row).
21. R2C2 and R4C2 are both dogs with one square between them, so R3C2 must be a cat.
22. R3C1 and R3C2 are both cats, so R3C3 must be a dog (no three in a row).
23. The = clue between R3C3 and R3C4 means they are the same. R3C3 is a dog, so R3C4 is a dog.
24. R3C3 and R3C4 are both dogs, so R3C5 must be a cat (no three in a row).
25. The = clue between R3C5 and R4C5 means they are the same. R3C5 is a cat, so R4C5 is a cat.
26. R3C4 and R5C4 are both dogs with one square between them, so R4C4 must be a cat.
27. R4C4 and R4C5 are both cats, so R4C3 must be a dog (no three in a row).
28. R4C2 and R4C3 are both dogs, so R4C1 must be a cat (no three in a row).
29. R3C1 and R4C1 are both cats, so R5C1 must be a dog (no three in a row).
30. R1C5 and R3C5 are both cats with one square between them, so R2C5 must be a dog.
31. R2C5 and R2C6 are both dogs, so R2C4 must be a cat (no three in a row).
32. Row 2 already has its 5 dogs, so R2C9 and R2C10 must be cats.
33. Row 3 already has its 5 cats, so R3C9 and R3C10 must be dogs.
34. Imagine R5C9 were a dog: following the rules from there soon forces a contradiction, so R5C9 must be a cat.
35. The = clue between R5C9 and R5C10 means they are the same. R5C9 is a cat, so R5C10 is a cat.
36. R5C9 and R5C10 are both cats, so R5C8 must be a dog (no three in a row).
37. Imagine R7C5 were a dog: following the rules from there soon forces a contradiction, so R7C5 must be a cat.
38. Imagine R6C5 were a cat: following the rules from there soon forces a contradiction, so R6C5 must be a dog.
39. Imagine R9C6 were a dog: following the rules from there soon forces a contradiction, so R9C6 must be a cat.
40. Imagine R7C8 were a dog: following the rules from there soon forces a contradiction, so R7C8 must be a cat.
41. The = clue between R7C8 and R8C8 means they are the same. R7C8 is a cat, so R8C8 is a cat.
42. R7C8 and R8C8 are both cats, so R6C8 must be a dog (no three in a row).
43. The × clue between R6C8 and R6C9 means they are different. R6C8 is a dog, so R6C9 is a cat.
44. R5C8 and R6C8 are both dogs, so R4C8 must be a cat (no three in a row).
45. R7C8 and R8C8 are both cats, so R9C8 must be a dog (no three in a row).
46. R5C9 and R6C9 are both cats, so R4C9 must be a dog (no three in a row).
47. R5C9 and R6C9 are both cats, so R7C9 must be a dog (no three in a row).
48. Column 8 already has its 5 cats, so R10C8 must be dogs.
49. The × clue between R10C8 and R10C9 means they are different. R10C8 is a dog, so R10C9 is a cat.
50. Imagine R1C9 were a cat: following the rules from there soon forces a contradiction, so R1C9 must be a dog.
51. Row 1 already has its 5 dogs, so R1C10 must be cats.
52. Imagine R7C7 were a cat: following the rules from there soon forces a contradiction, so R7C7 must be a dog.
53. The × clue between R7C7 and R8C7 means they are different. R7C7 is a dog, so R8C7 is a cat.
54. The × clue between R8C7 and R8C6 means they are different. R8C7 is a cat, so R8C6 is a dog.
55. R8C7 and R8C8 are both cats, so R8C9 must be a dog (no three in a row).
56. R7C9 and R8C9 are both dogs, so R9C9 must be a cat (no three in a row).
57. Column 6 already has its 5 dogs, so R10C6 must be cats.
58. The = clue between R10C6 and R10C7 means they are the same. R10C6 is a cat, so R10C7 is a cat.
59. R10C6 and R10C7 are both cats, so R10C5 must be a dog (no three in a row).
60. R9C5 and R10C5 are both dogs, so R8C5 must be a cat (no three in a row).
61. The = clue between R8C5 and R8C4 means they are the same. R8C5 is a cat, so R8C4 is a cat.
62. R8C4 and R8C5 are both cats, so R8C3 must be a dog (no three in a row).
63. The × clue between R8C3 and R8C2 means they are different. R8C3 is a dog, so R8C2 is a cat.
64. R8C7 and R10C7 are both cats with one square between them, so R9C7 must be a dog.
65. Row 8 already has its 5 cats, so R8C1 and R8C10 must be dogs.
66. R7C10 and R8C10 are both dogs, so R6C10 must be a cat (no three in a row).
67. R5C10 and R6C10 are both cats, so R4C10 must be a dog (no three in a row).
68. R7C10 and R8C10 are both dogs, so R9C10 must be a cat (no three in a row).
69. Row 4 already has its 5 dogs, so R4C7 must be cats.
70. Column 10 already has its 5 cats, so R10C10 must be dogs.
71. Imagine R5C2 were a dog: following the rules from there soon forces a contradiction, so R5C2 must be a cat.
72. Row 5 already has its 5 cats, so R5C7 must be dogs.
73. R5C7 and R7C7 are both dogs with one square between them, so R6C7 must be a cat.
74. Imagine R6C1 were a cat: following the rules from there soon forces a contradiction, so R6C1 must be a dog.
75. R5C1 and R6C1 are both dogs, so R7C1 must be a cat (no three in a row).
76. Column 1 already has its 5 dogs, so R9C1 and R10C1 must be cats.
77. Imagine R6C2 were a cat: following the rules from there soon forces a contradiction, so R6C2 must be a dog.
78. R6C1 and R6C2 are both dogs, so R6C3 must be a cat (no three in a row).
79. R5C3 and R6C3 are both cats, so R7C3 must be a dog (no three in a row).
80. R7C3 and R8C3 are both dogs, so R9C3 must be a cat (no three in a row).
81. R9C1 and R9C3 are both cats with one square between them, so R9C2 must be a dog.
82. Row 6 already has its 5 cats, so R6C4 must be dogs.
83. R5C4 and R6C4 are both dogs, so R7C4 must be a cat (no three in a row).
84. R7C4 and R8C4 are both cats, so R9C4 must be a dog (no three in a row).
85. Row 7 already has its 5 dogs, so R7C2 must be cats.
86. Column 2 already has its 5 cats, so R10C2 must be dogs.
87. Column 3 already has its 5 dogs, so R10C3 must be cats.
88. Row 10 already has its 5 cats, so R10C4 must be dogs.