Cats & Dogs #295: 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 R1C6 and R1C7 means they are the same. R1C6 is a dog, so R1C7 is a dog.
2. The = clue between R6C7 and R6C8 means they are the same. R6C7 is a cat, so R6C8 is a cat.
3. The × clue between R7C1 and R7C2 means they are different. R7C1 is a cat, so R7C2 is a dog.
4. The × clue between R10C3 and R10C2 means they are different. R10C3 is a cat, so R10C2 is a dog.
5. R1C6 and R1C7 are both dogs, so R1C5 must be a cat (no three in a row).
6. R1C6 and R1C7 are both dogs, so R1C8 must be a cat (no three in a row).
7. The = clue between R1C8 and R2C8 means they are the same. R1C8 is a cat, so R2C8 is a cat.
8. R6C7 and R6C8 are both cats, so R6C6 must be a dog (no three in a row).
9. R6C7 and R6C8 are both cats, so R6C9 must be a dog (no three in a row).
10. The = clue between R6C9 and R5C9 means they are the same. R6C9 is a dog, so R5C9 is a dog.
11. R5C8 and R5C9 are both dogs, so R5C7 must be a cat (no three in a row).
12. R5C8 and R5C9 are both dogs, so R5C10 must be a cat (no three in a row).
13. R5C7 and R6C7 are both cats, so R4C7 must be a dog (no three in a row).
14. R5C7 and R6C7 are both cats, so R7C7 must be a dog (no three in a row).
15. R1C8 and R2C8 are both cats, so R3C8 must be a dog (no three in a row).
16. R3C8 and R5C8 are both dogs with one square between them, so R4C8 must be a cat.
17. R5C9 and R6C9 are both dogs, so R4C9 must be a cat (no three in a row).
18. R4C8 and R4C9 are both cats, so R4C10 must be a dog (no three in a row).
19. R5C9 and R6C9 are both dogs, so R7C9 must be a cat (no three in a row).
20. R5C10 and R6C10 are both cats, so R7C10 must be a dog (no three in a row).
21. R7C10 and R9C10 are both dogs with one square between them, so R8C10 must be a cat.
22. Imagine R4C4 were a cat: following the rules from there soon forces a contradiction, so R4C4 must be a dog.
23. The = clue between R4C4 and R5C4 means they are the same. R4C4 is a dog, so R5C4 is a dog.
24. The = clue between R5C4 and R5C5 means they are the same. R5C4 is a dog, so R5C5 is a dog.
25. R5C4 and R5C5 are both dogs, so R5C3 must be a cat (no three in a row).
26. R5C4 and R5C5 are both dogs, so R5C6 must be a cat (no three in a row).
27. R4C4 and R5C4 are both dogs, so R3C4 must be a cat (no three in a row).
28. Imagine R2C6 were a dog: following the rules from there soon forces a contradiction, so R2C6 must be a cat.
29. R2C6 and R2C8 are both cats with one square between them, so R2C7 must be a dog.
30. R1C7 and R2C7 are both dogs, so R3C7 must be a cat (no three in a row).
31. Imagine R3C5 were a cat: following the rules from there soon forces a contradiction, so R3C5 must be a dog.
32. The = clue between R3C5 and R3C6 means they are the same. R3C5 is a dog, so R3C6 is a dog.
33. R3C5 and R5C5 are both dogs with one square between them, so R4C5 must be a cat.
34. The × clue between R4C5 and R4C6 means they are different. R4C5 is a cat, so R4C6 is a dog.
35. Imagine R6C3 were a cat: following the rules from there soon forces a contradiction, so R6C3 must be a dog.
36. Imagine R6C5 were a cat: following the rules from there soon forces a contradiction, so R6C5 must be a dog.
37. R5C5 and R6C5 are both dogs, so R7C5 must be a cat (no three in a row).
38. Imagine R7C3 were a dog: following the rules from there soon forces a contradiction, so R7C3 must be a cat.
39. R7C3 and R7C5 are both cats with one square between them, so R7C4 must be a dog.
40. Imagine R7C6 were a dog: following the rules from there soon forces a contradiction, so R7C6 must be a cat.
41. Row 7 already has its 5 cats, so R7C8 must be dogs.
42. Imagine R8C6 were a dog: following the rules from there soon forces a contradiction, so R8C6 must be a cat.
43. R7C6 and R8C6 are both cats, so R9C6 must be a dog (no three in a row).
44. Column 6 already has its 5 dogs, so R10C6 must be cats.
45. The = clue between R10C6 and R10C5 means they are the same. R10C6 is a cat, so R10C5 is a cat.
46. R10C3 and R10C5 are both cats with one square between them, so R10C4 must be a dog.
47. R10C5 and R10C6 are both cats, so R10C7 must be a dog (no three in a row).
48. Column 7 already has its 5 dogs, so R8C7 must be cats.
49. R8C6 and R8C7 are both cats, so R8C5 must be a dog (no three in a row).
50. R8C6 and R8C7 are both cats, so R8C8 must be a dog (no three in a row).
51. R7C8 and R8C8 are both dogs, so R9C8 must be a cat (no three in a row).
52. The = clue between R9C8 and R9C7 means they are the same. R9C8 is a cat, so R9C7 is a cat.
53. R9C7 and R9C8 are both cats, so R9C9 must be a dog (no three in a row).
54. Column 8 already has its 5 cats, so R10C8 must be dogs.
55. R10C7 and R10C8 are both dogs, so R10C9 must be a cat (no three in a row).
56. Imagine R1C3 were a cat: following the rules from there soon forces a contradiction, so R1C3 must be a dog.
57. Imagine R4C1 were a dog: following the rules from there soon forces a contradiction, so R4C1 must be a cat.
58. Imagine R3C1 were a cat: following the rules from there soon forces a contradiction, so R3C1 must be a dog.
59. The = clue between R3C1 and R3C2 means they are the same. R3C1 is a dog, so R3C2 is a dog.
60. R3C1 and R3C2 are both dogs, so R3C3 must be a cat (no three in a row).
61. R3C3 and R5C3 are both cats with one square between them, so R4C3 must be a dog.
62. R4C3 and R4C4 are both dogs, so R4C2 must be a cat (no three in a row).
63. Row 3 already has its 5 dogs, so R3C9 must be cats.
64. R3C9 and R4C9 are both cats, so R2C9 must be a dog (no three in a row).
65. The × clue between R2C9 and R2C10 means they are different. R2C9 is a dog, so R2C10 is a cat.
66. Row 3 already has its 5 dogs, so R3C10 must be cats.
67. R2C10 and R3C10 are both cats, so R1C10 must be a dog (no three in a row).
68. Column 10 already has its 5 cats, so R10C10 must be dogs.
69. Row 10 already has its 5 dogs, so R10C1 must be cats.
70. Imagine R1C1 were a dog: following the rules from there soon forces a contradiction, so R1C1 must be a cat.
71. Imagine R1C2 were a dog: following the rules from there soon forces a contradiction, so R1C2 must be a cat.
72. Imagine R1C4 were a cat: following the rules from there soon forces a contradiction, so R1C4 must be a dog.
73. Row 1 already has its 5 dogs, so R1C9 must be cats.
74. Column 4 already has its 5 dogs, so R2C4 must be cats.
75. R2C4 and R2C6 are both cats with one square between them, so R2C5 must be a dog.
76. Column 4 already has its 5 dogs, so R8C4 must be cats.
77. The = clue between R8C4 and R8C3 means they are the same. R8C4 is a cat, so R8C3 is a cat.
78. R8C3 and R8C4 are both cats, so R8C2 must be a dog (no three in a row).
79. R7C2 and R8C2 are both dogs, so R6C2 must be a cat (no three in a row).
80. R4C2 and R6C2 are both cats with one square between them, so R5C2 must be a dog.
81. R7C2 and R8C2 are both dogs, so R9C2 must be a cat (no three in a row).
82. R7C3 and R8C3 are both cats, so R9C3 must be a dog (no three in a row).
83. Row 5 already has its 5 dogs, so R5C1 must be cats.
84. R4C1 and R5C1 are both cats, so R6C1 must be a dog (no three in a row).
85. Row 8 already has its 5 cats, so R8C1 and R8C9 must be dogs.
86. Column 1 already has its 5 cats, so R2C1 and R9C1 must be dogs.
87. Row 9 already has its 5 dogs, so R9C4 and R9C5 must be cats.
88. Column 2 already has its 5 dogs, so R2C2 must be cats.
89. R2C2 and R2C4 are both cats with one square between them, so R2C3 must be a dog.