Cats & Dogs #221: 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 R2C6 means they are the same. R1C6 is a cat, so R2C6 is a cat.
2. The = clue between R2C8 and R1C8 means they are the same. R2C8 is a dog, so R1C8 is a dog.
3. The × clue between R4C2 and R4C1 means they are different. R4C2 is a dog, so R4C1 is a cat.
4. The × clue between R5C3 and R5C4 means they are different. R5C3 is a dog, so R5C4 is a cat.
5. The × clue between R5C4 and R5C5 means they are different. R5C4 is a cat, so R5C5 is a dog.
6. The × clue between R7C6 and R7C7 means they are different. R7C6 is a dog, so R7C7 is a cat.
7. The = clue between R8C9 and R8C8 means they are the same. R8C9 is a cat, so R8C8 is a cat.
8. R2C4 and R2C6 are both cats with one square between them, so R2C5 must be a dog.
9. R8C8 and R8C9 are both cats, so R8C7 must be a dog (no three in a row).
10. R8C8 and R8C9 are both cats, so R8C10 must be a dog (no three in a row).
11. The = clue between R8C10 and R7C10 means they are the same. R8C10 is a dog, so R7C10 is a dog.
12. R1C6 and R2C6 are both cats, so R3C6 must be a dog (no three in a row).
13. The × clue between R3C6 and R4C6 means they are different. R3C6 is a dog, so R4C6 is a cat.
14. R1C8 and R2C8 are both dogs, so R3C8 must be a cat (no three in a row).
15. R7C10 and R8C10 are both dogs, so R6C10 must be a cat (no three in a row).
16. R7C10 and R8C10 are both dogs, so R9C10 must be a cat (no three in a row).
17. Imagine R4C8 were a dog: following the rules from there soon forces a contradiction, so R4C8 must be a cat.
18. The = clue between R4C8 and R4C9 means they are the same. R4C8 is a cat, so R4C9 is a cat.
19. R4C8 and R4C9 are both cats, so R4C10 must be a dog (no three in a row).
20. R3C8 and R4C8 are both cats, so R5C8 must be a dog (no three in a row).
21. Imagine R3C5 were a dog: following the rules from there soon forces a contradiction, so R3C5 must be a cat.
22. Imagine R4C5 were a cat: following the rules from there soon forces a contradiction, so R4C5 must be a dog.
23. R4C5 and R5C5 are both dogs, so R6C5 must be a cat (no three in a row).
24. Imagine R8C4 were a cat: following the rules from there soon forces a contradiction, so R8C4 must be a dog.
25. The = clue between R8C4 and R8C5 means they are the same. R8C4 is a dog, so R8C5 is a dog.
26. R8C4 and R8C5 are both dogs, so R8C3 must be a cat (no three in a row).
27. R8C4 and R8C5 are both dogs, so R8C6 must be a cat (no three in a row).
28. Imagine R1C4 were a cat: following the rules from there soon forces a contradiction, so R1C4 must be a dog.
29. Imagine R9C3 were a cat: following the rules from there soon forces a contradiction, so R9C3 must be a dog.
30. The = clue between R9C3 and R10C3 means they are the same. R9C3 is a dog, so R10C3 is a dog.
31. Imagine R3C3 were a cat: following the rules from there soon forces a contradiction, so R3C3 must be a dog.
32. R3C3 and R5C3 are both dogs with one square between them, so R4C3 must be a cat.
33. Row 4 already has its 5 cats, so R4C4 must be dogs.
34. The × clue between R4C4 and R3C4 means they are different. R4C4 is a dog, so R3C4 is a cat.
35. Imagine R1C2 were a dog: following the rules from there soon forces a contradiction, so R1C2 must be a cat.
36. The × clue between R1C2 and R2C2 means they are different. R1C2 is a cat, so R2C2 is a dog.
37. R2C2 and R4C2 are both dogs with one square between them, so R3C2 must be a cat.
38. Imagine R1C1 were a cat: following the rules from there soon forces a contradiction, so R1C1 must be a dog.
39. Imagine R1C3 were a dog: following the rules from there soon forces a contradiction, so R1C3 must be a cat.
40. Imagine R1C5 were a cat: following the rules from there soon forces a contradiction, so R1C5 must be a dog.
41. Column 5 already has its 5 dogs, so R7C5, R9C5 and R10C5 must be cats.
42. Imagine R2C3 were a dog: following the rules from there soon forces a contradiction, so R2C3 must be a cat.
43. Imagine R2C7 were a dog: following the rules from there soon forces a contradiction, so R2C7 must be a cat.
44. Imagine R2C1 were a cat: following the rules from there soon forces a contradiction, so R2C1 must be a dog.
45. R1C1 and R2C1 are both dogs, so R3C1 must be a cat (no three in a row).
46. R3C1 and R4C1 are both cats, so R5C1 must be a dog (no three in a row).
47. R5C1 and R5C3 are both dogs with one square between them, so R5C2 must be a cat.
48. Row 3 already has its 5 cats, so R3C7 must be dogs.
49. R3C7 and R4C7 are both dogs, so R5C7 must be a cat (no three in a row).
50. R5C7 and R7C7 are both cats with one square between them, so R6C7 must be a dog.
51. Row 3 already has its 5 cats, so R3C9 and R3C10 must be dogs.
52. R3C10 and R4C10 are both dogs, so R2C10 must be a cat (no three in a row).
53. R3C10 and R4C10 are both dogs, so R5C10 must be a cat (no three in a row).
54. Row 2 already has its 5 cats, so R2C9 must be dogs.
55. R2C9 and R3C9 are both dogs, so R1C9 must be a cat (no three in a row).
56. Row 1 already has its 5 cats, so R1C7 must be dogs.
57. Column 7 already has its 5 dogs, so R9C7 must be cats.
58. R9C5 and R9C7 are both cats with one square between them, so R9C6 must be a dog.
59. Column 7 already has its 5 dogs, so R10C7 must be cats.
60. R10C5 and R10C7 are both cats with one square between them, so R10C6 must be a dog.
61. Column 10 already has its 5 cats, so R10C10 must be dogs.
62. Imagine R5C6 were a dog: following the rules from there soon forces a contradiction, so R5C6 must be a cat.
63. R4C6 and R5C6 are both cats, so R6C6 must be a dog (no three in a row).
64. R6C6 and R6C7 are both dogs, so R6C8 must be a cat (no three in a row).
65. R6C8 and R6C10 are both cats with one square between them, so R6C9 must be a dog.
66. R6C8 and R8C8 are both cats with one square between them, so R7C8 must be a dog.
67. R7C8 and R7C10 are both dogs with one square between them, so R7C9 must be a cat.
68. R7C9 and R8C9 are both cats, so R9C9 must be a dog (no three in a row).
69. Row 5 already has its 5 cats, so R5C9 must be dogs.
70. Column 9 already has its 5 dogs, so R10C9 must be cats.
71. R10C7 and R10C9 are both cats with one square between them, so R10C8 must be a dog.
72. Column 8 already has its 5 dogs, so R9C8 must be cats.
73. Imagine R6C2 were a cat: following the rules from there soon forces a contradiction, so R6C2 must be a dog.
74. Imagine R6C1 were a dog: following the rules from there soon forces a contradiction, so R6C1 must be a cat.
75. Imagine R6C3 were a dog: following the rules from there soon forces a contradiction, so R6C3 must be a cat.
76. R6C3 and R6C5 are both cats with one square between them, so R6C4 must be a dog.
77. R6C3 and R8C3 are both cats with one square between them, so R7C3 must be a dog.
78. The × clue between R7C3 and R7C2 means they are different. R7C3 is a dog, so R7C2 is a cat.
79. R6C4 and R8C4 are both dogs with one square between them, so R7C4 must be a cat.
80. Row 7 already has its 5 cats, so R7C1 must be dogs.
81. Imagine R8C1 were a dog: following the rules from there soon forces a contradiction, so R8C1 must be a cat.
82. R8C1 and R8C3 are both cats with one square between them, so R8C2 must be a dog.
83. Imagine R9C1 were a cat: following the rules from there soon forces a contradiction, so R9C1 must be a dog.
84. R9C1 and R9C3 are both dogs with one square between them, so R9C2 must be a cat.
85. Row 9 already has its 5 cats, so R9C4 must be dogs.
86. The × clue between R9C4 and R10C4 means they are different. R9C4 is a dog, so R10C4 is a cat.
87. Column 1 already has its 5 dogs, so R10C1 must be cats.
88. Row 10 already has its 5 cats, so R10C2 must be dogs.