Cats & Dogs #294: 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 R1C2 and R1C1 means they are the same. R1C2 is a cat, so R1C1 is a cat.
2. The × clue between R4C1 and R4C2 means they are different. R4C1 is a dog, so R4C2 is a cat.
3. The × clue between R7C7 and R6C7 means they are different. R7C7 is a cat, so R6C7 is a dog.
4. R1C1 and R1C2 are both cats, so R1C3 must be a dog (no three in a row).
5. R1C1 and R3C1 are both cats with one square between them, so R2C1 must be a dog.
6. Imagine R3C2 were a cat: following the rules from there soon forces a contradiction, so R3C2 must be a dog.
7. Imagine R3C3 were a dog: following the rules from there soon forces a contradiction, so R3C3 must be a cat.
8. The = clue between R3C3 and R4C3 means they are the same. R3C3 is a cat, so R4C3 is a cat.
9. R3C3 and R3C4 are both cats, so R3C5 must be a dog (no three in a row).
10. R4C2 and R4C3 are both cats, so R4C4 must be a dog (no three in a row).
11. R3C3 and R4C3 are both cats, so R2C3 must be a dog (no three in a row).
12. R2C1 and R2C3 are both dogs with one square between them, so R2C2 must be a cat.
13. R3C3 and R4C3 are both cats, so R5C3 must be a dog (no three in a row).
14. The × clue between R5C3 and R6C3 means they are different. R5C3 is a dog, so R6C3 is a cat.
15. The × clue between R6C3 and R6C2 means they are different. R6C3 is a cat, so R6C2 is a dog.
16. The × clue between R6C3 and R6C4 means they are different. R6C3 is a cat, so R6C4 is a dog.
17. The × clue between R6C4 and R6C5 means they are different. R6C4 is a dog, so R6C5 is a cat.
18. R4C4 and R6C4 are both dogs with one square between them, so R5C4 must be a cat.
19. Imagine R4C5 were a dog: following the rules from there soon forces a contradiction, so R4C5 must be a cat.
20. R4C5 and R4C6 are both cats, so R4C7 must be a dog (no three in a row).
21. R4C5 and R6C5 are both cats with one square between them, so R5C5 must be a dog.
22. The = clue between R5C5 and R5C6 means they are the same. R5C5 is a dog, so R5C6 is a dog.
23. R5C5 and R5C6 are both dogs, so R5C7 must be a cat (no three in a row).
24. Imagine R4C8 were a cat: following the rules from there soon forces a contradiction, so R4C8 must be a dog.
25. R4C7 and R4C8 are both dogs, so R4C9 must be a cat (no three in a row).
26. The × clue between R4C9 and R4C10 means they are different. R4C9 is a cat, so R4C10 is a dog.
27. Imagine R2C7 were a dog: following the rules from there soon forces a contradiction, so R2C7 must be a cat.
28. The = clue between R2C7 and R2C8 means they are the same. R2C7 is a cat, so R2C8 is a cat.
29. R2C7 and R2C8 are both cats, so R2C6 must be a dog (no three in a row).
30. R2C7 and R2C8 are both cats, so R2C9 must be a dog (no three in a row).
31. Imagine R1C10 were a cat: following the rules from there soon forces a contradiction, so R1C10 must be a dog.
32. The × clue between R1C10 and R2C10 means they are different. R1C10 is a dog, so R2C10 is a cat.
33. The × clue between R2C10 and R3C10 means they are different. R2C10 is a cat, so R3C10 is a dog.
34. The × clue between R3C10 and R3C9 means they are different. R3C10 is a dog, so R3C9 is a cat.
35. R3C9 and R4C9 are both cats, so R5C9 must be a dog (no three in a row).
36. R3C10 and R4C10 are both dogs, so R5C10 must be a cat (no three in a row).
37. Imagine R3C8 were a cat: following the rules from there soon forces a contradiction, so R3C8 must be a dog.
38. R3C8 and R4C8 are both dogs, so R5C8 must be a cat (no three in a row).
39. R5C8 and R6C8 are both cats, so R7C8 must be a dog (no three in a row).
40. The × clue between R7C8 and R8C8 means they are different. R7C8 is a dog, so R8C8 is a cat.
41. R8C8 and R8C10 are both cats with one square between them, so R8C9 must be a dog.
42. Imagine R6C10 were a cat: following the rules from there soon forces a contradiction, so R6C10 must be a dog.
43. Imagine R7C9 were a dog: following the rules from there soon forces a contradiction, so R7C9 must be a cat.
44. The = clue between R7C9 and R7C10 means they are the same. R7C9 is a cat, so R7C10 is a cat.
45. R7C10 and R8C10 are both cats, so R9C10 must be a dog (no three in a row).
46. Column 10 already has its 5 dogs, so R10C10 must be cats.
47. Imagine R5C1 were a cat: following the rules from there soon forces a contradiction, so R5C1 must be a dog.
48. The × clue between R5C1 and R6C1 means they are different. R5C1 is a dog, so R6C1 is a cat.
49. The × clue between R6C1 and R7C1 means they are different. R6C1 is a cat, so R7C1 is a dog.
50. R5C1 and R5C3 are both dogs with one square between them, so R5C2 must be a cat.
51. Imagine R7C2 were a cat: following the rules from there soon forces a contradiction, so R7C2 must be a dog.
52. R7C1 and R7C2 are both dogs, so R7C3 must be a cat (no three in a row).
53. R6C2 and R7C2 are both dogs, so R8C2 must be a cat (no three in a row).
54. R6C3 and R7C3 are both cats, so R8C3 must be a dog (no three in a row).
55. Column 2 already has its 5 cats, so R9C2 and R10C2 must be dogs.
56. Imagine R8C1 were a dog: following the rules from there soon forces a contradiction, so R8C1 must be a cat.
57. Imagine R6C6 were a dog: following the rules from there soon forces a contradiction, so R6C6 must be a cat.
58. Row 6 already has its 5 cats, so R6C9 must be dogs.
59. Imagine R7C4 were a dog: following the rules from there soon forces a contradiction, so R7C4 must be a cat.
60. Row 7 already has its 5 cats, so R7C6 must be dogs.
61. Imagine R8C4 were a cat: following the rules from there soon forces a contradiction, so R8C4 must be a dog.
62. R8C3 and R8C4 are both dogs, so R8C5 must be a cat (no three in a row).
63. Row 8 already has its 5 cats, so R8C6 must be dogs.
64. R7C6 and R8C6 are both dogs, so R9C6 must be a cat (no three in a row).
65. Row 8 already has its 5 cats, so R8C7 must be dogs.
66. Imagine R9C4 were a dog: following the rules from there soon forces a contradiction, so R9C4 must be a cat.
67. R9C4 and R9C6 are both cats with one square between them, so R9C5 must be a dog.
68. Imagine R1C5 were a dog: following the rules from there soon forces a contradiction, so R1C5 must be a cat.
69. Imagine R2C4 were a cat: following the rules from there soon forces a contradiction, so R2C4 must be a dog.
70. R2C3 and R2C4 are both dogs, so R2C5 must be a cat (no three in a row).
71. Column 5 already has its 5 cats, so R10C5 must be dogs.
72. The = clue between R10C5 and R10C4 means they are the same. R10C5 is a dog, so R10C4 is a dog.
73. R10C2 and R10C4 are both dogs with one square between them, so R10C3 must be a cat.
74. R10C4 and R10C5 are both dogs, so R10C6 must be a cat (no three in a row).
75. Column 3 already has its 5 cats, so R9C3 must be dogs.
76. R9C2 and R9C3 are both dogs, so R9C1 must be a cat (no three in a row).
77. The × clue between R9C1 and R10C1 means they are different. R9C1 is a cat, so R10C1 is a dog.
78. Column 4 already has its 5 dogs, so R1C4 must be cats.
79. R1C4 and R1C5 are both cats, so R1C6 must be a dog (no three in a row).
80. R1C6 and R2C6 are both dogs, so R3C6 must be a cat (no three in a row).
81. Row 3 already has its 5 cats, so R3C7 must be dogs.
82. Imagine R1C7 were a cat: following the rules from there soon forces a contradiction, so R1C7 must be a dog.
83. R1C6 and R1C7 are both dogs, so R1C8 must be a cat (no three in a row).
84. Row 1 already has its 5 cats, so R1C9 must be dogs.
85. Column 7 already has its 5 dogs, so R9C7 must be cats.
86. R9C6 and R9C7 are both cats, so R9C8 must be a dog (no three in a row).
87. R9C8 and R9C10 are both dogs with one square between them, so R9C9 must be a cat.
88. Column 7 already has its 5 dogs, so R10C7 must be cats.
89. R10C6 and R10C7 are both cats, so R10C8 must be a dog (no three in a row).
90. Row 10 already has its 5 dogs, so R10C9 must be cats.