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# 122H - subset - Solution

Fangz17 May 12th, 2013 62 Never
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1. [(0, 1, 0), (0, 2, 0)] [-9, 9]
2. [(0, 1, 0), (0, 2, 0), (0, 3, 0), (0, 4, 0)] [-9, 9, -6, 6]
3. [(0, 3, 0), (0, 4, 0)] [-6, 6]
4. [(0, 0, 3), (0, 0, 4), (0, 0, 5)] [-1, -9, 10]
5. [(0, 1, 1), (0, 1, 2)] [8, -8]
6. [(0, 1, 2), (0, 1, 3), (0, 1, 4)] [-8, 7, 1]
7. [(0, 2, 1), (0, 3, 1), (0, 4, 1), (0, 5, 1)] [-1, 6, -3, -2]
8. [(0, 0, 2), (1, 0, 2)] [-5, 5]
9. [(0, 0, 2), (1, 0, 2), (2, 0, 2), (3, 0, 2)] [-5, 5, 1, -1]
10. [(2, 0, 2), (3, 0, 2)] [1, -1]
11. [(0, 2, 1), (0, 2, 2), (0, 2, 3), (0, 2, 4), (0, 2, 5)] [-1, 0, -2, -2, 5]
12. [(0, 2, 2), (0, 3, 2), (0, 4, 2), (0, 5, 2)] [0, -7, -3, 10]
13. [(0, 3, 2), (0, 4, 2), (0, 5, 2)] [-7, -3, 10]
14. [(0, 3, 0), (0, 3, 1)] [-6, 6]
15. [(0, 0, 3), (0, 1, 3), (0, 2, 3), (0, 3, 3), (0, 4, 3)] [-1, 7, -2, -7, 3]
16. [(0, 2, 3), (0, 3, 3), (0, 4, 3), (0, 5, 3), (0, 6, 3), (0, 7, 3)] [-2, -7, 3, 3, 5, -2]
17. [(0, 4, 0), (0, 4, 1), (0, 4, 2)] [6, -3, -3]
18. [(0, 1, 4), (0, 2, 4), (0, 3, 4)] [1, -2, 1]
19. [(0, 4, 2), (0, 4, 3)] [-3, 3]
20. [(3, 0, 4), (4, 0, 4)] [9, -9]
21. [(0, 3, 4), (0, 4, 4)] [1, -1]
22. [(0, 4, 0), (0, 4, 1), (0, 4, 2), (0, 4, 3), (0, 4, 4), (0, 4, 5), (0, 4, 6)] [6, -3, -3, 3, -1, 3, -5]
23. [(1, 0, 4), (2, 0, 4), (3, 0, 4), (4, 0, 4), (5, 0, 4), (6, 0, 4)] [-8, 2, 9, -9, 3, 3]
24. [(0, 4, 3), (0, 4, 4), (0, 4, 5), (0, 4, 6)] [3, -1, 3, -5]
25. [(2, 0, 4), (3, 0, 4), (4, 0, 4), (5, 0, 4), (6, 0, 4), (7, 0, 4)] [2, 9, -9, 3, 3, -8]
26. [(0, 2, 5), (0, 3, 5)] [5, -5]
27. [(4, 0, 5), (5, 0, 5)] [-1, 1]
28. [(5, 0, 5), (6, 0, 5)] [1, -1]
29. [(0, 1, 6), (0, 2, 6), (0, 3, 6), (0, 4, 6)] [-6, 8, 3, -5]
30. [(0, 3, 6), (0, 4, 6), (0, 5, 6), (0, 6, 6), (0, 7, 6)] [3, -5, -10, 9, 3]
31. [(0, 0, 7), (0, 1, 7), (0, 2, 7), (0, 3, 7)] [1, 0, -6, 5]
32. [(2, 0, 7), (3, 0, 7), (4, 0, 7), (5, 0, 7), (6, 0, 7)] [-8, -6, 7, 8, -1]
33. [(1, 0, 0), (1, 1, 0), (1, 2, 0), (1, 3, 0)] [0, -1, 0, 1]
34. [(1, 1, 0), (1, 2, 0), (1, 3, 0)] [-1, 0, 1]
35. [(1, 0, 0), (1, 0, 1), (1, 0, 2), (1, 0, 3), (1, 0, 4)] [0, -4, 5, 7, -8]
36. [(1, 0, 1), (1, 0, 2), (1, 0, 3), (1, 0, 4)] [-4, 5, 7, -8]
37. [(2, 1, 0), (3, 1, 0), (4, 1, 0)] [2, 4, -6]
38. [(1, 2, 0), (1, 3, 0), (1, 4, 0)] [0, 1, -1]
39. [(1, 3, 0), (1, 4, 0)] [1, -1]
40. [(4, 1, 0), (5, 1, 0), (6, 1, 0)] [-6, 3, 3]
41. [(1, 1, 0), (1, 1, 1), (1, 1, 2)] [-1, 10, -9]
42. [(1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 1, 4), (1, 1, 5)] [10, -9, 10, -3, -8]
43. [(1, 1, 1), (1, 1, 2), (1, 1, 3), (1, 1, 4), (1, 1, 5), (1, 1, 6)] [10, -9, 10, -3, -8, 0]
44. [(1, 2, 0), (1, 2, 1), (1, 2, 2)] [0, 4, -4]
45. [(1, 2, 1), (1, 2, 2)] [4, -4]
46. [(1, 2, 5), (1, 2, 6)] [5, -5]
47. [(0, 1, 2), (1, 1, 2), (2, 1, 2), (3, 1, 2), (4, 1, 2), (5, 1, 2), (6, 1, 2), (7, 1, 2)] [-8, -9, 10, 4, 10, -4, 2, -5]
48. [(1, 2, 4), (1, 2, 5), (1, 2, 6), (1, 2, 7)] [5, 5, -5, -5]
49. [(1, 3, 0), (1, 3, 1), (1, 3, 2), (1, 3, 3), (1, 3, 4), (1, 3, 5), (1, 3, 6), (1, 3, 7)] [1, 1, 6, 5, -9, 8, -5, -7]
50. [(5, 1, 4), (6, 1, 4)] [6, -6]
51. [(1, 5, 4), (1, 6, 4), (1, 7, 4)] [0, -9, 9]
52. [(1, 6, 4), (1, 7, 4)] [-9, 9]
53. [(1, 1, 5), (1, 2, 5), (1, 3, 5), (1, 4, 5)] [-8, 5, 8, -5]
54. [(1, 0, 6), (1, 1, 6), (1, 2, 6), (1, 3, 6), (1, 4, 6)] [6, 0, -5, -5, 4]
55. [(0, 1, 7), (1, 1, 7), (2, 1, 7)] [0, -1, 1]
56. [(1, 1, 7), (2, 1, 7)] [-1, 1]
57. [(1, 7, 0), (1, 7, 1), (1, 7, 2), (1, 7, 3)] [2, -10, 0, 8]
58. [(0, 1, 7), (1, 1, 7), (2, 1, 7), (3, 1, 7), (4, 1, 7)] [0, -1, 1, -4, 4]
59. [(1, 1, 7), (2, 1, 7), (3, 1, 7), (4, 1, 7)] [-1, 1, -4, 4]
60. [(3, 1, 7), (4, 1, 7)] [-4, 4]
61. [(2, 1, 0), (2, 2, 0), (2, 3, 0)] [2, -7, 5]
62. [(2, 1, 0), (2, 2, 0), (2, 3, 0), (2, 4, 0), (2, 5, 0)] [2, -7, 5, 1, -1]
63. [(2, 4, 0), (2, 5, 0)] [1, -1]
64. [(2, 0, 5), (2, 0, 6)] [-10, 10]
65. [(0, 2, 1), (1, 2, 1), (2, 2, 1), (3, 2, 1), (4, 2, 1)] [-1, 4, -5, 9, -7]
66. [(2, 1, 6), (2, 1, 7)] [-1, 1]
67. [(0, 2, 2), (1, 2, 2), (2, 2, 2)] [0, -4, 4]
68. [(1, 2, 2), (2, 2, 2)] [-4, 4]
69. [(2, 2, 3), (2, 2, 4)] [-8, 8]
70. [(2, 0, 3), (2, 1, 3), (2, 2, 3), (2, 3, 3)] [4, 1, -8, 3]
71. [(2, 3, 2), (2, 3, 3)] [-3, 3]
72. [(2, 3, 0), (2, 3, 1), (2, 3, 2), (2, 3, 3), (2, 3, 4)] [5, -10, -3, 3, 5]
73. [(2, 0, 3), (2, 1, 3), (2, 2, 3), (2, 3, 3), (2, 4, 3), (2, 5, 3)] [4, 1, -8, 3, -7, 7]
74. [(2, 3, 1), (2, 3, 2), (2, 3, 3), (2, 3, 4), (2, 3, 5)] [-10, -3, 3, 5, 5]
75. [(2, 4, 3), (2, 5, 3)] [-7, 7]
76. [(1, 2, 4), (2, 2, 4), (3, 2, 4), (4, 2, 4), (5, 2, 4)] [5, 8, 2, -6, -9]
77. [(2, 4, 5), (2, 4, 6), (2, 4, 7)] [10, -9, -1]
78. [(2, 5, 2), (2, 5, 3), (2, 5, 4), (2, 5, 5)] [-3, 7, 4, -8]
79. [(2, 5, 3), (2, 5, 4), (2, 5, 5), (2, 5, 6)] [7, 4, -8, -3]
80. [(3, 2, 6), (4, 2, 6)] [-10, 10]
81. [(0, 2, 6), (1, 2, 6), (2, 2, 6), (3, 2, 6), (4, 2, 6), (5, 2, 6)] [8, -5, -7, -10, 10, 4]
82. [(2, 6, 2), (2, 6, 3), (2, 6, 4), (2, 6, 5)] [9, -6, -8, 5]
83. [(2, 1, 7), (2, 2, 7), (2, 3, 7), (2, 4, 7), (2, 5, 7), (2, 6, 7)] [1, 2, 7, -1, -3, -6]
84. [(4, 2, 7), (5, 2, 7), (6, 2, 7), (7, 2, 7)] [-1, 2, 7, -8]
85. [(2, 6, 7), (2, 7, 7)] [-6, 6]
86. [(3, 0, 0), (3, 1, 0)] [-4, 4]
87. [(0, 3, 0), (1, 3, 0), (2, 3, 0)] [-6, 1, 5]
88. [(3, 0, 3), (3, 0, 4)] [-9, 9]
89. [(0, 3, 0), (1, 3, 0), (2, 3, 0), (3, 3, 0), (4, 3, 0), (5, 3, 0)] [-6, 1, 5, -1, -8, 9]
90. [(3, 1, 0), (3, 2, 0), (3, 3, 0), (3, 4, 0), (3, 5, 0)] [4, 3, -1, -8, 2]
91. [(3, 3, 0), (4, 3, 0), (5, 3, 0)] [-1, -8, 9]
92. [(4, 3, 1), (5, 3, 1)] [8, -8]
93. [(3, 1, 4), (3, 1, 5), (3, 1, 6)] [1, -10, 9]
94. [(1, 3, 2), (2, 3, 2), (3, 3, 2)] [6, -3, -3]
95. [(0, 3, 2), (1, 3, 2), (2, 3, 2), (3, 3, 2), (4, 3, 2), (5, 3, 2), (6, 3, 2)] [-7, 6, -3, -3, -9, 6, 10]
96. [(3, 3, 2), (3, 4, 2), (3, 5, 2), (3, 6, 2), (3, 7, 2)] [-3, 2, 3, -10, 8]
97. [(4, 3, 3), (5, 3, 3)] [0, 0]
98. [(3, 6, 3), (3, 7, 3)] [6, -6]
99. [(3, 3, 6), (3, 3, 7)] [7, -7]
100. [(3, 2, 4), (3, 3, 4), (3, 4, 4), (3, 5, 4)] [2, -4, -6, 8]
101. [(3, 3, 4), (3, 4, 4), (3, 5, 4), (3, 6, 4)] [-4, -6, 8, 2]
102. [(6, 3, 4), (7, 3, 4)] [-10, 10]
103. [(3, 0, 5), (3, 1, 5), (3, 2, 5), (3, 3, 5)] [3, -10, 6, 1]
104. [(5, 3, 5), (6, 3, 5), (7, 3, 5)] [-8, 7, 1]
105. [(3, 6, 0), (3, 6, 1)] [-8, 8]
106. [(3, 0, 6), (3, 1, 6), (3, 2, 6), (3, 3, 6), (3, 4, 6), (3, 5, 6), (3, 6, 6), (3, 7, 6)] [-4, 9, -10, 7, -8, 4, 10, -8]
107. [(1, 3, 7), (2, 3, 7)] [-7, 7]
108. [(2, 3, 7), (3, 3, 7)] [7, -7]
109. [(3, 4, 7), (3, 5, 7)] [-4, 4]
110. [(1, 4, 0), (2, 4, 0)] [-1, 1]
111. [(4, 0, 2), (4, 0, 3), (4, 0, 4), (4, 0, 5), (4, 0, 6), (4, 0, 7)] [-3, -3, -9, -1, 9, 7]
112. [(4, 2, 1), (4, 3, 1), (4, 4, 1), (4, 5, 1), (4, 6, 1)] [-7, 8, 4, 3, -8]
113. [(1, 4, 2), (2, 4, 2)] [-5, 5]
114. [(4, 1, 2), (4, 2, 2), (4, 3, 2)] [10, -1, -9]
115. [(4, 3, 0), (4, 3, 1)] [-8, 8]
116. [(4, 1, 3), (4, 2, 3), (4, 3, 3), (4, 4, 3)] [1, -8, 0, 7]
117. [(4, 1, 3), (4, 2, 3), (4, 3, 3), (4, 4, 3), (4, 5, 3)] [1, -8, 0, 7, 0]
118. [(4, 3, 1), (4, 3, 2), (4, 3, 3), (4, 3, 4), (4, 3, 5), (4, 3, 6)] [8, -9, 0, -9, 4, 6]
119. [(1, 4, 4), (2, 4, 4), (3, 4, 4)] [8, -2, -6]
120. [(2, 4, 4), (3, 4, 4), (4, 4, 4)] [-2, -6, 8]
121. [(2, 4, 4), (3, 4, 4), (4, 4, 4), (5, 4, 4), (6, 4, 4)] [-2, -6, 8, -9, 9]
122. [(4, 4, 4), (4, 5, 4), (4, 6, 4)] [8, -7, -1]
123. [(5, 4, 4), (6, 4, 4)] [-9, 9]
124. [(2, 4, 4), (3, 4, 4), (4, 4, 4), (5, 4, 4), (6, 4, 4), (7, 4, 4)] [-2, -6, 8, -9, 9, 0]
125. [(5, 4, 4), (6, 4, 4), (7, 4, 4)] [-9, 9, 0]
126. [(4, 5, 4), (4, 6, 4), (4, 7, 4)] [-7, -1, 8]
127. [(4, 0, 5), (4, 1, 5)] [-1, 1]
128. [(4, 7, 1), (4, 7, 2)] [10, -10]
129. [(4, 7, 1), (4, 7, 2), (4, 7, 3), (4, 7, 4)] [10, -10, -8, 8]
130. [(4, 7, 3), (4, 7, 4)] [-8, 8]
131. [(4, 3, 7), (4, 4, 7), (4, 5, 7)] [9, -5, -4]
132. [(4, 5, 7), (4, 6, 7)] [-4, 4]
133. [(3, 5, 0), (4, 5, 0)] [2, -2]
134. [(5, 5, 0), (5, 6, 0)] [-7, 7]
135. [(5, 2, 0), (5, 3, 0), (5, 4, 0), (5, 5, 0), (5, 6, 0), (5, 7, 0)] [-10, 9, -5, -7, 7, 6]
136. [(6, 5, 0), (7, 5, 0)] [4, -4]
137. [(5, 0, 1), (5, 1, 1)] [-8, 8]
138. [(4, 5, 1), (5, 5, 1), (6, 5, 1), (7, 5, 1)] [3, -1, 0, -2]
139. [(5, 1, 6), (5, 1, 7)] [-9, 9]
140. [(2, 5, 2), (3, 5, 2)] [-3, 3]
141. [(5, 5, 2), (6, 5, 2)] [6, -6]
142. [(1, 5, 2), (2, 5, 2), (3, 5, 2), (4, 5, 2), (5, 5, 2), (6, 5, 2), (7, 5, 2)] [1, -3, 3, -10, 6, -6, 9]
143. [(3, 5, 3), (4, 5, 3), (5, 5, 3)] [10, 0, -10]
144. [(4, 5, 3), (5, 5, 3), (6, 5, 3)] [0, -10, 10]
145. [(5, 5, 3), (6, 5, 3)] [-10, 10]
146. [(5, 3, 0), (5, 3, 1), (5, 3, 2), (5, 3, 3), (5, 3, 4), (5, 3, 5), (5, 3, 6), (5, 3, 7)] [9, -8, 6, 0, 6, -8, 3, -8]
147. [(5, 0, 4), (5, 1, 4), (5, 2, 4)] [3, 6, -9]
148. [(5, 4, 3), (5, 4, 4), (5, 4, 5)] [5, -9, 4]
149. [(5, 0, 5), (5, 1, 5), (5, 2, 5)] [1, 7, -8]
150. [(1, 5, 5), (2, 5, 5)] [8, -8]
151. [(5, 5, 5), (5, 5, 6), (5, 5, 7)] [1, 5, -6]
152. [(5, 5, 6), (6, 5, 6)] [5, -5]
153. [(0, 5, 7), (1, 5, 7)] [1, -1]
154. [(5, 7, 0), (5, 7, 1)] [6, -6]
155. [(5, 7, 1), (5, 7, 2)] [-6, 6]
156. [(1, 5, 7), (2, 5, 7), (3, 5, 7)] [-1, -3, 4]
157. [(3, 5, 7), (4, 5, 7)] [4, -4]
158. [(0, 5, 7), (1, 5, 7), (2, 5, 7), (3, 5, 7), (4, 5, 7), (5, 5, 7), (6, 5, 7), (7, 5, 7)] [1, -1, -3, 4, -4, -6, 4, 5]
159. [(2, 5, 7), (3, 5, 7), (4, 5, 7), (5, 5, 7), (6, 5, 7), (7, 5, 7)] [-3, 4, -4, -6, 4, 5]
160. [(6, 0, 0), (6, 1, 0), (6, 2, 0), (6, 3, 0), (6, 4, 0), (6, 5, 0)] [4, 3, -9, 1, -3, 4]
161. [(1, 6, 0), (2, 6, 0), (3, 6, 0), (4, 6, 0), (5, 6, 0)] [2, -10, -8, 9, 7]
162. [(6, 2, 0), (6, 3, 0), (6, 4, 0), (6, 5, 0), (6, 6, 0)] [-9, 1, -3, 4, 7]
163. [(6, 0, 1), (6, 0, 2), (6, 0, 3), (6, 0, 4), (6, 0, 5), (6, 0, 6), (6, 0, 7)] [6, 3, 0, 3, -1, -10, -1]
164. [(6, 1, 1), (6, 2, 1), (6, 3, 1)] [8, 1, -9]
165. [(3, 6, 1), (4, 6, 1)] [8, -8]
166. [(6, 3, 1), (6, 4, 1), (6, 5, 1), (6, 6, 1), (6, 7, 1)] [-9, 2, 0, 2, 5]
167. [(1, 6, 2), (2, 6, 2)] [-9, 9]
168. [(0, 6, 2), (1, 6, 2), (2, 6, 2), (3, 6, 2), (4, 6, 2), (5, 6, 2)] [-3, -9, 9, -10, 6, 7]
169. [(6, 2, 3), (6, 2, 4), (6, 2, 5)] [0, -9, 9]
170. [(6, 2, 4), (6, 2, 5)] [-9, 9]
171. [(1, 6, 3), (2, 6, 3)] [6, -6]
172. [(6, 3, 1), (6, 3, 2), (6, 3, 3)] [-9, 10, -1]
173. [(2, 6, 3), (3, 6, 3)] [-6, 6]
174. [(5, 6, 3), (6, 6, 3), (7, 6, 3)] [-1, -8, 9]
175. [(6, 5, 3), (6, 6, 3), (6, 7, 3)] [10, -8, -2]
176. [(3, 6, 4), (4, 6, 4), (5, 6, 4), (6, 6, 4)] [2, -1, 5, -6]
177. [(6, 6, 5), (7, 6, 5)] [2, -2]
178. [(1, 6, 6), (2, 6, 6), (3, 6, 6), (4, 6, 6), (5, 6, 6), (6, 6, 6)] [7, -3, 10, -8, -9, 3]
179. [(6, 6, 1), (6, 6, 2), (6, 6, 3), (6, 6, 4), (6, 6, 5), (6, 6, 6)] [2, 7, -8, -6, 2, 3]
180. [(6, 6, 6), (6, 6, 7)] [3, -3]
181. [(0, 6, 7), (1, 6, 7), (2, 6, 7), (3, 6, 7)] [7, 5, -6, -6]
182. [(6, 4, 7), (6, 5, 7), (6, 6, 7), (6, 7, 7)] [-2, 4, -3, 1]
183. [(7, 2, 0), (7, 3, 0), (7, 4, 0)] [4, -9, 5]
184. [(0, 7, 2), (1, 7, 2), (2, 7, 2)] [-6, 0, 6]
185. [(7, 0, 2), (7, 1, 2), (7, 2, 2)] [2, -5, 3]
186. [(7, 2, 0), (7, 2, 1), (7, 2, 2)] [4, -7, 3]
187. [(4, 7, 2), (5, 7, 2), (6, 7, 2)] [-10, 6, 4]
188. [(7, 2, 5), (7, 2, 6), (7, 2, 7)] [1, 7, -8]
189. [(6, 7, 2), (7, 7, 2)] [4, -4]
190. [(7, 2, 3), (7, 3, 3)] [-10, 10]
191. [(7, 1, 3), (7, 2, 3), (7, 3, 3), (7, 4, 3)] [7, -10, 10, -7]
192. [(7, 2, 3), (7, 3, 3), (7, 4, 3), (7, 5, 3)] [-10, 10, -7, 7]
193. [(7, 4, 3), (7, 5, 3)] [-7, 7]
194. [(2, 7, 4), (3, 7, 4), (4, 7, 4), (5, 7, 4)] [-8, 3, 8, -3]
195. [(7, 4, 0), (7, 4, 1), (7, 4, 2), (7, 4, 3), (7, 4, 4), (7, 4, 5), (7, 4, 6)] [5, 5, 5, -7, 0, -7, -1]
196. [(7, 0, 5), (7, 1, 5), (7, 2, 5)] [5, -6, 1]
197. [(7, 0, 5), (7, 1, 5), (7, 2, 5), (7, 3, 5), (7, 4, 5), (7, 5, 5)] [5, -6, 1, 1, -7, 6]
198. [(7, 3, 5), (7, 4, 5), (7, 5, 5)] [1, -7, 6]
199. [(1, 7, 6), (2, 7, 6)] [10, -10]
200. [(5, 7, 6), (6, 7, 6)] [0, 0]
201. [(0, 7, 7), (1, 7, 7), (2, 7, 7)] [-4, -2, 6]
202. [(0, 7, 7), (1, 7, 7), (2, 7, 7), (3, 7, 7)] [-4, -2, 6, 0]
203. [(0, 1, 7)] [0]
204. [(0, 2, 2)] [0]
205. [(0, 6, 4)] [0]
206. [(1, 0, 0)] [0]
207. [(1, 1, 6)] [0]
208. [(1, 2, 0)] [0]
209. [(1, 5, 4)] [0]
210. [(1, 7, 2)] [0]
211. [(3, 0, 1)] [0]
212. [(3, 7, 7)] [0]
213. [(4, 3, 3)] [0]
214. [(4, 5, 3)] [0]
215. [(5, 3, 3)] [0]
216. [(5, 4, 7)] [0]
217. [(5, 7, 6)] [0]
218. [(6, 0, 3)] [0]
219. [(6, 1, 7)] [0]
220. [(6, 2, 3)] [0]
221. [(6, 5, 1)] [0]
222. [(6, 7, 6)] [0]
223. [(7, 1, 1)] [0]
224. [(7, 1, 6)] [0]
225. [(7, 4, 4)] [0]
226. [(7, 7, 5)] [0]
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