若100之內的6個相異正整數其倒數和等於1，求此6數和的最小值。

100之內的6個相異正整數其倒數和等於1，只有229組解，而6數和的最小值為50。
3 + 4 + 6 + 10 + 12 + 15 = 50
3 + 4 + 6 + 9 + 12 + 18 = 52
3 + 4 + 6 + 8 + 12 + 24 = 57
3 + 4 + 5 + 10 + 15 + 20 = 57
3 + 4 + 5 + 9 + 18 + 20 = 59
2 + 6 + 9 + 10 + 15 + 18 = 60
3 + 4 + 6 + 7 + 14 + 28 = 62
2 + 5 + 10 + 12 + 15 + 20 = 64
3 + 4 + 5 + 8 + 20 + 24 = 64
3 + 4 + 5 + 10 + 12 + 30 = 64
2 + 6 + 8 + 10 + 15 + 24 = 65
2 + 5 + 9 + 12 + 18 + 20 = 66
2 + 6 + 8 + 9 + 18 + 24 = 67
2 + 6 + 7 + 12 + 14 + 28 = 69
2 + 5 + 8 + 12 + 20 + 24 = 71
3 + 4 + 6 + 8 + 10 + 40 = 71
2 + 5 + 9 + 10 + 18 + 30 = 74
3 + 4 + 6 + 7 + 12 + 42 = 74
3 + 4 + 5 + 8 + 15 + 40 = 75
2 + 5 + 7 + 14 + 20 + 28 = 76
2 + 6 + 8 + 10 + 12 + 40 = 78
3 + 4 + 5 + 9 + 12 + 45 = 78
2 + 5 + 8 + 10 + 24 + 30 = 79
2 + 4 + 10 + 15 + 21 + 28 = 80
2 + 4 + 10 + 15 + 20 + 30 = 81
3 + 4 + 5 + 7 + 20 + 42 = 81
2 + 4 + 9 + 18 + 21 + 28 = 82
2 + 4 + 12 + 14 + 15 + 35 = 82
2 + 5 + 6 + 20 + 21 + 28 = 82
2 + 5 + 8 + 12 + 15 + 40 = 82
2 + 6 + 7 + 10 + 15 + 42 = 82
2 + 4 + 9 + 18 + 20 + 30 = 83
2 + 4 + 11 + 12 + 22 + 33 = 84
2 + 6 + 7 + 9 + 18 + 42 = 84
2 + 4 + 10 + 15 + 18 + 36 = 85
2 + 4 + 10 + 14 + 20 + 35 = 85
2 + 5 + 8 + 10 + 20 + 40 = 85
2 + 5 + 9 + 10 + 15 + 45 = 86
2 + 4 + 8 + 21 + 24 + 28 = 87
2 + 5 + 6 + 18 + 20 + 36 = 87
2 + 4 + 8 + 20 + 24 + 30 = 88
2 + 5 + 7 + 12 + 20 + 42 = 88
2 + 6 + 7 + 8 + 24 + 42 = 89
2 + 4 + 8 + 18 + 24 + 36 = 92
2 + 4 + 10 + 12 + 24 + 40 = 92
2 + 5 + 6 + 14 + 30 + 35 = 92
2 + 5 + 6 + 15 + 24 + 40 = 92
2 + 5 + 8 + 9 + 24 + 45 = 93
2 + 4 + 9 + 15 + 20 + 45 = 95
2 + 4 + 10 + 15 + 16 + 48 = 95
2 + 5 + 7 + 10 + 30 + 42 = 96
2 + 4 + 9 + 16 + 18 + 48 = 97
2 + 5 + 6 + 16 + 20 + 48 = 97
2 + 4 + 8 + 15 + 30 + 40 = 99
3 + 4 + 5 + 6 + 36 + 45 = 99
2 + 6 + 7 + 8 + 21 + 56 = 100
2 + 4 + 8 + 16 + 24 + 48 = 102
2 + 4 + 9 + 12 + 30 + 45 = 102
3 + 4 + 6 + 8 + 9 + 72 = 102
2 + 4 + 8 + 14 + 35 + 40 = 103
2 + 3 + 20 + 21 + 28 + 30 = 104
2 + 4 + 7 + 21 + 28 + 42 = 104
2 + 4 + 7 + 20 + 30 + 42 = 105
2 + 5 + 6 + 12 + 36 + 45 = 106
2 + 3 + 18 + 21 + 28 + 36 = 108
2 + 4 + 9 + 15 + 18 + 60 = 108
2 + 4 + 10 + 12 + 20 + 60 = 108
2 + 4 + 9 + 12 + 27 + 54 = 108
2 + 5 + 6 + 15 + 20 + 60 = 108
3 + 4 + 5 + 6 + 30 + 60 = 108
2 + 3 + 18 + 20 + 30 + 36 = 109
2 + 4 + 7 + 18 + 36 + 42 = 109
2 + 6 + 8 + 9 + 12 + 72 = 109
2 + 5 + 7 + 9 + 42 + 45 = 110
2 + 4 + 8 + 14 + 28 + 56 = 112
2 + 4 + 8 + 15 + 24 + 60 = 113
2 + 3 + 15 + 24 + 30 + 40 = 114
2 + 4 + 7 + 21 + 24 + 56 = 114
2 + 5 + 6 + 12 + 30 + 60 = 115
2 + 5 + 8 + 9 + 20 + 72 = 116
3 + 4 + 5 + 6 + 28 + 70 = 116
2 + 3 + 16 + 21 + 28 + 48 = 118
2 + 3 + 15 + 21 + 35 + 42 = 118
2 + 3 + 14 + 24 + 35 + 40 = 118
2 + 5 + 6 + 14 + 21 + 70 = 118
2 + 3 + 16 + 20 + 30 + 48 = 119
2 + 4 + 7 + 16 + 42 + 48 = 119
2 + 3 + 15 + 20 + 36 + 45 = 121
2 + 5 + 8 + 10 + 16 + 80 = 121
2 + 4 + 7 + 18 + 28 + 63 = 122
2 + 3 + 16 + 18 + 36 + 48 = 123
2 + 4 + 6 + 30 + 36 + 45 = 123
2 + 4 + 9 + 12 + 24 + 72 = 123
2 + 5 + 6 + 12 + 28 + 70 = 123
2 + 4 + 8 + 12 + 42 + 56 = 124
2 + 4 + 8 + 12 + 40 + 60 = 126
2 + 3 + 14 + 24 + 28 + 56 = 127
2 + 3 + 12 + 30 + 36 + 45 = 128
2 + 3 + 15 + 21 + 28 + 60 = 129
2 + 4 + 6 + 26 + 39 + 52 = 129
2 + 4 + 10 + 14 + 15 + 84 = 129
2 + 4 + 6 + 27 + 36 + 54 = 129
2 + 3 + 15 + 20 + 30 + 60 = 130
2 + 4 + 7 + 15 + 42 + 60 = 130
2 + 4 + 9 + 10 + 45 + 60 = 130
2 + 4 + 8 + 16 + 20 + 80 = 130
2 + 4 + 9 + 14 + 18 + 84 = 131
2 + 5 + 6 + 14 + 20 + 84 = 131
2 + 3 + 15 + 18 + 36 + 60 = 134
2 + 3 + 12 + 27 + 36 + 54 = 134
2 + 3 + 12 + 26 + 39 + 52 = 134
2 + 3 + 14 + 20 + 35 + 60 = 134
2 + 4 + 6 + 24 + 42 + 56 = 134
2 + 4 + 8 + 12 + 36 + 72 = 134
2 + 3 + 15 + 18 + 35 + 63 = 136
2 + 4 + 8 + 14 + 24 + 84 = 136
2 + 4 + 10 + 12 + 18 + 90 = 136
2 + 4 + 6 + 24 + 40 + 60 = 136
2 + 5 + 6 + 15 + 18 + 90 = 136
2 + 4 + 9 + 10 + 40 + 72 = 137
2 + 3 + 15 + 20 + 28 + 70 = 138
2 + 3 + 12 + 24 + 42 + 56 = 139
2 + 3 + 14 + 21 + 30 + 70 = 140
2 + 4 + 6 + 28 + 30 + 70 = 140
2 + 3 + 12 + 24 + 40 + 60 = 141
2 + 3 + 14 + 18 + 42 + 63 = 142
3 + 4 + 5 + 6 + 25 + 100 = 143
2 + 3 + 15 + 16 + 48 + 60 = 144
2 + 4 + 6 + 24 + 36 + 72 = 144
2 + 4 + 6 + 22 + 44 + 66 = 144
2 + 5 + 6 + 10 + 55 + 66 = 144
2 + 3 + 12 + 28 + 30 + 70 = 145
2 + 3 + 16 + 20 + 24 + 80 = 145
2 + 4 + 8 + 12 + 33 + 88 = 147
2 + 4 + 7 + 15 + 35 + 84 = 147
2 + 4 + 9 + 12 + 22 + 99 = 148
2 + 4 + 7 + 14 + 44 + 77 = 148
2 + 5 + 7 + 8 + 56 + 70 = 148
2 + 5 + 6 + 10 + 50 + 75 = 148
2 + 3 + 12 + 22 + 44 + 66 = 149
2 + 3 + 12 + 24 + 36 + 72 = 149
2 + 5 + 6 + 12 + 25 + 100 = 150
2 + 4 + 9 + 10 + 36 + 90 = 151
2 + 5 + 6 + 10 + 48 + 80 = 151
2 + 3 + 14 + 21 + 28 + 84 = 152
2 + 3 + 10 + 40 + 42 + 56 = 153
2 + 3 + 14 + 20 + 30 + 84 = 153
2 + 4 + 6 + 20 + 55 + 66 = 153
2 + 4 + 7 + 14 + 42 + 84 = 153
2 + 4 + 8 + 12 + 32 + 96 = 154
2 + 4 + 6 + 21 + 44 + 77 = 154
2 + 3 + 15 + 16 + 40 + 80 = 156
2 + 3 + 15 + 17 + 34 + 85 = 156
2 + 3 + 10 + 36 + 45 + 60 = 156
2 + 3 + 14 + 18 + 36 + 84 = 157
2 + 4 + 6 + 20 + 50 + 75 = 157
2 + 4 + 8 + 11 + 44 + 88 = 157
2 + 4 + 6 + 24 + 33 + 88 = 157
2 + 3 + 12 + 20 + 55 + 66 = 158
2 + 3 + 10 + 35 + 45 + 63 = 158
2 + 3 + 15 + 18 + 30 + 90 = 158
2 + 5 + 6 + 10 + 45 + 90 = 158
2 + 3 + 12 + 21 + 44 + 77 = 159
2 + 4 + 6 + 21 + 42 + 84 = 159
2 + 4 + 6 + 20 + 48 + 80 = 160
2 + 3 + 10 + 35 + 42 + 70 = 162
2 + 3 + 14 + 18 + 35 + 90 = 162
2 + 3 + 12 + 24 + 33 + 88 = 162
2 + 3 + 12 + 20 + 50 + 75 = 162
2 + 3 + 10 + 36 + 40 + 72 = 163
2 + 3 + 12 + 21 + 42 + 84 = 164
2 + 4 + 6 + 24 + 32 + 96 = 164
2 + 4 + 6 + 19 + 57 + 76 = 164
2 + 3 + 15 + 20 + 25 + 100 = 165
2 + 3 + 12 + 20 + 48 + 80 = 165
2 + 3 + 10 + 30 + 55 + 66 = 166
2 + 3 + 14 + 16 + 48 + 84 = 167
2 + 4 + 6 + 20 + 45 + 90 = 167
2 + 4 + 6 + 25 + 30 + 100 = 167
2 + 3 + 12 + 19 + 57 + 76 = 169
2 + 3 + 12 + 24 + 32 + 96 = 169
2 + 4 + 7 + 13 + 52 + 91 = 169
2 + 4 + 6 + 22 + 36 + 99 = 169
2 + 3 + 10 + 30 + 50 + 75 = 170
2 + 3 + 11 + 24 + 44 + 88 = 172
2 + 3 + 12 + 25 + 30 + 100 = 172
2 + 3 + 12 + 20 + 45 + 90 = 172
2 + 3 + 10 + 28 + 60 + 70 = 173
2 + 3 + 10 + 30 + 48 + 80 = 173
2 + 3 + 12 + 22 + 36 + 99 = 174
2 + 3 + 10 + 33 + 40 + 88 = 176
2 + 4 + 6 + 18 + 63 + 84 = 177
2 + 3 + 14 + 15 + 60 + 84 = 178
2 + 3 + 11 + 21 + 66 + 77 = 180
2 + 3 + 10 + 30 + 45 + 90 = 180
2 + 3 + 9 + 45 + 55 + 66 = 180
2 + 4 + 6 + 18 + 60 + 90 = 180
2 + 3 + 12 + 18 + 63 + 84 = 182
2 + 3 + 10 + 32 + 40 + 96 = 183
2 + 3 + 10 + 26 + 65 + 78 = 184
2 + 3 + 9 + 45 + 50 + 75 = 184
2 + 3 + 9 + 42 + 56 + 72 = 184
2 + 3 + 12 + 18 + 60 + 90 = 185
2 + 3 + 10 + 27 + 54 + 90 = 186
2 + 3 + 9 + 40 + 60 + 72 = 186
2 + 4 + 8 + 10 + 72 + 90 = 186
2 + 3 + 9 + 45 + 48 + 80 = 187
2 + 4 + 5 + 55 + 60 + 66 = 192
2 + 4 + 7 + 12 + 78 + 91 = 194
2 + 4 + 5 + 50 + 60 + 75 = 196
2 + 3 + 9 + 36 + 63 + 84 = 197
2 + 4 + 5 + 48 + 60 + 80 = 199
2 + 3 + 10 + 25 + 60 + 100 = 200
2 + 3 + 9 + 36 + 60 + 90 = 200
2 + 3 + 10 + 24 + 72 + 90 = 201
2 + 3 + 9 + 35 + 63 + 90 = 202
2 + 4 + 5 + 44 + 70 + 77 = 202
2 + 4 + 5 + 45 + 63 + 84 = 203
2 + 4 + 5 + 45 + 60 + 90 = 206
2 + 3 + 9 + 33 + 72 + 88 = 207
2 + 4 + 5 + 42 + 70 + 84 = 207
2 + 3 + 9 + 33 + 66 + 99 = 212
2 + 4 + 5 + 40 + 72 + 90 = 213
2 + 3 + 9 + 32 + 72 + 96 = 214
2 + 4 + 5 + 38 + 76 + 95 = 220
2 + 3 + 10 + 22 + 90 + 99 = 226
2 + 3 + 8 + 63 + 72 + 84 = 232
2 + 3 + 8 + 60 + 72 + 90 = 235
2 + 3 + 8 + 56 + 78 + 91 = 238
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