Re: 2680 challenge

From: The Last Danish Pastry (clivet_at_gmail.com)
Date: 01/23/05 

Date: Sun, 23 Jan 2005 21:12:08 -0000

"Patrick Hamlyn" <path@multipro.N_OcomSP_AM.au> wrote in message
news:u3l7v0dkmugcnbdaiimsafnhfdreqf7b3d@4ax.com...

> "The Last Danish Pastry" <clivet@gmail.com> wrote:
>
> >The text file
> >http://www.pisquaredoversix.force9.co.uk/2680.txt
> >consists of 2680 lines. Each line contains five integers. Each of these
> >integers is in the range 0 to 244. The challenge is to select 49 of the
2680
> >lines in such a way that each of the numbers from 0 to 244 is present in
the
> >selection.
> >
> >I do not know if there is a solution to this challenge.
>
> Can't give you a solution, but here is a partial containing 45 'disjoint'
lines:
> 5 6 11 12 19
> 29 35 36 37 42
> 33 39 40 41 48
> 99 147 148 149 196
> 103 151 152 153 202
> 133 175 182 189 238
> 139 181 188 195 244
> 1 8 9 15 245
> 7 14 49 56 105
> 13 20 55 62 111
> 43 44 91 92 141
> 46 47 96 97 145
> 197 198 203 204 211
> 200 201 208 209 215
> 224 231 232 233 239
> 230 235 236 237 243
> 2 3 50 51 100
> 4 52 53 54 101
> 21 28 77 84 126
> 27 34 83 90 132
> 38 45 80 87 136
> 108 150 157 164 199
> 112 154 161 210 217
> 118 160 167 216 223
> 142 190 191 240 241
> 143 192 193 194 242
> 10 16 17 18 23
> 22 70 71 72 119
> 25 26 75 76 124
> 63 64 113 114 162
> 61 67 68 69 74
> 79 85 86 93 94
> 32 81 88 95 137
> 120 168 169 218 219
> 206 207 212 213 220
> 214 221 222 227 228
> 131 138 173 180 229
> 135 183 184 185 234
> 24 31 66 73 122
> 60 102 109 158 165
> 172 178 179 186 187
> 58 59 106 107 156
> 110 115 116 117 123
> 121 127 128 129 134
> 163 170 171 176 177

Thanks for that. I already know several sets of 48 disjoint lines. Here is
one such set which excludes just the numbers (0 49 98 147 196):

   1 2 9 10 16
   3 4 51 52 101
   5 53 54 55 102
   6 11 12 13 19
   7 14 63 70 112
   8 56 57 58 107
  15 21 22 23 28
  17 59 66 73 122
  18 60 67 116 123
  20 27 62 69 118
  24 25 30 31 38
  26 74 75 76 125
  29 35 36 37 42
  32 39 40 45 46
  33 34 81 82 131
  41 83 90 97 146
  43 44 93 94 142
  47 48 95 96 145
  50 99 106 113 155
  61 108 109 110 158
  64 71 72 77 78
  65 114 115 162 163
  68 117 124 159 166
  79 84 85 86 92
  80 129 130 177 178
  87 88 135 136 185
  89 137 138 139 186
  91 126 133 140 182
 100 148 149 198 199
 103 104 151 152 201
 105 154 161 168 210
 111 153 160 167 202
 119 120 127 128 134
 121 170 171 172 220
 132 181 188 223 230
 141 189 190 239 240
 143 191 192 241 242
 144 193 194 195 243
 150 156 157 164 165
 169 175 176 183 184
 173 174 179 180 187
 197 203 204 205 212
 200 206 207 208 213
 209 214 215 216 222
 211 217 218 219 224
 221 226 227 228 234
 225 231 232 233 238
 229 235 236 237 244 

-- 
Clive Tooth
http://www.clivetooth.dk
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