On New Years Day, Penny resolved to make poverty history.
Unfortunately Penny was penniless and asking her relatives for cash seemed a bit passe, so she asked them to contribute goats.
Frankie, Mark, Dolly, Squidly, Ruby and Draco each sent goat vouchers. Each of the vouchers was for a three figure number of goats. Penny was delighted with the response, over 5200 goats in total. Even better, she found that after using 11 of the goats to pay local administrative expenses, each of the beneficiaries would receive exactly 32 goats.
Curiously she noticed that the each of the donations was the product of exactly six prime numbers. If Frankie gave more than Mark, who gave more than Dolly, who gave more than Squidly, who gave more than Ruby, who gave more than Draco, how many did each give?
(In reply to
re(3): computer solution by Mindrod)
I'm not understanding the 2^5 with regard to the factorization routine. The factorization routine is one that I use whenever I have to factor an integer into primesnot specifically written for this problem.
The first several test divisors the way the loop is written are:
7 11 13 17 19 23 29 31 37 41 43 47 49 53 59 61 67 71 73 77 79 83 89 91 97 101 103 107 109 113 119 121 127 131 133 137 139 143 149 151 157 161 163 167 169 173 179 181 187 191 193 197 199 203 209 211 217 221 223 227 229 233 239 241 247 251 253 257 259 263 269 271 277 281 283 287 289 293 299 301
If the ' 37 line were left out they would be:
7 11 13 17 19 23 29 31 35 37 41 43 47 53 55 59 61 65 67 71 77 79 83 85 89 91 95 101 103 107 109 113 115 119 125 127 131 133 137 139 143 149 151 155 157 161 163 167 173 175 179 181 185 187 191 197 199 203 205 209 211 215 221 223 227 229 233 235 239 245 247 251 253 257 259 263 269 271 275 277 281 283 287 293 295 299 301 305 307 311 317
The first difference is an unnecessary division by 35, but later, more importantly, division by 73 is left out. Perhaps your comment is related to this specific problem's not needing a prime so high as any of these. Again, the reason is that I used a generalized factorization subroutine, using a cycle of 30 to avoid trying any multiples of 2, 3 or 5, after the initial trials by those numbers outside the loop.

Posted by Charlie
on 20060219 15:39:45 