A wealthy man had three sons all of whom were quite good at math and logic. To get a share of his inheritance each had to correctly determine a positive integer which he had chosen. He told them that the number had four different non-zero decimal digits, in ascending order.
He prepared three sealed envelopes each of which contained a number. The first contained the product of the four digits, the second contained the sum of the squares of the four digits, the third contained the sum of the product of the first two digits and the product of the last two digits, and the envelopes were clearly marked as such. He showed the three envelopes to the three sons and had them each take one at random. Each one saw the number inside his envelope but didn't see the number inside the other two envelopes.
The sons were stationed at three different computers so that they couldn't communicate with one another (but were linked to the father's computer). After one hour they could submit a number or decline. Anyone who submitted a wrong answer would be eliminated and get nothing. If one or more submitted the correct answer they would each receive a share of the inheritance, and the contest would end with the others getting nothing. If no one submitted the correct answer they would be instructed to work on the problem for another hour. The process would repeat as often as necessary. Each of the sons decided not to submit an answer unless they sure it was correct.
At the end of the first hour no one had submitted an answer.
At the end of the second hour no one had submitted an answer.
At the end of the third hour no one had submitted an answer.
At the end of the fourth hour all three of them submitted the correct answer!
Can you determine the number?
(In reply to
computer solution by Charlie)
In the lists that follow, at each stage the numbers that are unique within the column in the current group are marked with an asterisk, indicating in the first three groups that that any line with an asterisk should be dropped in the next group, and in the last that if all three are marked with an asterisk, it is the answer
126
1234 24* 30* 14*
1235 30* 39* 17*
1236 36* 50* 20*
1237 42* 63* 23
1238 48 78 26
1239 54* 95 29*
1245 40* 46* 22*
1246 48 57* 26
1247 56* 70* 30
1248 64* 85* 34
1249 72 102 38
1256 60 66* 32*
1257 70* 79* 37*
1258 80* 94 42
1259 90 111 47
1267 84 90 44
1268 96 105 50
1269 108 122* 56
1278 112* 118* 58
1279 126 135* 65*
1289 144 150 74
1345 60 51* 23
1346 72 62* 27*
1347 84 75* 31*
1348 96 90 35*
1349 108 107* 39
1356 90 71* 33*
1357 105* 84* 38
1358 120 99 43
1359 135* 116* 48
1367 126 95 45*
1368 144 110 51
1369 162* 127* 57
1378 168 123 59
1379 189* 140* 66
1389 216 155 75
1456 120 78 34
1457 140* 91* 39
1458 160* 106* 44
1459 180 123 49*
1467 168 102 46
1468 192 117* 52
1469 216 134 58
1478 224* 130 60
1479 252 147 67*
1489 288 162* 76
1567 210 111 47
1568 240 126 53
1569 270 143 59
1578 280 139* 61*
1579 315* 156* 68
1589 360 171 77*
1678 336 150 62
1679 378 167* 69
1689 432 182 78
1789 504 195* 79*
2345 120 54* 26
2346 144 65* 30
2347 168 78 34
2348 192 93* 38
2349 216 110 42
2356 180 74* 36*
2357 210 87* 41*
2358 240 102 46
2359 270 119 51
2367 252 98* 48
2368 288 113* 54
2369 324* 130 60
2378 336 126 62
2379 378 143 69
2389 432 158 78
2456 240 81* 38
2457 280 94 43
2458 320* 109* 48
2459 360 126 53
2467 336 105 50
2468 384* 120* 56
2469 432 137* 62
2478 448* 133* 64
2479 504 150 71
2489 576 165 80
2567 420 114 52
2568 480 129* 58
2569 540 146* 64
2578 560* 142 66
2579 630 159* 73*
2589 720 174 82*
2678 672 153* 68
2679 756 170 75
2689 864 185* 84
2789 1008 198* 86
3456 360 86* 42
3457 420 99 47
3458 480 114 52
3459 540 131* 57
3467 504 110 54
3468 576 125* 60
3469 648* 142 66
3478 672 138* 68
3479 756 155 75
3489 864 170 84
3567 630 119 57
3568 720 134 63*
3569 810* 151* 69
3578 840 147 71
3579 945* 164* 78
3589 1080 179* 87
3678 1008 158 74
3679 1134* 175* 81*
3689 1296* 190* 90*
3789 1512 203* 93
4567 840 126 62
4568 960* 141* 68
4569 1080 158 74
4578 1120* 154* 76
4579 1260* 171 83*
4589 1440* 186* 92*
4678 1344* 165 80
4679 1512 182 87
4689 1728* 197* 96*
4789 2016* 210* 100*
5678 1680* 174 86
5679 1890* 191* 93
5689 2160* 206* 102*
5789 2520* 219* 107*
6789 3024* 230* 114*
43
1238 48* 78 26*
1249 72* 102 38*
1259 90* 111 47
1267 84* 90* 44*
1268 96* 105 50
1289 144 150 74
1358 120 99 43
1368 144 110 51
1378 168 123* 59
1389 216 155 75
1456 120 78 34
1467 168 102 46
1469 216 134* 58*
1567 210* 111 47
1568 240 126 53
1569 270 143 59
1678 336 150 62
1689 432 182 78
2347 168 78 34
2349 216 110 42*
2358 240 102 46
2359 270 119 51
2378 336 126 62
2379 378* 143 69*
2389 432 158 78
2457 280* 94* 43
2459 360* 126 53
2467 336 105 50
2479 504 150 71
2489 576* 165* 80*
2567 420 114 52
2679 756 170 75
3457 420 99 47
3458 480* 114 52
3467 504 110 54*
3479 756 155 75
3489 864* 170 84*
3567 630* 119 57*
3578 840 147* 71
3678 1008* 158 74
4567 840 126 62
4569 1080* 158 74
4679 1512* 182 87*
22
1289 144 150 74*
1358 120 99 43*
1368 144 110* 51
1389 216* 155 75
1456 120 78 34
1467 168 102 46
1568 240 126 53*
1569 270 143* 59*
1678 336 150 62
1689 432 182* 78
2347 168 78 34
2358 240 102 46
2359 270 119* 51
2378 336 126 62
2389 432 158* 78
2467 336 105* 50*
2479 504* 150 71*
2567 420 114* 52*
2679 756 170* 75
3457 420 99 47*
3479 756 155 75
4567 840* 126 62
7
1456 120* 78 34
1467 168 102 46
1678 336 150* 62
2347 168 78 34
2358 240* 102 46
2378 336 126* 62
3479 756* 155* 75*
1
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Posted by Charlie
on 2004-12-26 21:02:25 |
re: computer solution--listing improvement
