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 Inheritance Envelopes (Posted on 2004-12-24)
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?

 See The Solution Submitted by Jim Rating: 3.5000 (4 votes)

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 re: computer solution--listing improvement | Comment 2 of 4 |
(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 `

 Posted by Charlie on 2004-12-26 21:02:25

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