Captain John Smith left his $64,827 inheritance to his 9 heirs, consisting of a married son, wife and child; a married daughter, husband, and child; and a stepson, wife and child.

The will stipulated that each husband was to get as much more than his wife as she got more than her child, this difference being the same for all 3 families.

The money consisted entirely of one-dollar bills and each heir received a package of sealed envelopes, each envelope containing as many one-dollar bills as there were sealed envelopes in his or her package.

How much did each heir received, if they received different amounts?

Family 1: 4, 3364, 6724 (total 10092)

Family 2: 2116, 5476, 8836 (total 16428)

Family 3: 9409, 12769, 16129 (total 38307)

Nine different inheritances, total 64827

Each husband got 3360 more than his wife

Each wife got 3360 more than their child.

The differential, 3360, is the same for each family.

The key is recognizing that each inheritance must be a square, since the dollars per package = number of packages.  Then just make a table of all triads for husband-wife-child; and then find three of these which total to 64827, and which have the same difference between husband-wife as wife-child.

Needless to say, I did this with a computer program, though there may be other approaches.

Posted by ed bottemiller on 2008-08-01 17:24:38