| Math Puzzler
Here is a scenario which occurred many millenia ago:
The patriarch of a wealthy family was on his deathbed and wanted to divide his gold among his eight sons who were all very very greedy. Wishing to favor the oldest son (as tradition would have it) but also to reward the more cunning of his progeny, he made the following decree:
The oldest son is to propose a plan for dividing up the gold. The sons are all to vote on this plan, and if it receives at least half of the votes (four or more) then that will be the way the gold is divided. If this plan does not receive half of the votes, the oldest son gets nothing, the next oldest proposes a plan, and there is another vote, now among the remaining seven. Again at least half of the vote (still four or more) is required, and failure removes this son from the process. This is to continue until some son's plan receives at least half of the votes of the remaining heirs.
Assuming that these sons will do anything to get the most gold possible for themselves, how much (if any) will the oldest son be able to inherit?
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