Hi Jim I graduated from kindergarten 80 years ago. But I'm afraid don't see "reasoning behind a $15 and $9 split". In all the economic systems I know of a person pays the same price for buying or selling a good independent of whether he is rich or poor. What did you have in mind? At 10:27 AM 8/10/2007, you wrote:
Either way, this problem is suitable for a kindergarten entrance exam.
With arithmetic like 5 minus 8/3 = 7/3? You've got to be kidding!
If instead of $8 to be divided there were $24 to be divided, so that we could avoid fractions, this problem might be suitable for discussion in grade school. But I think there are economic/ethical issues of what constitutes fairness, in addition to purely mathematical issues. Without a clearer discussion of this, I don't think the puzzle has a single "right" answer. (Though I suspect that the 7-to-1 split is preferable. Maybe consideration of related scenarios with more extreme numbers could make this clearer.)
If I ran an elite grade school and wanted to use this problem or some variant as the basis for admission, I'd change the story so that the third party pays $24 instead of $8, so that the use of fractions could be avoided. I'd ask the students how they thought the money should be divided, and why. If their answer involved a $15 and $9 split, I'd explain the reasoning behind a $21 and $3 split; and if their answer involved a $21 and $3 split, I'd explain the reasoning behind a $15 and $9 split. The kids I'd most want to admit to the school would be those who could see that both answers make a kind of sense, and who find this cognitive dissonance both frustrating and enjoyable. ("Hey, that's weird; hey, this is fun!")
Speaking of which: Anyone out there care to help me resolve my own cognitive dissonance? Because I'm still unsure which way of splitting the money should be called "fair"! (I have a feeling that there's an Arrow-like theorem lurking here that says that certain seemingly compelling characteristics that fairness should have are actually incompatible.)
Jim
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