The first four men (the poorest) would pay nothing.

The fifth would pay $1.

The sixth would pay $3.

The seventh would pay $7.

The eighth would pay $12.

The ninth would pay $18.

The tenth man (the richest) would pay $59.

So, that's what they decided to do.

The ten men drank in the bar every day and seemed quite happy with the arrangement, until one day, the owner threw them a curve. "Since you are all such good customers," he said, "I'm going to reduce the cost of your daily beer by $20."

Drinks for the ten now cost just $80.

The group still wanted to pay their bill the way we pay our taxes so the first four men were unaffected. They would still drink for free. But what about the other six men -- the paying customers? How could they divide the $20 windfall so that everyone would get his "fair share"?

They realized that $20 divided by six is $3.33. But if they subtracted that from everybody's share, then the fifth man and the sixth man would each end up being paid to drink their beer.

The bar owner suggested it would be fair to reduce each man's bill by roughly the same percentage as he was paying before, and he proceeded to work out the amounts each should pay. And so:

The....

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