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The famous negotiator William Ury has a nice story about how to solve difficult negotiations.

"Well, the subject of difficult negotiation reminds me of one of my favorite stories from the Middle East, of a man who left to his three sons 17 camels. To the first son, he left half the camels.

To the second son, he left a third of the camels, and to the youngest son, he left a ninth of the camels.

Well three sons got into a negotiation. Seventeen doesn't divide by two. It doesn't divide by three. It doesn't divide by nine. Brotherly tempers started to get strained.

Finally, in desperation, they went and they consulted a wise old woman.

The wise old woman thought about their problem for a long time, and finally she came back and said, "Well, I don't know if I can help you, but at least, if you want, you can have my camel.

So then they had 18 camels. The first son took his half -- half of 18 is nine. The second son took his third -- a third of 18 is six. The youngest son took his ninth -- a ninth of 18 is two. You get 17.

They had one camel left over. They gave it back to the wise old woman."

I love this story, but one thing just bothered me.

If the wise old woman is the paragon of wise mediation, how come she makes nothing off of solving this difficult negotiation?

She gives a camel, solves a hard problem and gets nothing back for solving the impossible.  That doesn't seem like a great business model.

Although her reputation as a problem solver grew, she still couldn't make any money solving the variants of the problem: dividing candy at Valentine's, dividing tracts of land, corporate votes, etc. Although, she did get a lot of speaking gigs - which helped.

She tried everything. But, she couldn't make the solution scale. Two groups of 17 still returned no profit.

The wise old woman was getting frustrated. She declared that "it was impossible" to make a profit solving this type of fair division problem.

Her grand-daughter, however, saw through the riddle.

She was a camel broker, matching buyers with sellers of camels.

She immediately began the 18 Lot Camel market, selling lots of camels of 18, but at near cost.

Bewildered, the wise old woman wondered how the both of them were going to survive making next to nothing on each transaction.  How was volume going to help?

Yetn when the next group of claimants who needed the wise woman's assistance had now had 35 camels and not 17 that they needed help with. And her daughter was excited. Why?

Well, the wise old woman did her negotiating trick again. She added her one camel to get 36, gave 18 or 1/2 to the first claimant, 12 or 1/3 to the second claimant, and 4 or 1/9 to the last claimant. 

Lo and behold there were 2 camels left, which the wise woman took as her fee.

She made a one camel profit - all because her daughter created a competitive market for 18 lot camels! Even though groups of 17 or 18 claimants were not profitable for the wise women, putting both groups together to form a bigger group with 35 camels was.

Sometimes, 0 + 0 = 1.   

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