### Distributed Descriptive Statistics and Magic

Here’s an interesting problem. Anyone know of a solution to this?

There are 24 wizards in the land of Network. They live spread out far from one another, because if too many of them got too close, the concentration of magical power would create a singularity and destroy the universe. They are all aware of one another’s existence, and have a way of communicating one-on-one between any two of them, but because of the distances involved, communicating saps a lot more mana than their normal magic (which they do locally in their towers).

Each wizard wants to learn the new ultimate spell. They find that, in order to learn the spell, they need an unbroken sequence of Celestial Numbers of a certain size. Each of them has collected a set of Celestial Numbers (which are unique, i.e., only one wizard can have the number 33.7). Unfortunately, they are all jumbled up and each wizard has a different number of them, so none of the wizards can learn the spell.

It is decided that the wizards must work together to get each wizard an unbroken sequence of roughly the same size, by distributing their Numbers amongst themselves. The question the wizards are now pondering is how to actually do it.

If they could all get together in the same place and write their Numbers (or at least a sample) on one big piece of parchment, they could determine the distribution, split it up into a 24-quantile, and use the quantile ranges to divide the Numbers into 24 sets of roughly equal size.

So, without getting together, and keeping communication to a minimum, what is the most efficient way for them to determine reasonably accurate quantile ranges to split up the Numbers?

Oct 10th, 2008
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