Professor X smokes a pipe. He carries two identical matchboxes, originally containing 20 matches each. When he lights his pipe, he chooses a matchbox at random and lights his pipe with one match and discards the used match.

There will eventually arise an occasion when he first selects a matchbox with only one match in it. At this point, what is the expected number of matches in the other box?

(In reply to New print out of previous solution by Dan Rosen)

Per my previous post, there might even be one remaining in the "other" box, that is, both boxes are reduced to one, and then professor X will choose one of these, and then the situation will occur as specified in the second paragraph, of the professor actually choosing a box with only one match in it. So the summation should at least start with 1. I'm still confident of my original analysis, especially as the simulation agreed, within variations due to chance, with the calculated result.

Edited on June 29, 2010, 11:44 am

Posted by Charlie on 2010-06-29 11:42:53