Math and boats

Some of you may remember I've been working on a model of the famos clipper Cutty Sark for quite a while now.  Actually I started the project on our honeymoon in 2001.  Sadly it won't be completed before Brioche is born, but most of the work is done and I just have to work on the rigging.  Check out how cool it is sofar:

 

As for the math part, here's a puzzle for all of you hard-core computer scientists:

Given two people, A and B that can communicate to each other in an asymmetric way: A can send 1 object (byte/block, etc) to B in the same amount of time that would take B to send A k objects.  This is similar to a DSL connection where the up-link is much slower than the down-link.  The question is: can you come up with a communication protocol that allows A to send stuff faster to B, by making use of the ability of B to send stuff to A.  In the extreme, if A has a 1kb file that he wants to send to B, B could randomly generate 1kb files and send them to A until he guesses As file.  At that moment A simply sends an OK back to B.  Clearly this is not realistic, but can you do it in a less naive way?  I have a feeling there's a solution out there but I don't know what it is.  BTW, if you are wondering of the practical applications, you're not too serious about theory :)

Well,  that's all for now.
 
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