Results of Zeno's Challenge #34: Unlimited Key Lime Pie
Over 300 patrons submitted answers to this challenge, which is repeated below. I include Dr. Daniel Stankiewicz' clever reply for your enjoyment!
Maggie and Charles have just returned to the Coffeehouse after a nice trip abroad, and welcome the new patrons. It seems that Charles has done some reading on management skills, and some other reading as well, and that he has a theoretical idea about how to serve, at least in principle, Maggie's wonderful Key Lime pie. Or so he thinks. Seems that they always run out of this great item, and dear Charles has an idea about how to remedy it, if only in principle. Here's his idea:
"Now look, Maggie. Theoretically, we could serve your Key Lime pie to as many who show up. We will serve your pie to those who want some, no matter how many so desire, as follows. Tell them to follow this rule: Take half the portion and give the remainder to the next person. By following this rule, the pie would go on to serve everyone, no matter how many!!!"
Aside from the question of how much each patron would receive, is Charles' claim that, theoretically, an unlimited number of patrons could be served SOMETHING true??? What an idea, if only in principle!!
Dr. Daniel Stankiewicz' Reply
comments: For this argument I will assume that key lime pie is a substance unto itself (not separate crust and filling, etc.) Because the pie is a definite amount of matter, it must be possible to break it into the smallest amount possible that still has all the "properties" of key lime pie, whatever they may be. We'll call them KLPs (Key Lime Pie units) The division will work only until there are 2 (or three, in case the total number of pie units was odd to begin with and we round down to the next whole unit) KLPs left. If there are N KLPs to start, only [Log base 2 N] customers will recieve key lime pie. Now, as to whether everyone would recieve SOMETHING is a question of where the smallness of particles is finite. And I don't know that. But not everyone would get pie. Otherwise we may in fact be, at the lowest level, not carbon but key-lime-pie based organisms. Haha.....ha..ha.....ha.