Ron Barnette's Zeno's Coffeehouse Challenge #60 Result

This challenge prompted over 200 replies, which is most appreciated!

I have listed below the original challenge, followed by several respondents' thoughts on the matter. I want to thank ALL respondents for their thoughtful time taken with Zeno's Coffeehouse, and to encourage your continued support, as critical thinking exercises are explored for mental growth and recreation. Minds need exercising with shared, reflective thinking.

Thanks!...Ron Barnette

## Unlimited Coffee??

kc, a new patron of the Coffeehouse from China, sent me a suggested topic for a new challenge. What follows is my reformulation of kc's idea, as I appreciated this entry from a new part of the world for Zeno's Coffeehouse involvement.
Thanks, kc, and let me welcome you and your friends to Zeno's!

I seems that good Charles forgot to order for Maggie and the Coffeehouse a new supply of Zeno's excellent coffee. He now fears that during this evening and until they receive a new supply they will run out of coffee! Not good. Hearing of this, kc, a self-professed Zeno-type individual, posed the following hypothetical solution:
"1. Suppose that a pot of coffee were set out for the customers who were all instructed to do the following (let's assume that they can do this): take your share, divide your share in half, and share the remaining half with another, either from the pot or from another who shared with you their own half-share.
2. Suppose that coffee amounts can be divided without losing the constituency of being coffee.
Given these suppositions, wouldn't this hypothetical solution at least resolve the matter of not running out of coffee? Although not everyone would receive their desired share, it would follow that everyone would receive, theoretically, some coffee..no matter how many patrons show up for coffee! Am I wrong???"

A couple of responses, and thanks for these! Ron

From 'Nobody':
comments: No one runs out of coffee, no matter how many times it is divided, if no one actually drinks the stuff.   So in this case it is theoretically possible.
Although coffee is constituted by thousands of various chemicals, let us assume that it is contituted by only one kind of molecule.  Under this supposition, it is theoretically possible to come to an impasse depending on the amount of times the coffee is divided (assuming the half-part retained is always consumed)as there can theoretically come the time when someone has only one molecule of coffee and is unable therefore to divide it and still have coffee.

And from Cody:
comments: At first glance, mathematically this is sound.  If each cup was filled to a quantity x, then it was split, every person would have a quantity of x/2.  The second split would leave every patron with x/4, the third x/8 and so on.  Ultimately, every person would have an amount of coffee (c) such that c=x(2^s), where x is the original cup of coffee and s is the degree of splitting that has occurred.  While a graph of c will show that it approaches zero, it will go on infinitely, never actually reaching zero.  Thus, every patron will get a bit (a VERY VERY small bit) of coffee.

This is all find mathematically.  What it fails to take into account is that the patrons of Zeno's Coffeehouse like to drink their coffee, which will take the amount of coffee to zero and leave none for the remaining patrons.

Still, an excellent variant of Zeno's tortoise racing Achilles!

Please keep up your Zeno's patronage, as we seek to provoke thoughts...