Barnette's Zeno's Coffeehouse
Challenge #60 Result
This challenge prompted over 200 replies, which is
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
mental growth and recreation. Minds need exercising with shared,
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
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...