Ron Barnette's Zeno's Coffeehouse Challenge #47 Result
Dear Zeno's patrons: Here are the results....very creative suggestions...over 350!
First the challenge, as written, then some replies.....
One night at Zeno's, Maggie and Charles were discussing
again the importance of questions, perhaps out of respect for their mutual hero, Socrates,
who asked many questions in pursuit of the truth. At some point in their
conversation, Maggie removed from her purse three sealed envolopes, and explained that one
contained two 1-cent coins, one contained two 5-cent coins, and another contained one
1-cent coin and one 5-cent coin. She declined to identify which contained which.
Maggie then asked three waiters---John, Jim and Joe---to participate in an experiment, to
which they agreed. She then gave them each an envelope.
"I want each of you of open privately your envelope, and to tell Charles what is
inside---but I want you to lie about the contents!," instructed Maggie.
They agreed, as Charles watched on.
Joe reported that he had one 1-cent coin and one 5-cent coin.
John reported that he had two 1-cent coins.
Jim reported that he had two 5-cent coins.
"Now Charles," pressed Maggie, "I want you to come up with a procedure,
using the fewest possible questions, whereby you ask a waiter to pull out one coin he is
holding and show it, until you can deduce who is holding the envelope with the two
different coins."
OK, Zeno's patrons, give Charles a helping hand: What is the fewest possible number of questions he needs to ask to make his deduction, and to whom should he direct his first question??
One of the faithful Zeno patrons summarized a solution:
From Eric Dyer, in Ann Arbor, Michigan:
comments: Charles can do it in one question: just ask Joe. Right off the bat Charles
can eliminate the possibility for each waiter that he's holding the envelope he claims to
be holding. Joe can only be holding either the <1,1> or the <5,5> envelope, so
whichever coin he produces gives him away as holding the envelope with two of that coin.
Whichever one that turns out to be, it gives the guy Charles is looking for away.
Suppose Joe pulls out a penny, so he's got the <1,1> envelope. Since
Jim claimed to have the <5,5> envelope, we know he must have either the <1,1>
or the <1,5>. Joe has the <1,1>, so Jim must have the <1,5>.
If Joe pulls out a nickel, it gives John away through the same reasoning.
(btw, this is my first time here; I like this place!)
Thanks, Eric.....and visit Zeno's often!:)