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Dave
Homiak
Dear S-Plus
Colleagues,
A very sharp mathematician friend sent me this puzzle from
prison. Although not explicit, it has, in my opinion, fairly deep statistical
and probabilistic content. I thought some of you might enjoy thinking about
it. Please send me your thoughts at (nadas@env.med.nyu.edu) and I
will transmit them to my friend and summarize putative solutions for this
list. Here is the
puzzle:
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Early
release?
In a cost cutting measure brought on by the budget crisis, the
warden at the prison brought together four lifers and made them the following
offer:
“Intermittently and at my whim I will begin picking you, one at
a time, to come to this room and stand before those two unconnected light
switches. You may observe the positions of the switches and then you must
switch one of them. At this point you also have the option of telling me: ‘All
four of us, have by now, visited this room without the others.’ If this claim
is correct then all of you will be immediately released. If the claim is
wrong, you will all be executed.
I may pick the same person several
times in a row, but I will eventually pick every one of you. Once I have
picked you, I will eventually pick you again and again, ad infinitum, as long
as no one has made the claim. You each will be kept in total isolation except
for these visits. I will give you time here together to plan your strategy,
and when you have decided and leave here, I may change the way the switches
are now, but after that only you guys will be allowed to touch them. No
tricks.”
What should they do?
Arthur
Nádas
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