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Topic: POW writing to be done
Replies: 3   Last Post: Aug 1, 1997 11:34 AM

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Michelle Manes

Posts: 3
Registered: 12/3/04
Re: POW writing to be done
Posted: Aug 1, 1997 10:49 AM
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Elizabeth Ahlgren wrote:
> Our group just finished the elementary probelem of the week on the
> emperor's banquet.

You might be interested to know that, if you change the wording
to the more general "every nth person" instead of "every other
person," this is called the Josephus problem. To the best of
my knowledge, it is still unsolved.

> A similar probelem is the locker problem but the lockers are in a row,
> not in a circle. This turned out to be a version of mod math but we are
> unsure of how to write it up due to the powers of 2 that are involved.

If you're talking about this locker problem:

There's a row of 100 lockers. The first student runs down the
hall and closes every locker. The second student runs down the
hall and opens every other locker. The third student runs down
the hall and CHANGES every third locker (opens it if it was closed,
closes it if it was open). Etc. After the 100th student heads
down the hall, which of the lockers are open and which are closed?

The answer depends on facts about factorizations rather than
modular arithmetic or powers of two. Perhaps there's another
"locker problem"?


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