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Re: cotpi 41 - Counting locally prime numbers
Posted:
Feb 27, 2012 9:31 PM
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"Willem" <willem@toad.stack.nl> wrote in message
news:slrnjknn7r.2u3o.willem@toad.stack.nl...
> Mike Terry wrote:
> )> "Tonico" <Tonicopm@yahoo.com> wrote in message
> )>
news:f3c955d7-13fd-4f4a-bdcd-411c06f2c280@do4g2000vbb.googlegroups.com...
> )> > On Feb 27, 8:50 am, cotpi <puzz...@cotpi.com> wrote:
> )> ...
> )> > >
> )> > > Let A be a set of 10 consecutive integers. Let B be a subset of A
such
> )> > > that every element in A that is coprime to every other element in A
is
> )> > > present in B. What are the possible values for the cardinality of
B?
> )
> ) so that's 11, 13, 17, and 19. So the condition B must satisfy is that
it
> ) contains 11, 13, 17, and 19. So for this set A, subset B could have
> ) cardinalities 4,5,6,7,8,9,or 10.
>
> Pedantically, you are right. Practically, the intended wording is
> very likely "Let B be the subset of A that consists of every element
> in A that is coprime with every other element in A." Otherwise it
> would have been a trick question, and not a puzzle.
>
> Granted, both wordings were needlessly complex.
>
> An attempt at simple, but unambiguous wording:
>
> Given a set S of 10 consecutive integers, let N(S) be
> the number of integers in S that are coprime with all
> other integers in S. What are the possible values of N()?
Yep, that's what the OP meant, as confirmed in another post.
So... looking back at the thread anew, I find myself agreeing completely
with your reasoning in the very first reply! :-) Of course, we should show
that 1,2,3,4 are valid by finding example sequences exhibiting these
answers, but examples are easy to find.
Mike.
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