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Topic: cotpi 41 - Counting locally prime numbers
Replies: 32   Last Post: Feb 29, 2012 2:17 AM

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 quasi Posts: 9,097 Registered: 7/15/05
Re: cotpi 41 - Counting locally prime numbers
Posted: Feb 26, 2012 1:39 PM

On Sun, 26 Feb 2012 20:31:39 +0530, cotpi <puzzles@cotpi.com> wrote:

>From a set of ten consecutive integers, a subset is chosen such
>that every integer that is coprime to every other integer in the
>set is present in the subset. What are the possible sizes of the
>subset?

Let S be a set of 10 consecutive positive integers.

The S contains 5 even integers and 5 odd integers.

Suppose T is a subset of S such that the elements of T are pairwise
coprime. Then T has at most one even elements, hence T contains at
most 6 elements.

That 6 is possible can be seen using

S = {10, 11, ..., 19}

T = {11, 13, 15, 16, 17, 19}

Of course any subset of T also satisfies the requirements, hence
the possible sizes are 0 through 6 inclusive.

quasi

Date Subject Author
2/26/12 cotpi
2/26/12 Willem-Jan Monsuwe
2/26/12 Luis A. Rodriguez
2/26/12 Willem-Jan Monsuwe
2/26/12 quasi
2/26/12 Willem-Jan Monsuwe
2/26/12 quasi
2/26/12 Prai Jei
2/26/12 cotpi
2/28/12 Tim Little
2/26/12 Mike Terry
2/26/12 Mike Terry
2/26/12 Mike Terry
2/26/12 cotpi
2/26/12 Mike Terry
2/27/12 cotpi
2/27/12 J. Antonio Perez M.
2/27/12 Willem-Jan Monsuwe
2/27/12 Ted Schuerzinger
2/28/12 Willem-Jan Monsuwe
2/28/12 Ted Schuerzinger
2/27/12 Mike Terry
2/27/12 Mike Terry
2/27/12 Willem-Jan Monsuwe
2/27/12 Mike Terry
2/27/12 J. Antonio Perez M.
2/28/12 Willem-Jan Monsuwe
2/28/12 Mike Terry
2/28/12 J. Antonio Perez M.
2/27/12 Mike Terry
2/27/12 cotpi
2/26/12 cotpi
2/29/12 Tim Little