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**rimi****Member**- Registered: 2006-02-21
- Posts: 17

Here goes a simple permutation and combination puzzle..

There is a polygon with 10 sides.A point is there in the middle of the polygon and all the vertices are joined with the point and therefore producing 10 triangles.In exactly how many ways can you select three triangles no two of which are adjacent?

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**ganesh****Moderator**- Registered: 2005-06-28
- Posts: 21,302

10 x 7 x 4 = 280 Thats a guess

Nothing is better than reading and gaining more and more knowledge - Stephen William Hawking.

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Brxxt! Wrong!

If the first two triangles you select are as close to each other as you can get them, you get more choice for the third one, meaning that you can choose 300 in all.

But because of rotational and reflectional symmetry, only 15 of these are unique.

Why did the vector cross the road?

It wanted to be normal.

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**rimi****Member**- Registered: 2006-02-21
- Posts: 17

I repeat my question ....there is a point within a polygon of 10 sides , suppose ABCDEFGHIJ...take a point inside , say O.and join the vertices with this point producing 10 triangles,viz, AOB,BOC,COD,DOE,EOF,FOG,GOH,HOI,IOJ,JOA.

now you have got to select three triangles out of these 10 so that no two are adjacent.

Ganesh you are not right...there are actually less choices.

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