Tricky Triangle Question?

[zoombini]

The brain teaser is worded as:

Isolate the circles within the triangle so that they don't share any area with each other using only 2 lines.
The lines may not cross but can touch only once.

Now I can see that this is real easy if you are allowed to use curved lines.
(as in the 2nd image)

However, what if you MUST use straight ones?
We thikn that the question is just badly worded but should be straight lines only. Otherwise it ws too easy & the question is usually hard.

[danielf]

Originally Posted by zoombini

The brain teaser is worded as:



Now I can see that this is real easy if you are allowed to use curved lines.
(as in the 2nd image)

However, what if you MUST use straight ones?
We thikn that the question is just badly worded but should be straight lines only. Otherwise it ws too easy & the question is usually hard.

I think curved lines must be allowed. If it was straight lines, then it wouldn't make sense that they can touch only once. Two straight lines that touch (and don't cross) are overlapping lines.

[zoombini]

Unless they touch at only 1 end.

[danielf]

Originally Posted by zoombini

Unless they touch at only 1 end.

In which case they can only divide the space into three sections, and that is not going to be enough with 5 dots?

[SMHarman]

I really cannot see how this could be done with two straight lines (waits to be proved wrong), if they cannot cross.

The first line could only close of one of the spaces, leaving 4 in the next area, the next line could only knock another out.

If they can cross then you can take 4 of 5 easily and I would think some more about whetehr it could be 5/5.

Feel free to prove me wrong - but I don't think you can do it with two straight lines even if you allow them to cross.

[MetaWraith]

3 straight lines - easy (yes they do cross)
2 straight lines - don't see how this is possible

[altis]

one circle and one straight line

[Jerrek]

Originally Posted by Pem

Feel free to prove me wrong - but I don't think you can do it with two straight lines even if you allow them to cross.

You can't... You're esentially turning this into a bipartite graph. Using elementary combinatorics, it can be proven that this graph can't be turned into a bipartite graph because the total number of edges in conjunction with the 5 vertices requires a tripartite graph to exist.

You can even apply the 2-color, or 3-color theorem to this graph.

[Ramrod]

Originally Posted by Jerrek

You can't... You're esentially turning this into a bipartite graph. Using elementary combinatorics, it can be proven that this graph can't be turned into a bipartite graph because the total number of edges in conjunction with the 5 vertices requires a tripartite graph to exist.

You can even apply the 2-color, or 3-color theorem to this graph.

Speak English!

.....are you allowed to fold the triangle?

Originally Posted by Jerrek

You can't... You're esentially turning this into a bipartite graph. Using elementary combinatorics, it can be proven that this graph can't be turned into a bipartite graph because the total number of edges in conjunction with the 5 vertices requires a tripartite graph to exist.

You can even apply the 2-color, or 3-color theorem to this graph.

Just what I was thinking

[Alan Waddington]

Originally Posted by Ramrod

Speak English!

.....are you allowed to fold the triangle?

I was more thinking of screwing it up & lobbing it in the general direction of the bin, which will be a tricky shot from where I'm sitting, as it's not a straight line shot - not even two straight lines

From the way the puzzle is worded, I think the challenge here is to see if the person trying to solve it bothers to try it with non-straight lines. I can imagine that most people just try to use straight lines. It is similar to that one where you have to join the dots in a 3x3 matrix, a lot of people don`t take into account that they can go outside the square formed by the matrix.