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Guest Message by DevFuse

# 4 points, 2 lengths

Best Answer plasmid, 04 March 2013 - 03:35 AM

Without any sort of formal proof, I think that these are all possible shapes. Although I haven't yet fully convinced myself that the last shape I drew actually exists. It seems like it should though.

Spoiler for
Go to the full post

11 replies to this topic

### #1 bonanova

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Posted 02 March 2013 - 10:59 AM

Here's a quickie ... should take about a minute.

If you draw four points on a paper, no three of them collinear, they define six line segments.

If the points lie on the corners of a square, four of the segments are of length 1, say, and two are of length sqrt(2).

How many different configurations of four points give edges whose lengths are one of two values?

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #2 hhh3

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Posted 02 March 2013 - 03:01 PM

Spoiler for got one i think

Edited by hhh3, 02 March 2013 - 03:04 PM.

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alWaYs gaMe!!!

### #3 k-man

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Posted 02 March 2013 - 05:28 PM

Spoiler for seems to me

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### #4 bonanova

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Posted 03 March 2013 - 06:50 AM

There are more.
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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #5 plasmid

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Posted 04 March 2013 - 03:35 AM   Best Answer

Without any sort of formal proof, I think that these are all possible shapes. Although I haven't yet fully convinced myself that the last shape I drew actually exists. It seems like it should though.
Spoiler for

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### #6 bonanova

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Posted 04 March 2013 - 06:38 PM

Without any sort of formal proof, I think that these are all possible shapes. Although I haven't yet fully convinced myself that the last shape I drew actually exists. It seems like it should though.

Spoiler for

Yes, these are the complete set.
The last one has a simple explanation.
Can you find it?

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #7 superprismatic

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Posted 05 March 2013 - 01:37 AM

Do you know of any proof that this is a complete set?

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### #8 plasmid

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Posted 05 March 2013 - 06:54 AM

The last one has a simple explanation.
Can you find it?

Spoiler for a hand-waving proof for Bonanova

Do you know of any proof that this is a complete set?

I can prove it, although it's a bit brutish.
Spoiler for

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### #9 bonanova

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Posted 06 March 2013 - 09:42 AM

Hands well waved. But here's a clue for another answer.

Spoiler for what if

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

### #10 bonanova

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Posted 08 March 2013 - 03:47 AM

Without any sort of formal proof, I think that these are all possible shapes. Although I haven't yet fully convinced myself that the last shape I drew actually exists. It seems like it should though.

Spoiler for

Yes, these are the complete set.
The last one has a simple explanation.
Can you find it?

Spoiler for Think of

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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
- Bertrand Russell

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