Coffin Problem

[Steven G]

Hi, I have been working on a coffin problem that I feel that I almost have if I find the correct pythagorean triples to use. I was wondering if someone can tell me if I am following a good path.

The problem is can you draw a figure with 6 points on a plane, points are integer distances apart from other points and no 3 points are collinear?

I think this can be done and my work is below.
Please disregard the last two ens outside the box

As always, thanks for helping.

 

[Cubist]

I think I stumbled onto an answer. But mine doesn't look like a coffin (maybe a coffin for a tortoise?). Here's a hint:

Spoiler: Further hint

The above two triangles are the same Pythagorean triple - but scaled by different integers so that they are the same height

Spoiler: Answer

The top two red triangles are 3,4,5. One is scaled x3 and the other x4.
This gives a centre gap of 4*4-3*3=7. The height of the third red triangle is 2*(3*4)=24. So the tall Pythagorean triple is 7,24,25

 

[Steven G]

“Coffin problems” are extremely difficult math problems which, nevertheless, have elementary solutions. They were devised for and used by admission committees at Soviet universities in the 70’s and 80’s to keep Jewish candidates (and other “undesirables”) out of the most prestigious universities, such as Moscow State. Only undesirable candidates were asked these questions in the oral entrance exams.
Here is a list of coffin problems.
There is always a simple trick to solve these but there is no reason at all to see this trick. The logic from the colleges was that if someone complained that the problem given to them was extremely hard they could show them that the solution was trivial and they (the student) just wasn't bright enough to see the obvious solution. That way they could deny entry to any undesirables by given them these problems. How awful!