This was the day I had to do the roadworthiness test for my car. But the article won’t be about the result of all this. Well, I visited a toilet at the test place and then, all of a sudden, a problem came up into my brain. Now I can formulate it not to forget:

*Make three triangles using just six line segments!*

Well, not too complicated, could be given in some olympiad to some 4th or 5th grade students. However, the answer is not seen at once as well. So `draw` your solutions in comments! 😉

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And with 6 segments I can make 4…

Consider triangle ABC with D in the interior.

Draw AD, BD, and CD. We already have AB, BC, and CA.

And now we have 4 triangles: ABC, ABD, ACD, BCD.

Better than that? Let segments WX and YZ intersect at M. Draw WY, WZ, ZX and YX. 6 segments? But 8 triangles!

Thanks for commenting.

OK. Now let’s make this more complicated – draw those triangles with one stroke of pen (without tearing the pen away from the paper and without drawing the same line segment twice)!

Thanks for the hint. Now I can make 10:

AB, BC, CMD (M is on AB), DA (now we have a bowtie, but only 4 segments), AC, CPQ (P is on AMB, between A and M, Q is on AD).

10 is a lot. Can we get more?

OK, one step harder then 😉 It is now forbidden for any triangle to be completely inside any other triangle..

AB,BC,CD,DE (should look like letter “W”), EF (parallel to CD), then FA. That’s 4, but awfully boring.

I liked the old rules better. Can we just keep the old rules?

Well, it showed up that it is possible by using old rules.. Maybe the thing it is now to find the biggest possible count of triangles drawable using the old rules, but just with one stroke.. And then it would be nice to find some function that gives the biggest possible count for any given count of line segments.. or at least to find an algorithm – how to find such a function?

[…] yesterday. What’s interesting, both are linked to the same post of mine – the one about those toilet triangles So, you might ask, my dear reader – how can I find those toilet triangles in you WebLog, oh […]

How about a tetrahedron? A 3d figure, but still has the 4 triangles that you want..

Yes, you can draw a tetrahedron with 6 line segments, however it is not possible to draw it with just one stroke of a pen..

[…] par tualeti vai darbs tualetē – varu piedāvāt šādas vietnes apskati, ja interesē, pie kādām domām var nonākt tualetē, bet, ja ir vēlēšanās dabūt […]