28 replies to this topic

[curr3nt]

So... is it possible to get less than 34?

[Prof. Templeton]

So... is it possible to get less than 34?

Yes. pg may be on the road to a more efficient solution with a small modifications to his current design. I'm glad to see he didn't make the common mistake of trying to join the connections (circled) on the bottom and eliminating a number of supports on the top.

Spoiler for Wrong!

[plainglazed]

Spoiler for 33?

[bonanova]

OP says "Without bending, breaking or overlapping dowels, only connecting them at the ends ..."

[CaptainEd]

I see that other solutions have had the triangles impinge on the square, without connecting to it.

My question about the 33 solution is that I imagine the top and bottom squares collapsing to the left and right respectively, while still remaining pinched between the crab claws. So I think the squares are not actually firmed up.

[Yoruichi-san]

I've been trying to avoid thinking about this since I can foresee not getting any work done for the next week...*whistling*

Spoiler for My mafia instincts are kicking in...

Since Bon-chan has indicated he already knows the answer, perhaps it should be taken as a hint to the solution...;P

[plainglazed]

My question about the 33 solution is that I imagine the top and bottom squares collapsing to the left and right respectively, while still remaining pinched between the crab claws. So I think the squares are not actually firmed up.

Yeah, had similar concerns. Finally just went with it assuming the two squares shared a dowel and acted as if hinged as per the op. so if they collapsed, they would need to remain congruent parallelagrams and the claws would not permit. Even if it were to qualify, strongly doubt it's optimal.

[curr3nt]

I don't think the triangles would prevent the squares from moving right or left. The triangles only keep the distance between them from exceeding one unit but collapsed the distance between those two lines would still be one unit. It would stop collapsing when the top line is inline with the triangles point.

[Prof. Templeton]

Yes, it looks like that 33 solution is unstable. Although not optimal, I will give a hint to a better solution.

Spoiler for Imagine

Three tessellated hexagons. Remove some of the dowels and squeeze two of them closer together until you can put a square in the middle of them in a way that it is stable. There is another, better solution, but this one is almost as good.