Kangaroo Talk

bukind · joey Joined: 01 Oct 2006 Posts: 5

Hi,

This is a topological problem (I'm not sure how anyone would post an answer because it should be drawn).

So, let you have a picture in a frame with a rope attached to it. You have to put it on the wall using two nails in such a way that when any of the nail is removed from the wall the picture falls down.

WBR, Dima.

YuraT · Posted: Wed Jan 03, 2007 11:54 am Post subject: Re: A picture and two nails

Why can't you just hammer 2 nails into the wall and put picture on it like so (don't need a rope for this Smile

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X X

Remove any nail and picture will fall because gravity force will have a leg.

Cheers Wink

bukind · joey Joined: 01 Oct 2006 Posts: 5

Gena · Posted: Wed Jan 10, 2007 5:53 pm Post subject:

That's probably not the solution you are looking for bu it is legitimate. You either cut the loop or attach the original rope by the middle so you have to ends. You then proceed to tie a double loop like you do when you tie your boots. Then you drive the nails through the two loops. If either one is removed, the picture will swivel, the remaining loop will untie, and the picture will drop.

Gena · Posted: Thu Jan 11, 2007 3:03 pm Post subject:

I am guessing that there must be a qualification that the rope is frictionless. Otherwise there are tons of solutions, none of them is particularly interesting.

Gena · Posted: Wed Jan 24, 2007 6:29 pm Post subject:

Ok, I got it.

You hammer one nail in the wall regularly, head-up, swing the loop over it (say, from left to right, over the top), pull it down, and fix it with the second nail through the loop head-down. If the first nail is removed, the loop will slide off the second nail. If the second nail is removed, the loop is not fixed anymore and will slide back over the first one. The picture falls in either case.

bukind · joey Joined: 01 Oct 2006 Posts: 5

Gena · Posted: Mon Mar 12, 2007 9:50 am Post subject:

No, if the first nail is removed, you have a picture hanging on a nail that is inclined downward. The rope will slide right off.

bukind · joey Joined: 01 Oct 2006 Posts: 5

Ok, I see your point.

But as I say before this is a topological problem, having nothing to the real world. This is 2d problem actually
(w. r. t. the plane of the wall). In this problem you
have a closed flexible line (rope) and two points (nails).
The "rope" should pass around the "nails" in such a way,
that when any of the "nails" is disappear the "rope" doesn't
surround another one.

Gena · Posted: Tue Mar 13, 2007 3:03 am Post subject:

Do both nails have to be nailed into the wall?