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Conference rusure::math

Title:	Mathematics at DEC

Moderator:	RUSURE::EDP

Created:	Mon Feb 03 1986
Last Modified:	Fri Jun 06 1997
Last Successful Update:	Fri Jun 06 1997
Number of topics:	2083
Total number of notes:	14613

1666.0. "Golden Chain Problem" by TAV02::NITSAN (One side will make you larger) Sat Sep 19 1992 14:23

An athlete enters a large room. There are two adjacent golden chains
hanging from the ceiling all the way down to the floor. Assume the athlete's
height is A and the room's height is B >> A. Assume also the athlete has
very strong arms (i.e., he can climb any chain for any amount of time etc.),
*but* he's not allowed to jump down, only to slide back down using the
chain(s) until his feet touch the floor.

The athlete is equipped with a knife that can cut the chains. What is the
maximal length of chain he can take out of the room?

T.R	Title	User	Personal Name	Date	Lines
1666.1		AMCFAC::RABAHY	dtn 456-5689	`Mon Sep 21 1992 10:26`	13
	B+A Perhaps the athlete can make a cut in the top of the remaining chain and then shake it loose while standing on the floor. In which case the answer is 2B. Perhaps the athlete could climb the chains and break a hole in the ceiling large enough to pull himself and the chains through. Again, he can take all of the chain out of the room, 2B. Perhaps by cutting a single link from one of the chains and then proceeding to slice it up just so and put it back together in a different configuration with an much larger volume ...
1666.2	Going for the gold	VMSDEV::HALLYB	Fish have no concept of fire.	`Mon Sep 21 1992 10:38`	13
	I think we need to know if splicing the chain back together is permissible. And if so, how does one measure "length of chain"? Perhaps the number of links? My answer is 2B-<1 link>. Athlete climbs to the top, cuts all but 1 link fom chain 1, cuts all of chain 2, splices together chains 1 and 2 into one long chain which he then loops thru the 1 fixed link, climbs down the chain, cuts it at the bottom and pulls it thru the one link at the top. Assuming he can splice chains and reform the shape of the links. John
1666.3	2*B - epsilon	TAV02::NITSAN	One side will make you larger	`Mon Sep 21 1992 17:01`	7
	Well, actually this was the answer I knew (2B-epsilon). Perhaps the question would have been phrased better with "golden ropes" instead of chains, in which case the athlete should have performed the loop (of size epsilon) at the top... /Nitsan
1666.4		HANNAH::OSMAN	see HANNAH::IGLOO$:[OSMAN]ERIC.VT240	`Wed Sep 23 1992 16:18`	12
	Can the athlete get the chain swinging ? If so, then how about forming a very small loop near ceiling, threading the rest through the loop, hanging from the doubled chain, swinging until you are out of the room, then pull most everything out of the loop and into your hands. All you lose is the small loop's worth. Gee, sure wish I could draw pictures in notes... are we in the dark ages or what ? /Eric
1666.5	new interpretation of problem	53099::BUCHANAN	The was not found.	`Thu Sep 24 1992 12:41`	9
	If the 2 chains are close to one another, then the problem seems a bit vacuous. Suppose the two chains are a longer way (>2B) apart. I think that the best we can get away with is 8A. We are limited by the fact that if we wish to return to a chain, we must leave at least B-A hanging there. Cheers, Andrew.
1666.6	a belfry perhaps	53099::BUCHANAN	The was not found.	`Thu Sep 24 1992 12:45`	6
	In fact, for n chains we can get away with length: An2^n Cheers, Andrew.