Author |
Topic: Yet another S&F problem... (Read 618 times) |
|
JocK
Uberpuzzler
Gender: 
Posts: 877
|
 |
Yet another S&F problem...
« on: Dec 12th, 2004, 8:21am » |
 Quote  Modify
|
As part of the recent spate of Spider&Fly problems at this forum (Sir Col's S&F problem, THUDand BLUNDER's S&F problem), what about this one:
For a room of dimension a x b x c, what is the maximum 'Spider&Fly distance'?
|
| « Last Edit: Dec 12th, 2004, 8:25am by JocK » |
 IP Logged |
solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
xy - y = x5 - y4 - y3 = 20; x>0, y>0.
|
|
|
Sir Col
Uberpuzzler
impudens simia et macrologus profundus fabulae
Gender:
Posts: 1825
|
|
Re: Yet another S&F problem...
« Reply #1 on: Dec 12th, 2004, 10:40am » |
Quote Modify
|
I assume that that you're referring to the three "shortest" straight line distances? Otherwise you're asking for maximum distance between two points and clearly there is no upper bound or largest finite value.
In which case then I can't really answer it, as I will be indirectly answering my own problem in the easy section; I am asking for the minimum distance when the spider's path starts on the floor.
|
|
IP Logged |
mathschallenge.net / projecteuler.net
|
|
|
JocK
Uberpuzzler
Gender:
Posts: 877
|
|
Re: Yet another S&F problem...
« Reply #2 on: Dec 12th, 2004, 10:56am » |
Quote Modify
|
on Dec 12th, 2004, 10:40am, Sir Col wrote:| I assume that that you're referring to the three "shortest" straight line distances? Otherwise you're asking for maximum distance between two points and clearly there is no upper bound or largest finite value. |
|
Let me clarify: with the "S&F distance" of two points I mean the minimum distance for a trajectory across the walls (and/or floor and ceiling) between the two points.
Given the room dimensions a, b and c, what two points are at the maximum "S&F distance"?
So I am asking for the maximum value of the minimum distance given that you can chose the two endpoints at will 
|
|
IP Logged |
solving abstract problems is like sex: it may occasionally have some practical use, but that is not why we do it.
xy - y = x5 - y4 - y3 = 20; x>0, y>0.
|
|
|
Barukh
Uberpuzzler
Gender:
Posts: 2276
|
|
Re: Yet another S&F problem...
« Reply #3 on: Dec 14th, 2004, 11:56pm » |
Quote Modify
|
Here's an example I came with that may help to answer the general case:
Let a = 2, b = c = 1. Then, the shortest path between two opposite corners of the box is [sqrt]8, but the shortest distance between the centers of two opposite square faces is 3.
|
|
IP Logged |
|
|
|
|
RIDDLES SITE
WRITE MATH!
Home 
Help 
Search 
Members 
Login 
Register
Reply
Notify of replies
Send Topic
Print