Talk:Bridge and torch problem

Latest comment: 7 years ago by InternetArchiveBot in topic External links modified

Semi Formal Analysis section

edit

The section appears to be entirely WP:OR and also isn't particularly mathematically rigorous.

This is the vague discussion I remember from reading an analysis of it, I can't find the book it was in as yet.

To optimise we must find the sum. Labelling our 4 people(ABCD) in speed order, the total journeys where they are the slowest member is.

Because we know A<B<C<D we write D=C+n, C=B+m, B=A+l and then all our sums are in terms of gA+il+jm+kn. g=5, i>=3, j>=1, k>=1 so we can take 5A+3l+m+n as a theoretical minimum and see how much over each of our steps is.

A B C D      SUM      Reduced Sum
0 0 0 5  5A+5l+5m+5n  2l+4m+4n
0 0 2 3  5A+5l+5m+3n  2l+4m+2n
0 0 4 1  5A+5l+5m+n   2l+4m
0 1 1 3  5A+5l+4m+3n  2l+3m+2n
0 1 3 1  5A+5l+4m+n   2l+3m
0 2 0 3  5A+5l+3m+3n  2l+2m+2n
0 2 2 1  5A+5l+3m+n   2l+2m
0 3 1 1  5A+5l+2m+n   2l+ m
1 0 1 3  5A+4l+4m+3n  2l+3m+2n
1 0 3 1  5A+4l+4m+n   l +3m
1 1 0 3  5A+4l+3m+3n  l +2m+2n
1 1 2 1  5A+4l+3m+n   l +2m
1 2 1 1  5A+4l+2m+n   l +m 
1 3 0 1  5A+4l+1m+n   l        Possible Minimum
2 1 1 1  5A+3l+2m+n      m     Possible Minimum 

So we can see that our minimum depends on whether the gap between 1 and 2 or 1 and 3 is the smallest.

{1,3,0,1} is created by the standard {12,1,34,2,12} and {12,2,34,1,12} solutions and {2,1,1,1} is formed from the various orders of 1 shuttling people across {12,1,13,1,14}, {12,1,14,1,11}, {13,1,12,1,14}, {13,1,14,1,12}, {14,1,12,1,13}, {14,1,13,1,12}. In this case m>l (5-2=3 > 2-1=1) so taking 34 across together in the middle is the swifter solution (15 as opposed to 17). if ABCD were {1,4,6,10) then Shuttling is 22minutes and the standard is 23minutes.SPACKlick (talk) 11:24, 29 July 2014 (UTC)Reply

edit

Hello fellow Wikipedians,

I have just modified one external link on Bridge and torch problem. Please take a moment to review my edit. If you have any questions, or need the bot to ignore the links, or the page altogether, please visit this simple FaQ for additional information. I made the following changes:

When you have finished reviewing my changes, you may follow the instructions on the template below to fix any issues with the URLs.

This message was posted before February 2018. After February 2018, "External links modified" talk page sections are no longer generated or monitored by InternetArchiveBot. No special action is required regarding these talk page notices, other than regular verification using the archive tool instructions below. Editors have permission to delete these "External links modified" talk page sections if they want to de-clutter talk pages, but see the RfC before doing mass systematic removals. This message is updated dynamically through the template {{source check}} (last update: 5 June 2024).

  • If you have discovered URLs which were erroneously considered dead by the bot, you can report them with this tool.
  • If you found an error with any archives or the URLs themselves, you can fix them with this tool.

Cheers.—InternetArchiveBot (Report bug) 17:38, 25 July 2017 (UTC)Reply