Waldo Posted March 7, 2012 Share Posted March 7, 2012 Imagine 4 towns, spaced 1 mile apart from each other, forming the corners of a square. It is your job to make sure each town is connected to all the others, via a road system. But! Roads are expensive (made of gold), so what is the minimum distance of total road, that will connect up all the 4 towns? --- Some example configurations... 1. A square, such that the corners of the square, hit each village (total road used = 4 miles). 2. A circle, passing though each village (total road used = more than 4 miles). Link to comment Share on other sites More sharing options...
nikki-red Posted March 7, 2012 Share Posted March 7, 2012 Could you have just 2 roads in an X shape, with a cross-roads or roundabout in the middle? Link to comment Share on other sites More sharing options...
Deltic Posted March 7, 2012 Share Posted March 7, 2012 Imagine 4 towns, spaced 1 mile apart from each other, forming the corners of a square. It is your job to make sure each town is connected to all the others, via a road system. But! Roads are expensive (made of gold), so what is the minimum distance of total road, that will connect up all the 4 towns? --- Some example configurations... 1. A square, such that the corners of the square, hit each village (total road used = 4 miles). 2. A circle, passing though each village (total road used = more than 4 miles). 3miles? you don't need the 4th side of the square to satisfy your conditions. Link to comment Share on other sites More sharing options...
truman Posted March 7, 2012 Share Posted March 7, 2012 ....................................... Link to comment Share on other sites More sharing options...
HeadingNorth Posted March 7, 2012 Share Posted March 7, 2012 The two diagonals, crossing at the centre point of the square, would come to just about 2.82 miles. That cannot be improved upon - unless there is some caveat that the layout would not be permitted. Link to comment Share on other sites More sharing options...
HeadingNorth Posted March 7, 2012 Share Posted March 7, 2012 6.8miles? A 1 mile square with 2 diagonals? That's the correct answer if the layout requires that you can go from any town to any other town without passing through the other two towns. It's not clear if that is what the question requires; I suspect not. Link to comment Share on other sites More sharing options...
truman Posted March 7, 2012 Share Posted March 7, 2012 3miles? you don't need the 4th side of the square to satisfy your conditions. I think the X shape is shorter.. 2.8 miles? Link to comment Share on other sites More sharing options...
truman Posted March 7, 2012 Share Posted March 7, 2012 That's the correct answer if the layout requires that you can go from any town to any other town without passing through the other two towns. It's not clear if that is what the question requires; I suspect not. Yep,that's why I deleted my post ... and by doing that you just got in ahead of me.. Link to comment Share on other sites More sharing options...
Deltic Posted March 7, 2012 Share Posted March 7, 2012 The two diagonals, crossing at the centre point of the square, would come to just about 2.82 miles. That cannot be improved upon - unless there is some caveat that the layout would not be permitted. Annoyingly enough a Z shape was my first thought then i took a wrong turning from there. Link to comment Share on other sites More sharing options...
Waldo Posted March 7, 2012 Author Share Posted March 7, 2012 The two diagonals, crossing at the centre point of the square, would come to just about 2.82 miles. That cannot be improved upon - unless there is some caveat that the layout would not be permitted. Incorrect. It's close, but no cigar. Link to comment Share on other sites More sharing options...
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