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All Roads Lead To...
  July 2009
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All Roads Lead To...


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There’s no article this month, just a little puzzle to get your teeth into over lunch. There are no prizes to be won, just a bit of a mental challenge!

There are four towns – Upper Monitor, Delete Quay, Serialport and Caps Loch – all located on the corners of a 100 kilometre-sided square. The various town councils have been complaining about the lack of access between them, so the Highways Agency decides it will connect them. As a government body it wants to spend as little money as possible by building the shortest network of roads.
Road Layout diagram
“If we build roads from Upper Monitor to Delete Quay, to Caps Loch, to Serialport” says an assistant highways planner, “we’ll use 300 kilometres of road.”

His boss sucks air through his teeth. “That seems a lot of road,” he says, “and a lot of money. Don’t forget we’ve got the Minister’s travel expenses to think about.” He pauses for a second before getting a flash of inspiration. “I know, how about we use two diagonals. If you remember your Pythagoras, that would make (200 * √2)km – about 283km altogether. That’s a lot of tarmac saved!”

However, neither of these suggestions is the shortest network, so what would be? Can you link all the towns together using less than 283km of road?

To find out the solution click here -
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