Incan Traffic Engineering

[James B.]

You are a mild-mannered engineering student in that great land of Puzzleania. Your friend, who is a grad student in the Chronological Dept., calls you over one night to check out his home-made time travel machine. You are a little foolish from the brewskis you had to celebrate this (the chronological dept. considers a time travel device as good as a dissertation) and so you agree on a bet to go back to Peru in the time just before Pizzaro and see if you can change history.

The next day, you step into the time travel device. Your friend closes the door and hits the button. After the machine rattles and whirrs a bit, you suddenly find yourself right in Cuzco. As it so happens, the emperor has just had his royal fish dinner, and it was not fresh. He is a little surprised to see you, but your four years of high-school Quechua convince him that you are pretty smart. He learns that you know much about traffic, and so devises a problem for you. If you succeed, glory and honor. If not, you go off the cliff. The problem is this: The emperor wants fresh fish. His couriers know the amount of time it takes a reasonably fast courier to carry fish from one spot to another. In fact, the emperor has a whole table of these values, all encoded in knotted ropes. He wants to find out the shortest route. Now, as it just so happened, you brought scissors and a ruler with you. Using the scissors, ruler and knotted rope, how can you find the shortest combination of routes to the sea?

[DJC]

How about a lateral approach. Does the Emperor have a problem with fresh-water fish? Why not use the rope and scissors to construct a net, show them how to fish the nearby Huatanay and use the ruler to ensure the fish are of legal size. Should be a lot fresher than anything run in from the sea by any route.

[Lepton]

Are the rope lengths labeled in any sense?

If so, this puzzle seems easy. If not, impossibly hard.

Maybe I'm missing something.

[James B.]

Yes, you can label each route.

[James B.]

...but you don't need to label their lengths.

[ralphmerridew]

Will this work:

Assuming that the length of each rope is directly proportional to the length of the path: For each path, label each end with one of the two endpoints of that path. Then, for each intersection, tie all ends labeled with that intersection together. Have one person pull the end corresponding to the castle, and have another pull the ocean end until something is taut. The path corresponding to that is the shortest.


That ought to do it.

[James B.]

One last hint: the key to this puzzle is the fact that there is a network of roads.

[ralphmerridew]

Does my answer work?

[ChienFou]

In the late 1960's the science of traffic engineering was being developed in the UK, and I worked on some of the very early computer traffic models. We used to define a network, with many nodes and then build paths through the network from all nodes to all other nodes. This gave the path for any desired journey. We then found out how many people wanted to make each journey and loaded the network with all the journeys. This gave us the traffic load on each link in the network.

Tying lots of pieces of string together and pulling both ends was how it was done before that So, yes, ralphmerridew, you are right. Your method works.