Th Seven Bridges of Q'w'nis

The most recent US presidential election has left Rotary High Command in something of a quandary. The window on many of our most of our important higher governmental connections is now closing. No longer will we be able to send captured Kiwanians to secret sites in Eastern Europe to be enlightened on new, aggressive interrogation techniques. But Noon Rotary is not so easily discouraged, and it has occurred to some in High Command that the current political situation might give that pitiful minority of the club who are democrats added value added value, if only as hostages.

It was in this spirit that I, a mere Replacement Cog in the group’s organizational structure, was approached with the request of a favor requiring something of my mathematical training. The following story was related to me in regard to some black operations that are being carried out deep in enemy territory on behalf of Noon Rotary High Command by a group known simply as “the Agency.”

This region is known as Q’w’nis. It is occupied by a simple, though sinister, people who are famed for creating a special wheat cake covered with a sugary tree derivative in the month of December. There is a huge gorge that divides the region of Q’w’nis and in the middle of that gorge are two tall rock formations, much like what you see in monument valley. One of the formations is called B’tar and the other S’ryp.

The gorge itself is too wide to be spanned directly by a bridge of any type; nevertheless, the pieces of the region are bound together for purposes of transportation by great swinging bridges that make use of B’tar and S’ryp. On the south side of the gorge there are a total of three bridges. Two of these connect to B’tar and one to S’ryp. On the north side, there are also three which connect to B’tar and S’ryp in the same way. There is also a single bridge between B’tar and S’ryp. This means there are five bridges connecting to B’tar, three to S’ryp, and a total of seven bridges all together.

The Agency plans to destroy these bridges in order to disrupt trade in the region and have concocted the following plan. Land a helicopter secretly on B’tar and begin tracing a path across the bridges, destroying each one as they go. Then, having closed the path, get back into the helicopter and return home.They discovered a problem, however. Normally the Agency just comes up with these plans and does them, but this time one of the agents drew a map of the region and began tracing out the route ahead of time. He discovered that, no matter how he traversed the bridges, when all the bridges were destroyed, he was somewhere besides on B’tar with the helicopter.

This was a pretty green agent or he never would’ve planned it out ahead. He would’ve done his job and dealt with the consequences as they happened. However, it occurred to the Agency that they might be able to save the helicopter if they called in a consultant. That’s where I came in.

As is so often the case, they did not get the answer they wanted. It turns out that, regardless of the path their agent might take, he will wind up stranded away from the helicopter. Each of the bodies of land has an odd number of bridges attaching it to the rest. If you use up the bridges as you cross them, you will always wind up away from where you started.

“This is actually exactly like the old Seven Bridges of Konigsberg problem,” I said. “It was solved by Leonhard Euler centuries ago.”

“Konigsberg?” the contact said. “I’ve never heard of Konigsberg.”

“It’s called Kalingrad now,” I said. “It’s in Russia.”He said nothing but eyed me suspiciously. Getting no further feedback, I still proceeded.

“You know,” I said, “it occurs to me that if your purpose is just to disrupt travel you could leave the single bridge between B’tar and S’ryp intact, and take out the remaining six bridges from the B’tar-S’ryp end of it.”

On hearing that, he answered.“The Agency does not require you to tell us how to do our business.” And with that, he left.I wonder if this will get me any points with High Command.