There is a classic puzzle built around the old geography of Königsberg, Germany (now Kaliningrad, Russia). The city was built along a river with a number of bridges connecting the riverbanks and a large island in the river. The challenge was to devise a path whereby one could walk through the city, crossing every bridge, crossing each bridge only once (and without boating across the river or other cheats). The 18th century mathematician Leonard Euler proved mathematically that there was no possible route by which the puzzle could be solved.
In May, 1961, the editors of the Children’s Friend printed a puzzle that was very much like the Königsberg Bridges puzzle – but they threw in an eighth bridge to make the puzzle solvable. They also imagined that the river sprang from a source very near the city, such that you could walk around the head of the river (marked “Source”) without getting your feet wet. In other words, they cheated, and big time!
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They also wrote this framing story:
In olden days, some missionaries living on the island A found it necessary to pay a weekly visit to the church B. To do this they found it necessary to cross each of the eight bridges shown. At first they crossed some of the bridges two or three times in order to get around and see all the people. But after a while they were able to figure out a plan whereby they could get from A to B and pass over each of the eight bridges only once.
Can you map out the route the elders of Königsberg took on their weekly stroll?
See here for the solution given by the Children’s Friend. Is there a better solution?
They did cheat! But, seriously, there would have been a whole lot of frustrated children (and parents) in the church that month if they had written the problem in its classical form. And they couldn’t have consulted Wikipedia to discover that an eminent mathematician, Leonhard Euler, had proved that the 7-bridge problem had no solution.
Sadly, I don’t remember my six-year-old self attempting to solve this puzzle.
There are several solutions to this.
There was an elder on my mission who gave the original problem to other missionaries (especially to those he didn’t like). Some kept trying to solve it for several transfers. I was actually able to solve it with little trick. His rules were loose enough (basically don’t lift the pen from the paper). I folded the paper and thus created an additional “bridge”.
Heh, heh — I like the way you think, Niklas.
This brought to mind the Sister Missionaries of Regensburg. Specifically, my wife was a missionary there, and the sister missionaries lived on a mile long island in the middle of the Danube River. I pulled up a map and asked her to tell me about it again. She mentioned the ancient stone bridge she would cross every day, and one time after teaching off to the southwest, coming home to the island by another bridge and having a delightful bike ride along the western stretch of the island. “I’ll have to say, it was pretty neat living on that river. Very beautiful”
I love it, John.
I can’t tell you how happy it makes me to see Leonard Euler and the bridges of Königsberg on Keepa.
If there is anything virtuous, lovely, or of good report or praiseworthy, Mike, we seek after these things. 😀
My kids used to get annoyed at me when I’d jokingly solve mazes by going directly from start to finish by going around the entire maze—and here I find my approach effectively endorsed by the Children’s Friend! Go figure.