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In fact, this five room puzzle is mentioned in the Königsberg article and also has an article of its own:

https://en.wikipedia.org/wiki/Five_room_puzzle

Your grandfather would likely enjoy discussing it with you!

Wow thank you! So I just learned the proper name of this "puzzle", which my father also showed me a long time ago (and for which I used to fill pages and pages of trials even though I knew that it had no solution), and which I tried to render as an "applet toy", a couple of years ago on my blog (see my other comment below).

It's interesting that there exists a solution (shown in the Wikipedia article), if you build the rooms on a torus. That would be the equivalent of digging a tunnel between two rooms.

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