I read this beautiful puzzle in the book “Invitation to a Mathematical Festival” by Ivan Yashchenko.
Take a look at the figure below. A tourist wants to walk along the streets of Old Town from the train station (A) to his hotel (B). He wants the route to be as long as possible, but without visiting the same intersection twice, since he finds it boring. Draw the longest such route on the map, and prove that nothing longer is possible.
Please send your answers either directly on the blog site as comments, or to me at firstname.lastname@example.org. If you like the puzzle, please share it with others. If you have interesting puzzles to share, please send them to me at my e-mail given above.
Happy visiting the Old Town!