This is a beautiful geometry puzzle that my friend, Alok Mittal, gave to children in his Mathematical Circles class yesterday.
There are four towns at the corners of a perfect square with a side of 1 km. Your task is to connect these towns through a railroad such that all the four towns are connected such that the length of the railroad is the smallest. As an example, if you connect all the four sides of the square, then the length of the railroad is 4 km. If you connect any three sides, all the four towns are still connected, and the length is 3 km. Can you do better?
As always, please send your answers directly 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.