This is a very nice application of graph theory for children, a puzzle I picked up from the book “Mathematical Circles”, by Dmitri Fomin, Sergey Genkin and Ilia Itenberg.

There is a unique country (lets call it Strangistan), where there are exactly 100 roads between pair of cities and each city has exactly 3 roads going out of it. Show how that is possible or show that it is not possible.

I will be traveling on work and vacation from next weekend, and hence will not be very regular in my posts until the end of June.

As always, please send your answers directly to me at alokgoyal_2001@yahoo.com. 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 traveling on roads in Strangistan.