This is a relatively simple puzzle from Mathematical Circles by Dmitri Fomin, Sergey Genkin and Ilia Itenberg. Please do share this with your children, they should enjoy this.
In Smallville, there are 15 telephones. Can they be connected by wires so that each telephone is connected with exactly 5 others?
As always, please send your answers as comments within the blog (preferred), or send an e-mail to firstname.lastname@example.org. Please do share the puzzle with others if you like, and please also send puzzles that you have come across that you think I can share in this blog.