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 alokgoyal_2001@yahoo.com. 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.
Happy calling!
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Not possible.
Lets consider 5 slots in each telephone. Every wire will occupy 2 slots. Total slots 15*5=75.
Total wires require = 75/2 = 37.5 which is not an integer. Therefore not possible.
15 telephones and 5 connections means 75 ends – odd number. Not possible as one wire has 2 ends.