Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

A combinatorics problem on connecting the cities

  1. Dec 17, 2012 #1
    Fifteen cities are planned to be connected in such a way that each city has precisely one road leading to each of five other cities.How many such roads are to be constructed?

    This question was asked in a talent test conducted in our school.
    Last edited: Dec 17, 2012
  2. jcsd
  3. Dec 17, 2012 #2
    5*15=75 which is not an even number. So it is impossible.
  4. Dec 19, 2012 #3
    Hi! Rogerio
    Can you explain me clearly why is it impossible?
  5. Dec 19, 2012 #4


    User Avatar
    2017 Award

    Staff: Mentor

    Assuming that a road always leads from one city to another city, each city has 5 road ends connected to this city, so we have a total of exactly 75 road ends.
    Every road has 2 ends - the total number of road ends has to be even. 75 is not even.
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook