All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars    
perplexus dot info

Home > Just Math
Expanding the railroad line (Posted on 2017-12-26) Difficulty: 3 of 5
Each of the n stations on the national railroad sells tickets to all other stations.
If m new stations will be added, 46 additional sets of tickets will be printed.

How many stations are operating now?
How many new stations are to be added?

No Solution Yet Submitted by Ady TZIDON    
No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
spoiler | Comment 1 of 2
Since each stations offers tickets to each of the other stations, the total tickets offered is n(n-1).  Adding m new stations, the total rises to (n+m)(n+m-1).

Taking the difference we get m(m+2n-1)=46.

m will factor 46 and m=46 and m=23 lead to negative values for n.

Then we're left with two solutions (n,m)=(23,1) and (11,2).  Unless we take literally 'stations' as meaning more than one new station, both pairs solve the problem.

23 stations printed 506 distinct tickets and 24 stations will print 552.

11 stations printed 110 distinct tickets and 13 stations will print 156.

Edited on December 26, 2017, 9:37 am
  Posted by xdog on 2017-12-26 09:36:49

Please log in:
Login:
Password:
Remember me:
Sign up! | Forgot password


Search:
Search body:
Forums (0)
Newest Problems
Random Problem
FAQ | About This Site
Site Statistics
New Comments (6)
Unsolved Problems
Top Rated Problems
This month's top
Most Commented On

Chatterbox:
Copyright © 2002 - 2018 by Animus Pactum Consulting. All rights reserved. Privacy Information