perplexus.info :: Just Math : Expanding the railroad line

Expanding the railroad line (Posted on 2017-12-26)

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

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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

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