## January 29, 2009

### Train & tickets

Every station in a rail road issue every other station's ticket.
Some stations are added. Now they have to issue 46 more tickets.
The number of stations before and after addition is ? Secret Squïrrel said...

If I understand the Q correctly, each station issuing tickets for every other station means that if there are 5 stations, a total of 25 tickets are issued. This will always be a square number.

There is no difference of squares that equals 46 so the problem as it is stated has no solution. Solutions exist for 44 and 48 more tickets.

Sajal said...

if there are n stations thn total tickets issued =n*(n-1)
if k no of more station are added
then tickets issued=(n+k)*(n+k-1)
the difference of two is 46
the equation becomes
(k^2)+(2n-1)(k)-46=0
solve it for integer values
initial stations = 11
total =13 now Secret Squïrrel said...

I understand now! A ticket is not for a station of departure but for a particular destination. Hence, a station does not issue its own tickets - only those for other stations to which you can travel.

11 stations (110 tickets) to 13 (156) is definitely correct.

abhin said...

i think there will be 23 stations before addition and 24 stations after addition....
if there are three stations a,b and c
then total tickets issued in each station equals - 6 - ab,ac,bc,ba,ca,cb
Now if we add one more station we have to add 6 more tickets - ad,bd,cd,da,db,dc (which is - [current number of stations*2])
So for 46 new tickets to be added, the current number of stations have to be 23.