The complexity for change

I travel by the muni (public transport system in SFO, USA) to work, and you usually get a months pass for it. This month since I was traveling (out of USA) for most of it I decided to get a ticket for each trip, daily and twice a day after my return. The fare is 1.50 $.

Here is where it begins. The vending machine at my home stop will accept bills and coins, and will return change, but is out of service almost all the time. The option is to buy the ticket on the train, where the machine accepts 1$ bills only and any coins, but will not return money. So you need exactly $1.50 in change.

The question is what do you do to get change. At the embarcadero station, the station around where I work, there is a machine (say machine 1) that will change 20 $ and 10 $ bills for smaller bills. There is also a machine that will accept $ 1 bill (say machine 2) and give you change in coins. There is another machine (say machine 3) that will accept $1 and $5 bills and will give you 1 $ coins.

The ticket gate at the embarcadero station, where I pay the fare of $1.50 accepts only coins, and does not return change.

Here is the tricky maths. I had 20 $ bill. I ran in through machine 1, and got 2 # of 10 $ bills. I ran one fo the 10$ bills through machine 1 again and got two 5 $ bills. So, now I have 1# of 10 $ bill and 2 # of 5 $ bills of the initial 20$ that I had. I now ran the 5 $ bill through machine 3 and got 5# of 1 $ coins. Now I have 5# of 1 $ coins, 1# of 5 $ bill and 1# of 10 $ bill ( again 20 $ in all). I now need to pay $1.50 at the ticket gate in coins, but I only have either 1# of 1$ coin (I still need 5o cents in coins) 0r I have 2# of 1 $ coins (I need to get back 50 cents, which this machine will not give. It will also not give ticket for 2$ even if I am willing to forego my 50 cents). I now need to change 1$ coin to smaller change so as to get 50 cent coins (2 x 25 cents typically). Machine 2 accepts only 1 $ bill (not coin). So, here I am, with access to 3 automated machines, ran around between them, with still no solution to the problem. So, much for automation.

I then go to the newspaper vendor and request him for change, which he gladly gives. Should not all this gadgetry have a solution to this problem?

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