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Five transit centers are evenly spaced near the perimeter of a small city. Any two transit centers are connected by exactly one route. Additionally, from each transit center there is one route that extends into the suburbs in the shape of a large colorful lollipop. The five routes passing through the downtown area take 50 minutes to travel for all-stops buses and 40 minutes for express buses that stop only at transfer points. Buses on the remaining routes serve all stops. On perimeter routes they take half an hour to travel between transit centers, and on suburb routes 45 minutes to complete the loop and return to the same transit center.

Buses that enter a transit center are dynamically rerouted using a simple pattern. Each transit center employs the following mechanism independently. Regarless of the originating route, the first two buses are designated as express buses and the next two buses serve all stops in the heart of the city. The next three buses proceed in a clockwise manner among the three remaining routes, and then we start over. The pattern repeats in this rotation, sending out each bus as soon as it arrives.

If a bus driver comes in along a route of 40 minutes or less, he or she must continue operating the bus on whatever route it's reassigned to. Otherwise, the driver gets a break while a relief operator takes over the vehicle. The driver on break will serve as the relief for the next bus coming in on a route of 45 minutes or more. It's like a game of musical chairs, with buses always in use and hopefully only one person driving.

There are 62 operators on duty and as many buses in operation as necessary to keep them busy. How long is the average break?

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# Brain Teaser #91

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