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BMAT 2018 · Question 7 · Optimisation

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The lift in the hotel I am staying in takes 3 seconds to move between consecutive floors and when it stops at a floor it remains stationary for a minimum of 9 seconds to let people in and out. A screen inside the lift shows a list of the floors that it has been requested to stop at. When the lift moves off after stopping at a floor it always stops next at the closest floor on its list. If two floors are equally close in both directions, it continues in the direction in which it was previously travelling. The door of the lift has just closed after I have entered it at floor 11 and added floor 4 to the list of floors to be stopped at. The other floors currently on the list are floors 1, 6, 15 and 24.

Assuming that no further floors are added to the list, what is the minimum time that will elapse before the lift door opens at floor 4?