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# Lift Problem Watch

1. A lift is placed in a building of floors labelled 0 to . Before the lift departs the th floor, the number of people in the lift is . Once people have got off the lift they cannot go back onto it. Initially the lift is at floor 0 and moves upwards. Given that an individual can travel upwards no further than 2 floors (e.g. a person who gets on at floor 1 must leave the lift at the latest at floor 3), find the minimum number of people that use the lift in its first upwards pass.

I have modelled it for numerical scenarios e.g. 5 floors
ON OFF
floor 0 : 1 0
floor 1 : 3 0
floor 2 : 3 1
floor 3 : 1 3
floor 4 : 0 3

I notice that it appears to produce another binomial expansion of but I am not sure how to prove it algebraically.

Any pointers.

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Updated: September 2, 2016
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