Transfer the payload

Puzzle : Given a fleet of 50 trucks, each with a full fuel tank and a range of 100 miles, how far can you deliver a payload? You can transfer the payload from truck to truck, and you can transfer fuel from truck to truck. Extend your answer for n trucks
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solution ==>

point to be kept in mind : it is not given that they have to travel integral distances only .. so don't assume if not given.

in questions like this, usually a series is involved . so keep lookinv for pattern

concept : we should try to minimise the loss of fuel and in the end we should have one truck with full range fuel remaining

we'll have to start with all the trucks in the beginning .
after 2 km notice that we have spent 100 km range fuel and if we drop one truck we'll have 98 km range fuel that can refill all the remaining 49 trucks.

similarly from there after covering every 100 km drop one truck and refill the remaining

for second time , let us travel 'x' km . fuel spent = 49x if we drop one truck we'll have 100 - x fuel and we have to refill 48 trucks to 100 . means
100-x = 48x => x = 100/49

similarly for other distances

we have a series here

100/50 + 100/49 + 100/48 ...+...100/1

it is harmonic progression
approx sum = 450

this is possible only because trucks are allowed to travel non integral distances

final answer is 450 miles