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Load the trucks

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. Assume all the payload can fit in one truck.

SOLUTION : Let us start it with a smaller input. If there were only 1 truck, it would have simply gone till 100 miles. Suppose we have 2 trucks, everything else being same. We can take both trucks till 50 miles, so both will be left with half fuel, then we can put all the fuel in 1 truck, and it can further go till 100 miles. So, a total of 150 miles (100/2 + 100/1).

If we have 3 trucks, we can take all 3 trucks till 100/3 miles, so each of them will be left with two-third of fuel. In total they have a fuel equal to capacity of 2 trucks (I simply did 3 X 2/3 = 2). This fuel can be put in 2 trucks. Now, further analysis is same as case with 2 trucks. So, they can go a further 150 miles. So, a total of 183.33 miles (100/3 + 100/2 + 100/1).

Proceeding in this way, 50 trucks will cover a maximum of 100/50 + 100/49 + 100/48 + ...+100/2 +100/1 = 449.920533833

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