Problem - 4646
$\textbf{How Far Can You Go}$
There are $50$ motorcycles with a tank that has the capacity to go $100$ km. Using these $50$ motorcycles, what is the maximum distance that you can go?
$\textbf{Answer}$
The maximum distance you can reach is $350$ km.
$\textbf{Analysis}$
The answer is not $100\times 50=5000$ km because this will imply that all these motorcycles need to be pre-placed along the route at intervals of $100$ km. In fact, if the answer were $5000$ km, then this question would not be a brain teaser.
In order to travel as far as possible, we will need to bring all the motorcycles together. After $50$ km, the tanks in all the motorcycles are half-full. Then we consolidate these fuels and move on with $25$ motorcycles with full tanks.