This puzzle is unsolved. I don't know if there is a solution or how to solve it. I'm also not sure what type of puzzle this would be, so if anyone wants to correct the tags, feel free.
Imagine you have 38 Janets, one of whom is hiding a device which will reboot the Earth and all of humanity. The Judge is trying to find said device by searching each Janet one at a time, which might take her a minute or more. After her search, the Judge will kill the Janet if the Janet doesn't have the earth-rebooter-thingy.
The Janets are arranged in a line from left to right.
The Judge can start anywhere in the line and go in either direction, but once she starts in that direction, she can't change direction until she gets to the end of the line and has to start again.
The Janets don't know where or from which Janet the Judge is going to start searching.
The Judge finding the device is inevitable.
The Janets want to delay finding the device for as long as possible.
The question is, how would you decide beforehand which Janet to give the earth-rebooter-thingy to maximise the time it takes to find? Is this a solvable problem?