I got this questions which is quite interesting, I am in a museum, there are 100 rooms (numbered from 1 to 100) in this museum and each room has a picture in it. I go visit each room in the increasing order, but I can't go back in a room that I have already visited. When I am in a room I can steal the picture, earn his value and I have to go out of the museum (meaning that I only can steal one picture and when I am in the room 100 I am forced to steal the picture) or I can leave the picture here and move to the other room. What is your strategy in order to optimize the money you will earn.
Hint : I have assume that the price of the picture follows a uniform distribution from 1 to to 100. Enjoy