Optimal Stopping in a Sequential Picture-Selection Problem

Summary

The document poses a sequential choice problem: a decision-maker visits rooms in order, observes each picture’s value, and may take only one, with the final room forcing a choice. Values are assumed to follow a uniform distribution from one to one hundred. The goal is to choose a rule that maximizes expected proceeds while accounting for the inability to revisit earlier options.

This is an optimal stopping problem, akin to selecting among observed offers with a known value distribution and a finite horizon. A natural analysis would compare the current picture’s value with a continuation threshold that reflects the expected value of later opportunities, with a separate decision at the last room. However, the document only states the setup and hint; it gives no proposed strategy, derivation, or numerical expected payoff. It also does not clarify whether room values are independent draws, an assumption needed for the standard threshold analysis. The text therefore serves as a problem prompt rather than a complete solution.

Key ideas

• The problem allows only one selection from a sequence of observed values.
• Because earlier rooms cannot be revisited, each decision balances taking the current value against waiting.
• A finite horizon means the best continuation rule changes as fewer rooms remain.
• The uniform value distribution is given, but independence between room values is not specified.

Tags

# Interview questions pictures


# Interview questions pictures












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

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.