Secretary Problem – Selecting the Most Valuable Painting

Q: Secretary Problem – Selecting the Most Valuable Painting

This question evaluates optimal stopping theory, sequential decision-making under uncertainty, and expected-value reasoning in the classic secretary problem framed as a product/decision-making scenario.

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Question

Optimal Stopping: Choosing a Painting from 100 Rooms

You are invited to an island with 100 rooms, each containing one painting. You may enter the rooms one at a time in any order, but you cannot return to previous rooms. Upon seeing a painting, you must decide immediately whether to take it. You may take at most one painting.

Assume you can judge a painting’s value when you see it (cardinal value), and you don’t know which rooms contain which values before entering. Treat the order as effectively random.

What strategy maximizes the expected value of the painting you take?
How does the strategy change if you receive nothing unless you pick the single most valuable painting?

Secretary Problem – Selecting the Most Valuable Painting

Optimal Stopping: Choosing a Painting from 100 Rooms

Solution

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