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Product / Decision Making questions require understanding of core concepts and practice. PracHub provides solutions with explanations to help you master product / decision making interviews.

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This is a medium difficulty Product / Decision Making question, commonly asked during Onsite rounds at TikTok.

What role is this question designed for?

This question is commonly asked for Product Manager candidates at TikTok during technical interviews.

Secretary Problem – Selecting the Most Valuable Painting

Last updated: Mar 29, 2026

Quick Overview

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.

TikTok

Jul 4, 2025, 8:28 PM

Product Manager

Onsite

Product / Decision Making

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?

Solution

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