Steve Ballmer shares a challenging puzzle question used in Microsoft interviews about guessing a number between 1 and 100, offering monetary rewards based on the number of guesses taken with increasing penalties. Ballmer argues against playing, noting that the game has a negative expected value due to the difficulty of predicting his choice and the rules. Contrary to Ballmer’s statement, further analysis reveals that if he chooses numbers randomly, the game’s expected value is actually $0.20, suggesting the game could be in favor of the player with the right strategy. A potential explanation for this discrepancy is the inclusion or exclusion of the $0 value for six guesses in the game setup.
https://blog.jgc.org/2024/09/steve-ballmers-binary-search-interview.html