A simple solution to Ulam's liar game with one lie

TL;DR

This paper provides a straightforward proof for the minimum number of yes/no questions needed to identify an integer between one and one million when one untruthful answer is permitted, confirming Pelc's result.

Contribution

The paper offers a simple, accessible proof of Ulam's liar game solution for the case of one allowed lie, simplifying previous complex proofs.

Findings

Number of questions needed is 25 for one million integers with one lie allowed.

Provides a simplified proof of Pelc's result on Ulam's liar game.

Confirms the optimality of the question count in this setting.

Abstract

Ulam asked for the maximum number of questions required to determine an integer between one and one million by asking questions whose answer is `Yes' or `No' and where one untruthful answer is allowed. Pelc showed that the number of questions required is 25. Here we give a simple proof of this result.