100 prisoners and a lightbulb -- looking back

TL;DR

This paper reviews the history and recent optimization efforts of the classic 100 prisoners and a lightbulb puzzle, highlighting the author's improvements in reducing the average number of visits needed.

Contribution

The author optimized the communication strategy for the puzzle, lowering the average number of visits from over 3850 to below 3390, and summarizes the historical research and recent developments.

Findings

Optimized communication strategy reduced visits below 3390

No new ideas have emerged after the 2009 improvements

Historical solutions had higher average visits, recent efforts improved efficiency

Abstract

100 prisoners and a light bulb is a long standing mathematical puzzle. The problem was studied mostly in 2002 [5], 2003 [1], and 2004 [3]. Solutions in published articles had average number of visits above 3850, but best solutions on forums had (declared) average number of visits around 3500. I spent some time in 2007-2009 to optimize the communication strategy and I pushed the average number of visits below 3390, seems no new ideas appear after it. Recently I have met several people familiar with published papers from 2002-2003 but not knowing newer results. Even after 2009 several papers on the topic were published where the new results were not mentioned [4]. Whole book was written about the problem [2]. This is why I am writing this summary.