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Science
Jun 04, 2026
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Scientists Reveal Feynman's Formula for Optimal Holiday Restaurant Selection

AI Summary
Researchers decoded Richard Feynman's unpublished notes and derived a mathematical rule for deciding when to stop trying new restaurants while on a trip. Laboratory experiments with 2,520 participants show a simple linear threshold performs almost as well as Feynman's original solution.

A team of researchers from Princeton and Oxford has uncovered a decades‑old handwritten note by Richard Feynman that formulates a mathematical solution to the classic “restaurant‑stopping” problem faced by travelers.

Decoding Feynman's Hidden Stopping Problem

The study, published in the Proceedings of the National Academy of Sciences, reconstructs Feynman's original equation, which advises diners to keep trying new venues until a quality threshold is met. That threshold is not static; it declines more rapidly as the remaining nights in a city decrease, reflecting the diminishing value of future visits to a discovered gem.

  • Feynman's notes were handwritten in the 1970s after a lunch with friend Ralph Leighton.
  • The model assumes a fixed range of restaurant quality and equal probability of encountering any quality level.
  • When the distribution of restaurant quality is uneven, the optimal threshold shifts—higher when few gems exist, lower when most venues are above average.

Experimental Findings from 2,520 Participants

To test human behaviour, the authors recruited 2,520 volunteers for an online simulation where participants imagined staying in a city for varying lengths of time and chose restaurants from a grid.

  • Participants’ thresholds fell linearly with the proportion of nights remaining, rather than the rapid decline predicted by Feynman's formula.
  • Despite its simplicity, the linear rule performed comparably to the original solution in the simulated environment.

Implications for Decision‑Making and Tourism Behaviour

The findings bridge theoretical optimal‑stopping theory with everyday intuition, suggesting that people naturally adopt a decreasing‑threshold strategy when faced with limited opportunities. This insight could inform:

  • Tourism recommendation engines that adapt suggestions as a trip progresses.
  • Behavioral economics models of consumer search in other domains (e.g., housing, job hunting).
  • Design of AI assistants that balance exploration and exploitation in real‑time.

Future Directions for Adaptive Choice Models

The authors propose extending the model to dynamic environments where restaurant quality distributions change over time, and to incorporate personal preference heterogeneity. Real‑world field trials in travel apps could validate whether a linear decreasing threshold improves user satisfaction and discovery rates.