The Costco lost-partner problem: an unsolved math puzzle since 1976 whose best proven strategy says roll a die
aakashgupta · x · 2026-10-24
Steve Alpern's rendezvous search problem, posed in 1976, remains unsolved: two people lost in the same area want to find each other — what's the optimal way to move?
A viral video of two men circling a huge water tank illustrates the core difficulty: if both decide to "go left," they walk clockwise in lockstep and never close the distance; if they both turn around simultaneously, they just chase each other. Symmetry is the enemy.
The best proven strategies are randomized — roll a die to break symmetry, and sometimes simply stand still.
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