The surprising aperitif problem | Tangente

The surprising aperitif problem

Where should a platter of canapés be placed to satisfy the guests as well as possible? This seemingly innocuous problem has inspired brilliant developments over the centuries. It also illustrates how individual and collective optimization are often at odds—a seemingly paradoxical result.

Written by

PHILIPPE BOULANGER

PublishedJune 13, 2024UpdatedSeptember 19, 20261 min read

Several guests are seated around the table when their host brings in a platter laden with tempting canapés. This is an opportunity to begin the aperitif with a little puzzle: where should the platter go? In mathematics, however, we try to clarify precisely what our questions mean. Here, there are two ways to approach the problem of finding the ideal position for the platter.

Two problems for the price of one ---------------------------------

The first is to minimize the sum of the distances from the platter to the guests (problem S ): this is a macro-level optimization problem. The second seeks, whenever possible, to place all the guests at the same minimum distance from the platter (problem E ): here, the aim is to optimize while preserving equality between individuals.

For simplicity, we treat the guests and the platter as points; mathematicians are accustomed to such simplifications. The classic caricature is: "Assume a spherical cow!"

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