## [not] Le Monde puzzle

**I**n the spirit of the mathematical puzzles of ** Le Monde**, here is a puzzle that came to me during a family reunion last weekend.

During a dinner of 20 couples sitting at four tables with ten seats, everyone wants to share a table with everyone. The assembly decides to switch seats after each serving towards this goal. What is the minimal number of servings needed to ensure that every couple shared a table with every other couple at some point? And what is the optimal switching strategy?

**O**f course, extension of the solution to *k* couples,* n* tables and *p* seats (with *k<np*) would be great!

April 14, 2012 at 7:32 pm

This problem was actually suggested by my daughter Rachel, as she reminded me yesterday!

April 12, 2012 at 12:12 pm

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