Usenet Newsgroups : rec.puzzles Hall of Fame The rec.puzzles Hall of Fame is a compilation of over 500 of the most popular puzzles that have been posted and discussed in the rec.puzzles newsgroup. In most cases a detailed solution has been provided. Many of these puzzles also appear in Braingle's own collection.

rec.puzzles Newsgroup FAQ Hall of Fame alt.brain.teasers Newsgroup FAQ

This problem is unsolved.  A simple solution called the "Shephard
piano" has area 2.2074+, but this can be improved upon with local
modifications.  A solution exists with area 2.215649+.  It is known
that a maximum area exists, but not whether the shape achieving it is
symmetric, smooth, or even unique.

See Problem G5 in Croft, Falconer, and Guy, _Unsolved Porblems in
Geometry_, Springer-Verlag, 1991.

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