The Enigma column of New Scientist August 20 2005 issue presents this problem by Bob Walker:
A wind chime, with 10 chimes of lengths 1 cm to 10 cm, placed uniform distances apart around the circumference of a round disk so they are “balanced perfectly.” The 10 lengths of the chimes in this sequence form an 11-digit number. What’s the smallest possible number for balanced chimes?
Charles Petzold is a programmer/author, known to coders for writing a well-regarded text for Windows C developers. He has posted solutions to several New Scientist Enigma problems on his web site as C source code, including the above chime question.