RE: Best run Olympics to date in terms of cost control was Lillehammer, Norway in 1994. They built almost nothing new and used bulldozers to build natural amphitheaters, erected snow fences and planted trees to make natural windbreaks.
Next best run was probably Salt Lake City, 2002, which built little new and made good use of existing venues, including world class ski resorts.
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Here’s a suggestion — make these two sites the PERMANENT rotating venues for the Winter Olympics ( just like they do the Tennis Grand Slams for Wimbledon and the U.S. Open ).
Antarctica!