Hang around me long enough and invariably we will end up talking about how even seemingly intractable problems have solutions and how those solutions can be simple. I believe that with the application of enough creativity and brain power an elegant solution will come to the surface.
To me the test for elegant-ness is whether or not experts and the uninitiated both respond by saying: "Wow, what a cool idea!" I find exposure to elegant solutions to be one of the most inspiring things in life and I do what I can to expose myself to this type of greatness as much as possible. Here are a few of my favorite examples:
Rotary International Overhead Funding: All non profits struggle with the same problem: how much donated money should they use to pay for overhead? This is one of those double impact things because any money that goes to overhead does not go to the cause -- and also discourages people from donating. As a long time Rotarian, I am inspired by Rotary International's policy of placing all donations in the bank for three years before spending them, and then using the interest earned to fund overhead. With this policy, Rotary can truthfully state that 100% of your donation goes to the cause.
HBS Case of the Slow Elevator: While it is mostly an urban legend, there is the story of a business school class with the assignment of justifying the installation of faster elevators. The best answer -- install mirrors in each lobby so the customers will not mind waiting for slow elevators.
MicroFinance: Many organizations worldwide have now copied the model established by Grameen Bank to help raise the standard of living of the poorest people on earth. Simply, loan small amounts to women with a business idea. It works and Grameen Bank has now loaned over $7 Billion to 8 million people (in 2009 97% of the recipients were women) in over 83,000 villages.
Gamers Help Science: As reported in The Economist, Seth Cooper from the University of Washington created Foldit, a computer game that uses non-scientists to do useful scientific work. He has attracted 57,000 users who donate their time (while playing the engaging game) to do work that the most sophisticated analytical software tools cannot accomplish.
Wow, what a cool idea!