Harvard University has posed a challenge to its students: come up with an entrepreneurial solution to the world’s social problems and win $100,000. Harvard president Drew Faust announced the socially conscious contest for young entrepreneurs yesterday. In launching the competition, Harvard joins other Massachusetts universities that run competitions to encourage entrepreneurship. Massachusetts Institute of Technology has been running its $100K Entrepreneurship Competition for 22 years and the University of Massachusetts Amherst has its Innovation Challenge.