Transylvania County, North Carolina, tried to solve its child care shortage by spurring the development of small in-home day care facilities — but the effort ended up creating only two of them. In the mountains of western Colorado, Mesa County’s attempt to create 8,000 child care slots stalled at the 5,000 mark. And in Iowa, the state has crafted a program for publicly funded, privately operated day care centers that has alleviated — but not ended — the child care shortage in the state.