We give take home problems and have no issue with plagiarism. In fact we actively say use the internet, books, etc..., and we still get solutions that are wrong or do not even compile.
The ones that do come back and look good, give us a starting point for the interview. If the person did just copy it from somewhere else they have will have a hard time talking about the solution and various pros/cons.
This is how we do things as well. When I walk around our office I always see people looking at SO, Google and others. Why would I hold a candidate to a different standard?
