When I heard about this, I wrote a Python script to search allrecipes and find solutions (see here: https://github.com/sweeneyrod/three-food-problem). Unfortunately they seem to have changed their website format, so the code doesn't currently work. The most recent generated solutions I can find are: cheese, red wine, rump roast; corn, tart, dill pickle; hot pepper, cocoa, bun; apple, spinach, cup; cheddar, paprika, brown rice; split, tomato paste, maple syrup; crescent roll, cream cheese, apple pie; taco, pie, peanut butter; sour cream, honey, cup; vanilla, maraschino, grape;

As you can see, there are some problems with what things WordNet classes as foods.