//should be private, but made public for tests
public bool WorksFor(BookCollection bookCollection)
{
if (bookCollection.IsEmpty()) return false;
//e.g. a book collection fitting this profile: 1;2;3;3;4;4;5;5
//when grouped by GroupBooks, we would have two groups:
// first group: 1-book-per-title (2 items: (1) ; (2))
// second group: 2-books-per-title (3 items: (3;3) ; (4;4) ; (5;5))
var bookSets = GroupBooks(bookCollection);
bool exactlyTwoQuantitiesOfBooksRemain = bookSets.Count() == 2;
bool theSmallerGroupingContainsBooksSpanningTwoTitles = bookSets.First().Count() == 2;
bool theSmallerGroupingContainsOneBookPerTitle = bookSets.First().Key == 1;
bool theLargerGroupingContainsBooksSpanningThreeTitles = bookSets.Last().Count() == 3;
bool theLargerGroupingContainsTwoBooksPerTitle = bookSets.Last().Key == 2;
return exactlyTwoQuantitiesOfBooksRemain
&& theSmallerGroupingContainsBooksSpanningTwoTitles
&& theSmallerGroupingContainsOneBookPerTitle
&& theLargerGroupingContainsBooksSpanningThreeTitles
&& theLargerGroupingContainsTwoBooksPerTitle;
}
