Determining Cheryl's birthday logically with LINQ

gistfile1.cs

// for the problem description see: http://www.cnn.com/2015/04/15/living/feat-cheryl-birthday-math-problem-goes-viral/

	public class Birthday
	{
		public Birthday(string monthName, int dayOfMonth)
		{
			MonthName = monthName;
			DayOfMonth = dayOfMonth;
		}

		public override string ToString()
		{
			return MonthName + " " + DayOfMonth;
		}

		public int DayOfMonth { get; private set; }
		public string MonthName { get; private set; }
	}
	
	[TestFixture]
	public class CherylsBirthdayProblem
	{
		[Test]
		public void Should_be_able_to_determine_Cheryls_birthday_logically()
		{
			var potentialDates = new[]
			                     {
				                     new Birthday("May", 15),
				                     new Birthday("May", 16),
				                     new Birthday("May", 19),
				                     new Birthday("June", 17),
				                     new Birthday("June", 18),
				                     new Birthday("July", 14),
				                     new Birthday("July", 16),
				                     new Birthday("August", 14),
				                     new Birthday("August", 15),
				                     new Birthday("August", 17),
			                     };

			var afterStatement1 = AlbertDoesNotKnowAndKnowsThatBernardDoesNotKnowEither(potentialDates);
			var afterStatement2 = BernardNowKnows(afterStatement1);
			var afterStatement3 = AlbertAlsoKnows(afterStatement2);

			var result = afterStatement3.Single();
			if (result.ToString() != "July 16")
			{
				Assert.Fail("Incorrect result: " + result);
			}
			Console.WriteLine("Cheryl's birthday is " + result);
		}

		public IEnumerable<Birthday> AlbertDoesNotKnowAndKnowsThatBernardDoesNotKnowEither(IEnumerable<Birthday> birthdays)
		{
			// Albert doesn't know the date 
			// => the month he knows has multiple dates
			// Albert knows that Bernard does not know 
			// => the month he knows doesn't have any unique day-of-month values
			//    otherwise there would be the potential that Bernard could know.
			// so eliminate all months where ANY day-of-month is unique across the set

			var matches = birthdays
				.GroupBy(x => x.DayOfMonth)
				.SelectMany(x =>
				{
					var isUnique = !x.Skip(1).Any();
					return x.Select(y => new
					                     {
						                     IsUniqueDayOfMonth = isUnique,
						                     Birthday = y
					                     });
				})
				.GroupBy(x => x.Birthday.MonthName)
				.Where(x => x.All(y => !y.IsUniqueDayOfMonth))
				.SelectMany(x => x)
				.Select(x => x.Birthday);

			return matches;
		}

		public IEnumerable<Birthday> BernardNowKnows(IEnumerable<Birthday> birthdays)
		{
			// Bernard didn't know originally but, because of Albert's statement, now he does 
			// => the day-of-month Bernard knows is now unique
			// so, eliminate all birthdays where the day-of-month is not unique
			return birthdays
				.GroupBy(x => x.DayOfMonth)
				.Where(x => !x.Skip(1).Any())
				.SelectMany(x => x);
		}

		public IEnumerable<Birthday> AlbertAlsoKnows(IEnumerable<Birthday> birthdays)
		{
			// Albert didn't know originally but, because of Bernard's statement, now he does 
			// => the month Bernard knows is now unique
			// so, eliminate all birthdays where the month is not unique
			return birthdays
				.GroupBy(x => x.MonthName)
				.Where(x => !x.Skip(1).Any())
				.SelectMany(x => x);
		}
	}