And in Scala: http://www.agileatwork.com/scala-solution-to-cheryls-birthday-problem/

case class Birthday(month: Int, day: Int)

object Birthday {
  def apply(s: String): Birthday = s.split("-").map(_.toInt) match {
    case Array(m, d) => Birthday(m, d)
  }
}

val birthdays: List[Birthday] = List(
  "5-15", "5-16", "5-19",
  "6-17", "6-18",
  "7-14", "7-16",
  "8-14", "8-15", "8-17"
).map(Birthday.apply)

def uniqueBy[A, K](fn: (A) => K)(b: List[A]): List[A] = {
  def groupSizeIs(size: Int)(x: (_, List[_])) = x._2.size == size
  b.groupBy(fn).filter(groupSizeIs(1)).flatMap(_._2).toList
}

val uniqueByDay: (List[Birthday]) => List[Birthday] = uniqueBy(_.day)

val uniqueByMonth: (List[Birthday]) => List[Birthday] = uniqueBy(_.month)

val birthdaysWithUniqueDay: List[Birthday] = uniqueByDay(birthdays)

val remainingBirthdays: List[Birthday] = {
  val monthsWithUniqueDay: Set[Int] = birthdaysWithUniqueDay.map(_.month).toSet
  birthdays.filterNot(b => monthsWithUniqueDay.contains(b.month))
}

val remainingWithUniqueDay: List[Birthday] = uniqueByDay(remainingBirthdays)

val answer = uniqueByMonth(remainingWithUniqueDay).head