My attempt at Tony Morris's refactoring puzzle - see http://tmorris.net/posts/refactoring-puzzle/index.html

gistfile1.scala

object RefactorPuzzle {
  case class IntRdr[+A](read: Int => A) {
    def map[B](f: A => B): IntRdr[B] =
      IntRdr(f compose read)

    def flatMap[B](f: A => IntRdr[B]): IntRdr[B] =
      IntRdr(n => f(read(n)).read(n))
  }

  object IntRdr {
    def apply[A](a: A): IntRdr[A] =
      IntRdr(_ => a)
  }

  // Return all the Some values, or None if not all are Some.
  def runOptions[A](x: List[Option[A]]): Option[List[A]] =
    x.foldRight[Option[List[A]]](Option(Nil))((a, b) => a.flatMap(aa => b.map(aa :: _)))

  // Apply an Int to a list of int readers and return the list of return values.
  def runIntRdrs[A](x: List[IntRdr[A]]): IntRdr[List[A]] =
    x.foldRight[IntRdr[List[A]]](IntRdr(Nil))((a, b) => a.flatMap(aa => b.map(aa :: _)))

  // Code Duplication

  // *******      *************      *******      ***********
  // def runOptions[A](x: List[Option[A]]): Option[List[A]] =
  // def runIntRdrs[A](x: List[IntRdr[A]]): IntRdr[List[A]] =

  // ************      ***********      *************************************************
  // x.foldRight[Option[List[A]]](Option(Nil))((a, b) => a.flatMap(aa => b.map(aa :: _)))
  // x.foldRight[IntRdr[List[A]]](IntRdr(Nil))((a, b) => a.flatMap(aa => b.map(aa :: _)))

  //////////////////////////
  // My refactoring below //
  //////////////////////////

  trait RefactorPuzzleMonad[C[_]] {
    def point[A](a: A): C[A]
    def flatMap[A, B](m: C[A])(f: A => C[B]): C[B]
    def map[A, B](m: C[A])(f: A => B): C[B] = flatMap(m)(a => point(f(a)))
  }

  implicit val optMon: RefactorPuzzleMonad[Option] = new RefactorPuzzleMonad[Option] {
    def point[A](a: A): Option[A] = Some(a)
    def flatMap[A, B](m: Option[A])(f: (A) => Option[B]): Option[B] = m flatMap f
  }

  implicit val intRdrMon: RefactorPuzzleMonad[IntRdr] = new RefactorPuzzleMonad[IntRdr] {
    def point[A](a: A): IntRdr[A] = IntRdr(a)
    def flatMap[A, B](m: IntRdr[A])(f: (A) => IntRdr[B]): IntRdr[B] = m flatMap f
  }

  def runFoldR[A, C[_]](x: List[C[A]])(implicit m: RefactorPuzzleMonad[C]): C[List[A]] =
     x.foldRight(m.point(Nil: List[A]))((elem, acc) => m.flatMap(elem)(aa => m.map(acc)(aa :: _)))
}

That works but it doesn't need to be a Monad. An Applicative is enough.

Updated following Tony's comments