object Main extends App {
  case class State(a: Int, b: Int, sum:Int, prod:Int)
 
  val allPossibleStates:Seq[State] = for {
    i <- 1 to 99;
    j <- i to 99
  } yield State(i,j,i+j,i*j)
 
  (1 to 7).foldLeft(allPossibleStates)( (states, _) =>  
    states
     .groupBy(_.prod).filter(_._2.size > 1).flatMap(_._2)
     .groupBy(_.sum).filter(_._2.size > 1).flatMap(_._2)
     .toSeq
  ).groupBy(_.prod).filter(_._2.size == 1).flatMap(_._2)   
   .map(println)
}

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