object Main extends App {
	case class State(a: Int, b: Int, sum:Int, mul:Int)
 
    val allPossibleStates:Seq[State] = for {
      i <- 2 to 99;
      j <- i to 99
    } yield State(i,j,i+j,i*j)
 
    //Atlasām kopu ar visiem reizinājumiem, kuri ir iespējami - iegūstami vismaz 2 veidos
    val allPossibleMultiplications:Set[Int] = allPossibleStates
      .groupBy(_.mul)
      .collect{ case (key, seq) if seq.size >= 2 => key}
      .toSet
 
    //Tā kā Pēteris zināja, ka Jānis nezin, tad iespējami ir tikai tie varianti,
    //kuru summas var sadalīt saskaitāmajos, kuru reizinājumi ir iegūstami vismaz 2 veidos
    val petersStates:Seq[State] = allPossibleStates
      .groupBy(_.sum)
      .collect{case (key, seq) if seq.forall { el => allPossibleMultiplications.contains(el.mul) } => seq}
      .flatten
      .toSeq
 
    //Tā kā Jānis tagad zin atbildi, tas nozīmē, ka derīgi ir tikai tie stāvokļi,
    //kuros reizinājumu var iegūt tikai vienā veidā.
    val allPossibleStatesWhenJohnKnows:Seq[State] = petersStates
      .groupBy(_.mul)
      .collect{case (key, seq) if seq.size==1 => seq}
      .flatten
      .toSeq
 
    //Tā kā Pēteris tagad zin atbildi, tas nozīmē, ka derīgi ir tikai tie stāvokļi,
    //kuros summu var iegūt tikai vienā veidā.
    val allPossibleStatesWhenPeterKnows:Seq[State] = allPossibleStatesWhenJohnKnows
      .groupBy(_.sum)
      .collect{case (key, seq) if seq.size==1 => seq}
      .flatten
      .toSeq
 
    println(allPossibleStatesWhenPeterKnows)
}

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