math pyramides

case class Pyramide(a1: Int, a2: Int, a3: Int, a4: Int) {
  val sum11 = a1 + a2
  val sum12 = a2 + a3
  val sum13 = a3 + a4
  val sum21 = sum11 + sum12
  val sum22 = sum12 + sum13
  val sum = sum21 + sum22

  override def toString: String =
  s"""
     >      | $sum |
     >    | $sum21 | $sum22 |
     >  | $sum11 | $sum12 | $sum13 |
     >| $a1 | $a2 | $a3 | $a4 |""".stripMargin('>')
}

val allPyramides = List(75, 134, 182, 215).permutations.map(l ⇒ Pyramide(l(0), l(1), l(2), l(3))).toList
println("all pyramides:\n" + allPyramides.mkString("\n"))
println(allPyramides.size + " possible pyramides")
println(allPyramides.groupBy(_.sum).keys.size + " different sum at the end")

for (depart ← 1 to 250) {
  val pyramides = List(depart, depart + 1, depart + 2, depart + 3).permutations.map(l ⇒ Pyramide(l(0), l(1), l(2), l(3))).toList
  pyramides.filter(_.sum == 1000).foreach(println)
}

for (sum ← 1000 to 1100 ; depart ← 1 to 250) {
  val pyramide = Pyramide(depart, depart + 1, depart + 2, depart + 3)
  if (pyramide.sum == sum) println(pyramide)
}