LadybugClockPuzzleSim.scala

object LadybugClockPuzzleSim extends App {
import scala.util.Random

def mod(a: Int, b: Int) = (a % b + b) % b

val ns = (0 until 11).toSet

def rd: Int = Random.nextInt(2) * 2 - 1

val iterMoves = Iterator.continually(rd)

println(iterMoves.take(10).toSeq)

val debug = false

def sim(): Int = {

val iter = Iterator.iterate(11)(n => mod(n + rd,12))

val nSet = scala.collection.mutable.Set[Int]()

val visits = iter.takeWhile(n => { nSet.add(n); !ns.subsetOf(nSet) } ).toSeq

  if (debug) {
    println(s"v = $visits")
    println(s"last = ${visits.last}")
    println(s"size ${visits.size}")
    println(s"$nSet, ${nSet.size}")
  }
 
visits.last
}


val runs = 1000000

val counts = Iterator.continually(sim()).take(runs).toSeq.groupMapReduce(identity)(_ => 1)(_ + _)

println(counts)

val probabilities = counts.map{case(k, v)=> k -> v/runs.toDouble}

println(probabilities)

}

Notes.md

The ladybug clock puzzle

https://www.youtube.com/shorts/t3jZ2xGOvYg

https://onecompiler.com/scala/44b3ge6cg