yaworsw/euler-manager

---
:id: 339
:name: Peredur fab Efrawg
:url: https://projecteuler.net/problem=339
:content: "_\"And he came towards a valley, through which ran a river; and the borders
  of the valley were wooded, and on each side of the river were level meadows. And
  on one side of the river he saw a flock of white sheep, and on the other a flock
  of black sheep. And whenever one of the white sheep bleated, one of the black sheep
  would cross over and become white; and when one of the black sheep bleated, one
  of the white sheep would cross over and become black.\"_  \n[en.wikisource.org](http://en.wikisource.org/wiki/The_Mabinogion/Peredur_the_Son_of_Evrawc)\n\nInitially
  each flock consists of <var>n</var> sheep. Each sheep (regardless of colour) is
  equally likely to be the next sheep to bleat. After a sheep has bleated and a sheep
  from the other flock has crossed over, Peredur may remove a number of white sheep
  in order to maximize the expected final number of black sheep. Let E(<var>n</var>)
  be the expected final number of black sheep if Peredur uses an optimal strategy.\n\nYou
  are given that E(5) = 6.871346 rounded to 6 places behind the decimal point.  \nFind
  E(10 000) and give your answer rounded to 6 places behind the decimal point.\n\n"