yaworsw/euler-manager

---
:id: 430
:name: Range flips
:url: https://projecteuler.net/problem=430
:content: "<var>N</var> disks are placed in a row, indexed 1 to <var>N</var> from
  left to right.  \nEach disk has a black side and white side. Initially all disks
  show their white side.\n\nAt each turn, two, not necessarily distinct, integers
  <var>A</var> and <var>B</var> between 1 and <var>N</var> (inclusive) are chosen
  uniformly at random.  \nAll disks with an index from <var>A</var> to <var>B</var>
  (inclusive) are flipped.\n\nThe following example shows the case <var>N</var> =
  8. At the first turn <var>A</var> = 5 and <var>B</var> = 2, and at the second turn
  <var>A</var> = 4 and <var>B</var> = 6.\n\n![p430_flips.gif]({{ images_dir }}/p430_flips.gif)\n\nLet
  E(<var>N</var>, <var>M</var>) be the expected number of disks that show their white
  side after <var>M</var> turns.  \nWe can verify that E(3, 1) = 10/9, E(3, 2) = 5/3,
  E(10, 4) ≈ 5.157 and E(100, 10) ≈ 51.893.\n\nFind E(10<sup>10</sup>, 4000).  \nGive
  your answer rounded to 2 decimal places behind the decimal point.\n\n"