# Problem 394: Eating pie
Jeff eats a pie in an unusual way. The pie is circular. He starts with
slicing an initial cut in the pie along a radius. While there is at
least a given fraction F of pie left, he performs the following
procedure: - He makes two slices from the pie centre to any point of
what is remaining of the pie border, any point on the remaining pie
border equally likely. This will divide the remaining pie into three
pieces. - Going counterclockwise from the initial cut, he takes the
first two pie pieces and eats them. When less than a fraction F of pie
remains, he does not repeat this procedure. Instead, he eats all of the
remaining pie. For x ≥ 1, let E(x) be the expected number of times Jeff
repeats the procedure above with F = 1/x. It can be verified that E(1) =
1, E(2) ≈ 1.2676536759, and E(7.5) ≈ 2.1215732071. Find E(40) rounded to
10 decimal places behind the decimal point.