MathDB

Nils is playing a game with a bag originally containing

n

red and one black marble. He begins with a fortune equal to

1

. In each move he picks a real number

x

with

0 \le x \le y

, where his present fortune is

y

. Then he draws a marble from the bag. If the marble is red, his fortune increases by

x

, but if it is black, it decreases by

x

. The game is over after

n

moves when there is only a single marble left. In each move Nils chooses

x

so that he ensures a final fortune greater or equal to

Y

. What is the largest possible value of

Y

Problem Statement