A and B play a game. A has originally $1$ gram of gold and B has an unlimited amount. Each round goes as follows:
- A chooses and displays, $x$, a nonnegative real number no larger than the amount of gold that A has.
- Either B chooses to TAKE. Then A gives B $x$ grams of gold.
- Or B chooses to GIVE. Then B gives A $x$ grams of gold.
B TAKEs $n$ times and GIVEs $n$ times after which the game finishes.
Define $g(X)$ to be the smallest value of $n$ so that A can guarantee to have at least $X$ grams of gold at the end of the game. You are given $g(1.7) = 10$.
Find $g(1.9999)$.
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