An original math problem

[thylacine]

<font color="white"> O(\sqrt(n)) I guess. Not my area. Strategy, choose more common remaining color. </font>

[bigpooch]

It was your post on SMP that inspired me to post this
problem; it's helpful for part 3).

[thylacine]

[ QUOTE ]
It was your post on SMP that inspired me to post this
problem; it's helpful for part 3).

[/ QUOTE ]

I see. Nice.

[bigpooch]

Basically, pzhon answered it all but he wasn't explicit
about 4):

<font color="white">
A very rough approximation for the EV of the game for
general n is sqrt(pi*n) - 8 (including the $7 fee for the
privilege of playing) and the expected number of correct
guesses above n/2 is very roughly 1/2[sqrt(pi*n)-1].

It is a mere check to see that the game is +EV for n&gt;=21
and -EV for n&lt;=20.
</font>