Whoops about the "balls" and "boxes"- still thinking about last year :-P
OOPS! I'm still thinking about soccer balls! Whoops! Hope that doesn't get confusing, sorry about that.
Yep, half the boxes should be in a stack:
f(x) = n(x-n) = nx-x^2
f'(x) = n-2x = 0
x = n/2
f''(x) = -2, therefore n/2 is a maximum.
Yeah, the ax^2+bx+c was a clever hint :-D, especially tricky because it implied that there might be a projectile, since this is a generalization of the parabolic path of a flying object...
Unfortunately the c gets messy.
Have fun with the game! Good Luck!
Do you know if boxes on their side will count as 2 boxes?
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