Today, I went to grocery store (named H-E-B) and I got a irresistible offer. Buy 2 Nesquik cereal boxes and get a scholar kit (pencils, erasers, crayons, etc..) with the theme of the movie Kung Fu Panda 2 and also have the opportunity to get an iPad 2 if I win this little game:
Having $n$ players and a rectangular transparent box with measures $w$ for width, $l$ for length and $h$ for height find out how many balls (spouse balls are spherical) with radio $r$ are in the box if the box is full of balls. Each player have to give a guess, and wins the player who give the most correct answer. The correctness is giving in this way $|PlayerAnswer – RealAnswer|$, You win automatically if your correctness is $0$.
Then my question is: Does anyone have a good approach to solve this problem?
Special note: In the real game you don't know the measures.
Update: Video related
Best Answer
Wikipedia gives the approximate density of random packed spheres as $64\%,$ in contrast to the tightest packing of $\frac{\pi}{18}\approx 74\%.$ Good luck.