Difficulty: Easy, but fun. A new way to look at averages and the effect of an addition on the average, depending on n.
Difficulty: Linear programming.Any bets this will somehow work out to an integer?
Difficulty: Easy. Once you've got the details right.
Standard instructions for this series: No calculator allowed. Express answers in reduced form. Rationalize denominators. Radicals must be reduced. All numbers are base ten unless otherwise specified. Do not approximate radicals or π. Leave such answers as 1025π or √39, for example. Source: UVM Math Contest
answer 20, answer 21 and answer 21.