What is the average area of a random triangle made from three points uniformly chosen from inside of a fixed triangle of area 1?

Anyone having a go?

Air to air refuelling. Tanker has a range r when fully loaded. Fuel use is proportional to weight of aircraft and fuel is 75% of weight of fully fuelled tanker. Plan the flights to land a tanker x.r from take off base and what is number of tankers needed as a function of x?

You have a balance scale again and you only want to carry 4 weight and be able to compare any item to any whole number of units. What is the maximum weight you can compare against or any smaller whole number? Your starter is that having weights of 1 2 4 8 for a max of 15 seems the obvious answer but it is wrong.

There is perhaps an interesting relation to the harder balance scale and jewels problem though I am not sure solving this helps the jewels problem much.