Riddles, brain puzzles and mathematical problems

[BAndrew]

This is a classic. Some of you might know it.


We have 10 containers. Each container has a different type of gas. You know that the gases weight the same, except for one which has double the weight from the other gases. You want to find the heavier gas. You don't know where it is (i.e. you don't know in which container it is). You have a special electronic scale at your disposal, but it has enough energy for only one weighing. You can weight a combination of gases and you can weight the same gas (from the same container) multiple times. The only restriction is that you must find the heavier gas in only one weighing.

For example let's name the gases a,b,c,d,e,f,g,h,i,j (each gas from the corresponding container)

We can in one weighing calculate the value/weight of 2a + b + c +d + e + f + g +h + i + 3j or whatever combination we want.