Three baskets and transferring apples This is from a math contest, and I do not have the idea how to approach it:

There are 6, 7, and 11 apples in three baskets. The goal is to make
  all basket contain equal number of apples, but while transferring
  apples from one basket to another, one can transfer only the number of
  apples that is already contained in destination basket. Also, only
  three such transfers are allowed. Is that possible?

Obviously, the answer can be deduced by computer brute force simulation, but this is not the spirit of the desired answer.
I appreciate any idea.

From the rules it is obvious that you have to make transfers from baskets with more apples to baskets with less apples. Moreover, you have in total $24$ apples which means that you should aim at $8$ apples per basket (if possible). 
Now, working backwards, before the third transfer you need to make the move $$(8,4,12)\to(8,8,8)$$ But in order to achieve the state $(8,4,12)$ you need to go back to the first step and think of making all numbers even. Therefore a good initial transfer is $$(6,7,11)\to(6,14,4)$$ Now this allows the second transfer to be $$(6,14,4)\to(12,8,4)$$ and you are done. Summing up $$(7,11,6)\to(14,4,6)\to(8,4,12)\to(8,8,8)$$
