Question 10
In how many different ways can we express $2021$ as a sum using the numbers $1,2,4,8,16,32,64,128,256,512,1024$, where it is only allowed to have up to two occurrences of any of these eleven numbers? The order of summation does not matter. For example, $2+1+1$ and $1+2+1$ are considered the same way to express $4$. Show your full solution.