The numbers $1, 2^{1}, 2^{2}, 2^{3}, 2^{4}, 2^{5}$ are written on the board. It is allowed to erase any two numbers and replace them with their difference - a non-negative number.

Can the number 15 be the only number left on the board after several such operations?
The required sequence of operations is evident from the following record: $15=32-16-(8-4-2-1)$.

## Answer

It can.