Question 69
The natural numbers are arranged in a triangular table:$$\begin{array}{ccccccc}&&&1&&&\\&&2&3&4&&\\&5&6&7&8&9&\\10&11&12&13&14&15&16\end{array}$$The position of $N$ is the pair consisting of the first number in its row and the first number in its column. For instance 15 has position $(10,9)$. A number in position $(n,m)$ is well placed when $N=n+m$;12 and 14 are well placed, but 15 is not. Is $2^{2011}$ well placed?