Rows/Columns in Cantor's Diagonal Argument Imagine filling a grid diagonally, like in Cantor's diagonal argument:
\begin{array}{ |c|c|c|c|c|c|} 
 \hline
 1 & 3 & 6 & 10 & 15 & \dots \\ 
 2 & 5 & 9 & 14 & 20 & \dots \\ 
 4 & 8 & 13 & 19 & 26 & \dots \\ 
 7 & 12 & 18 & 25 & 33 & \dots \\ 
 11 & 17 & 24 & 32 & 41 & \dots \\
\vdots & \vdots & \vdots & \vdots & \vdots & \ddots \\
 \hline
\end{array}
My question is, given some $n$, what are the formulae that tell us which row and column it will get put in?
e.g. $C(1) = (1,1)$, $C(2) = (1,2)$, $C(3) = (2,1)$, ... $C(n) = (i_n,j_n)$; what are $i_n$ and $j_n$ in terms of $n$?

We have $C(i,\,j)=C(1,\,i+j-1)-i+1$, which you can write as a quadratic using $C(1,\,j)=j(j+1)/2$. Now you should be able to solve $C(i,\,j)=n$.
