Question 16
A checkerboard of $13$ rows and $17$ columns has a number written in each square, beginning in the upper left corner, so that the first row is numbered $1,$ $2,$ $\ldots,$ $17,$ the second row $18,$ $19,$ $\ldots,$ $34,$ and so on down the board. If the board is renumbered so that the left column, top to bottom, is $1,$ $2,$ $\ldots,$ $13,$ the second column $14,$ $15,$ $\ldots,$ $26$ and so on across the board, some squares have the same numbers in both numbering systems. Find the sum of the numbers in these squares (under either system).