MathDB
13x17 Checkerboard

Source:

March 21, 2008

Problem Statement

A checkerboard of 13 13 rows and 17 17 columns has a number written in each square, beginning in the upper left corner, so that the first row is numbered 1,2,,17 1, 2, \ldots , 17, the second row 18,19,,34 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,,13 1, 2, \ldots , 13, the second column 14,15,,26 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).
<spanclass=latexbold>(A)</span> 222<spanclass=latexbold>(B)</span> 333<spanclass=latexbold>(C)</span> 444<spanclass=latexbold>(D)</span> 555<spanclass=latexbold>(E)</span> 666 <span class='latex-bold'>(A)</span>\ 222 \qquad <span class='latex-bold'>(B)</span>\ 333 \qquad <span class='latex-bold'>(C)</span>\ 444 \qquad <span class='latex-bold'>(D)</span>\ 555 \qquad <span class='latex-bold'>(E)</span>\ 666