MathDB

16

Part of 2000 AMC 12/AHSME

Problems(1)

13x17 Checkerboard

Source:

3/21/2008
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=′latex−bold′>(A)</span> 222<spanclass=′latex−bold′>(B)</span> 333<spanclass=′latex−bold′>(C)</span> 444<spanclass=′latex−bold′>(D)</span> 555<spanclass=′latex−bold′>(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