43rd Swedish 2003 Problem 2 A lecture room has a rectangular array of chairs. There are 6 boys in each row and 8 girls in each column. 15 chairs are unoccupied. What can be said about the number of rows and columns?
(rows,cols) = (71,7), (29,9), (17,13), (15,15), (11,27), (9,69). Solution m rows, n cols. 6m boys, 8n girls, so mn = 6m + 8n + 15, so (m-8)(n-6) = 63. 43rd Swedish 2003 © John Scholes jscholes@kalva.demon.co.uk 11 January 2004 Last corrected/updated 11 Jan 04