In a class on magic squares at a large midwestern university, a graduate studnet named Carl was told to write a paper on arranging decimal digits in a 3 by 3 grid. Such an arrangement gives six three-digit positive integers: the three rows (left to right) and the three columns (top to bottom). Carl tried to show that if the integer K divided the three row-integers and the first two column-integers, then it also divided the three-digit integer in the last (right-most) column. Can you help Carl by showing that this is the case?The Answer
It can be shown, with a bit of algebraic amnipulation, that the dixth three-digit integer can be expressed as the sum of multiples of the other five.
NOTE: A complete and detailed solution for this problem may be obtained from the Math and Science secretary in Dana Hall.