a number theory question for those of you who know more number theory than i do (that would be most of you): i have a rug in my bathroom in the shape of a rectangle, surrounded by a border of constant width, surrounded by another border of constant width. i have often wondered whether any such rug can have integer dimensions with the three areas being equal. in other words, if the center rectangle is L by W, the inner border has width A, and the outer border has width B (with L, W, A, and B all being positive integers), can we have 2LW = (L+2A)(W+2A) and 3LW = (L+2A+2B)(W+2A+2B) ? i looked for small solutions with a computer and couldn't find any. did i not search far enough, or is there some number theoretic reason solutions do not exist? erich