[math-fun] squares

Question: You have 9 squares with side lengths 1,2,3,4,5,6,7,8,9. What is the smallest rectangle you can put them in? (smallest meaning smallest in area, and you put them in without overlap) A rectangle with area 1^2+...+9^2 won't work. Is there a standard technique for going at this type of question? I can make a pretty good stab at it, just by trial and error, and I'm fairly convinced I have the best possible, but how does one prove such a thing? Is there a general way to go about this with side lengths 1,2,3,....,n, or even with some random set of squares? Gary McGuire