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 November 1st, 2009, 08:18 AM #1 Newbie   Joined: Nov 2009 Posts: 2 Thanks: 0 Confused Problem How many ways are there to partition a 10 by 12 rectangle into four regions using sides x+a by x+b, where x, a, and b are positive integers? All I got is (x+10)(x+12) and then FOIL I am not sure if this is in any way correct which is why I am stuck. Any help is appreciated. November 1st, 2009, 10:16 AM #2 Member   Joined: Oct 2009 Posts: 39 Thanks: 0 Re: Confused Problem [quote="Scary69l"]How many ways are there to partition a 10 by 12 rectangle into four regions using sides x+a by x+b, where x, a, and b are positive integers? All I got is (x+10)(x+12) and then FOIL I am not sure if this is in any way correct which is why I am stuck. Any help is appreciated.[/quote The point is that BOTH x and a (or b) are integers. So side can be (1, 2, 3, 4...10) or (1, 2, 3...12). It gives you limited number of divisions. Side shows how many, let's called it, degrees of freedom (DOF) we have. If it is x=2 b=2 and a=1 then in 12 side we have of 8 of 4 (x+b) DOF and 9 od 3 (x+a) DOF. 8 because 12-4=8, in other words we can put side x+b in 8 positions. It is for ANY x or a or b. However x+a and x+b must be - if I understand properly the problem - divider of 12 or 10, and we have limitation to sum of them. And here I need clarification: is it that x+a corresponds to side 12 and x+b corresponds to side 10 or should they correspond BOTH? I need it because solution depends of it. For example if x+a corresponds to 12 AND x+b corresponds to 10 THEN we have x in both and it is very narrow 'space' for a and b (as it must be x+a divider of 12 and x+b divider of 10). Please clarify that means conditions. November 1st, 2009, 11:43 AM #3 Newbie   Joined: Nov 2009 Posts: 2 Thanks: 0 Re: Confused Problem I myself am completely confused with the question. Which is why I will probably skip it for now. Thanks for your help  Tags confused, problem Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post unknownuser Computer Science 1 May 29th, 2013 09:03 AM CPaul144 Algebra 3 December 4th, 2011 11:18 PM NathanielZhu Calculus 7 July 28th, 2010 04:42 AM mids1999 Applied Math 1 August 19th, 2009 11:06 AM mr.confused Algebra 1 October 17th, 2008 04:23 PM

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