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 June 12th, 2014, 10:11 PM #1 Senior Member   Joined: Nov 2013 Posts: 247 Thanks: 2 total cuboids possible based on minimum and maximum dimensions Lets assume that all the dimensions are integers. Lets also assume that the minimum dimension of any side is 1 and maximum is 17. How many cuboids are possible excluding perfect cubes and which ones are they? I think it is (17*17*17) - 17 or 17*17*16 which is another way of saying it for the total possibilities - cubes. Why? Well for any 2 dimensions they can be the same so at least 1 has to be different. There are also 17 integer cubes possible from 1x1x1 to 17x17x17 so because I am wanting cuboids that aren't cubes I subtract that from the total possibilities. Last edited by caters; June 12th, 2014 at 10:16 PM. June 14th, 2014, 01:13 PM #2 Senior Member   Joined: Sep 2012 From: British Columbia, Canada Posts: 764 Thanks: 53 I going to assume I'm interpreting your question correctly. You're also going to have to consider repeats. For example, a 2x3x4 cuboid is the same as a 3x2x4 cuboid and a 4x3x2 cuboid. There are 6 duplicates for some cuboids (specifically those with all sides distinct), and only 3 duplicates for others (those with two sides the same). Luckily, there's a formula for combinations with repeats. If you're choosing $r$ objects out of a total of $n$ things, and order doesn't matter but repetition is allowed, then the total number of ways to do this is $\displaystyle \binom{n+r-1}{r}$ In your case, $n=17$ and $r=3$, so the total number of cuboids that fit your criteria is $\displaystyle \binom{17+3-1}{3}-17=\binom{19}{3}-17=952$ Hope this helped. Thanks from caters Tags based, cuboids, dimensions, maximum, minimum, total 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 Mathforfun21 Calculus 1 May 14th, 2013 02:12 AM bilano99 Calculus 7 March 19th, 2013 04:56 PM mathkid Calculus 22 November 8th, 2012 09:19 PM panky Algebra 1 November 6th, 2011 06:59 AM Thrice Calculus 5 November 30th, 2010 11:18 PM

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