My Math Forum total cuboids possible based on minimum and maximum dimensions

 Probability and Statistics Basic Probability and Statistics Math Forum

 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 Display Modes Linear 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

 Contact - Home - Forums - Cryptocurrency Forum - Top