*To*: mathgroup@smc.vnet.net*Subject*: [mg10907] Re: [mg10817] Random Order of a Set of Numbers*From*: Wouter Meeussen <w.meeussen.vdmcc@vandemoortele.be>*Date*: Thu, 12 Feb 1998 20:15:51 -0500

At 21:01 10.02.98 -0500, JD Faith wrote: >HELP PLEASE... > >I'm a math moron looking for a formula to compute the following problem: >I need to generate a random list of the numbers 1-36, 33 times. The >idea being to replicate the drawing 0f the numbers 1-36 from a hat 33 >times. > >Any assistance is appreciated. Give your buddies a laugh by posting >responses to the Newsgroup or save me some pride by e-mailing me >directly. > >Thank you... > several mails recently touched on the topic of selecting random elements or reordering lists in a certain way. For all cases where numbers are drawn from a hat **without putting the selected numbers back in the hat, giving them a chance to come up again**, this operation amounts to a permutation of these objects. Now, permutations are best handled as ... permutations (on the integers). The add-on DiscreteMath`Permutations` lets you get at random permutations, with the somewhat surprising name RandomPermutation[ size ] (;-)) say that you have a list of 5 objects obj={first, sec, third, fourth,fifth} and you want to permute them, simply do jostle=RandomPermutation[ 5 ]; obj[[ jostle ]] if you define "jostle" with ":=" instead of " =" then you obtain a fresh randomjostle each time it is called\executed. Personally, I would have liked to see the function "Ordering[ list ]" as part of the DiscreteMath`Permutations` packages, instead of the heavy ..`Combinatorica` package where it now resides. It can however be made "by hand" with a one-liner : Ordering[ obj_List]:=Last /@ Sort[Transpose[{ obj , Range[Length[obj]] }] ] this nice function gives the permutation that puts obj into order : obj [[ Ordering @ obj ]] is equivalent to Sort [ obj ] The advantage is that such permutations can be written in cycle form, which makes them easier to "understand" : ToCycles[ ] and FromCycles[ ] will do just that. <<DiscreteMath`Permutations` Table[ RandomPermutation[36] , {33} ] will give J.D. Faith the table he wants. wouter. NV Vandemoortele Coordination Center Oils & Fats Applied Research Prins Albertlaan 79 Postbus 40 B-8870 Izegem (Belgium) Tel: +/32/51/33 21 11 Fax: +/32/51/33 21 75 vdmcc@vandemoortele.be