Re: [Phys-L] From a Math Prof (physics BS major) at my institution ( math challenge)

[Jeffrey Schnick <JSchnick@Anselm.Edu>]

> -----Original Message-----
> From: Phys-l [mailto:phys-l-bounces@phys-l.org] On Behalf Of Paul Nord
> Sent: Wednesday, February 26, 2014 5:47 PM
> To: Phys-L@Phys-L.org
> Subject: Re: [Phys-L] From a Math Prof (physics BS major) at my institution (
> math challenge)
>
> Is this with the same random seed?  If this is the same random seed, it is
> pretty obvious where you've cut the tail of the distribution.
>
> It does look like some of your most improbable events became more
> frequent.  But something that happens two times out of a million may need a
> larger statistical sample to be convincing.
>
> Why are you summing over sets of 21?
>
> Paul
>
>
> On Feb 26, 2014, at 3:50 PM, Jeffrey Schnick <JSchnick@Anselm.Edu> wrote:
>
> Old Code:
> > > getdist(1000000)
> totalrounds =           49     482    2723    9827   25707   52175   86488
> totalseq2 =              0      14     136     739    2712    7811   18039
> total =                  0       0       0      18     147    1063    5289
>
> > Here are the results with the new code:
> >
> > octave-3.2.4.exe:13> getdist2(1000000)
> > totalrounds =          46     436    2662    9580   25606   52869   87332
> > totalseq2 =             2      17     143     787    2708    7775   18031
> > total =                 0       0       1       9     161    1120    5359
> >
> > Elapsed time is 14113 seconds.
> > -----------------

Here are results using randperm.  (Code is below.)

octave-3.2.4.exe:46> getdist3(1000000)
totalrounds =      40     512    2824    9605   25362   52382   86908
totalseq2 =       1      12     174     786    2667    7612   17914
total =      0      0      1      9    142   1051   5341

Elapsed time is 60948 seconds.

> > Key:
> > Each result is 21 sets of 5 unique numbers between 1 and 35 inclusive.
> > totalrounds(1) = number of results with zero round numbers (10,20,30)
> > totalrounds(2) = number of results with one round number.
> > totalrounds(i) = number of results with i-1 round numbers.
> >
> > totalseq2(1) = number of results with zero sequences of two numbers in a
> row.
> > totalseq2(2) = number of results with one sequence of two numbers in a
> row.
> > totalseq2(i) = number of results with i-1 sequences of two numbers in a
> row.
> > total(1) = number of results with zero round numbers and zero sequences
> of two numbers in a row.
> > total(2) = number of results with one OR FEWER round numbers and one
> OR FEWER sequences of two numbers in a row.
> > total(i) = number of results with i-1 OR FEWER round numbers and i-1 OR
> FEWER sequences of two numbers in a row.
> > ------------------------
function dummy = getdist3(n)
    tic
    for m=1:n
        a=[ randperm(35)(1:5); randperm(35)(1:5); randperm(35)(1:5); ...
            randperm(35)(1:5); randperm(35)(1:5); randperm(35)(1:5); ...
            randperm(35)(1:5); randperm(35)(1:5); randperm(35)(1:5); ...
            randperm(35)(1:5); randperm(35)(1:5); randperm(35)(1:5); ...
            randperm(35)(1:5); randperm(35)(1:5); randperm(35)(1:5); ...
            randperm(35)(1:5); randperm(35)(1:5); randperm(35)(1:5); ...
            randperm(35)(1:5); randperm(35)(1:5); randperm(35)(1:5); ];
        a=sort(a,2);
        nrounds(m)=sum(10==a(:)) + sum(20==a(:)) + sum(30==a(:));
        nseq2(m)=0;
        for i=1:21
            b=diff(a(i,:));
            nseq2(m)=nseq2(m)+sum(1==b);
        end
    end


    for i=0:6
        totalrounds(i+1)=sum(i==nrounds);
    end
    totalrounds=totalrounds
    
    for i=0:6
        totalseq2(i+1)=sum(i==nseq2);
    end
    totalseq2=totalseq2
    
    for i=0:6
        total(i+1)= sum( nseq2<=i & nrounds<=i );
    end
    total=total
    
    toc