@acer I dont get a numerical answer to your final two lines of code. just returns the above.

using maple 18.

@Carl Love 

the quote comes from pp 25 of  http://www.nessis.org/nessis11/marcus.pdf 

which references pp8-10 http://www.ratingscentral.com/Doc/NewTTRS.pdf 

see also

http://www.ratingscentral.com/HowItWorks.php

BTW I did contact the author......

@Carl Love Fantastic! Here is the result of 3 iterations.

I wonder if you or someone else can assist in speeding up the calculation. according to the paper  "Because integrands are functions of playing-strength difference, integrals are convolutions and may be rapidly calculated via the FFT". any suggestions for my maple sheet?

@Kitonum 

found this at:

http://us4.campaign-archive1.com/?u=6ae8427d1f6f3b8d6da57d629&id=b8168c8f89&e=77fe5c923a

Thanks @Kitonum and C.Love. Happy xmas /new year

@Kitonum 

i'll have to take your word for it.  for 1. when i run it, it takes a long time and i get error "maple cannot allocate enough memory...". i'm using M18, 64bit, 2GHz,8GB ram

well done Kitonum. this extends this worksheet by Dr Khan

http://www.maplesoft.com/applications/view.aspx?SID=4901

given seeds [25,75,1,8,5,10] and the aim is 863 how can NumbersGame produce a similar output to

(25+75-5)x(10-1)+ 8.

(each seed can only be used as many times as it appears).

@acer nd Kitonum thanks

In case your wondering....

You would get a better response from forum members if you demonstrated you had a go at the problem beforehand, instead of expecting us to do your homework for you.

@acer too easy...

Thanks @Carl Love and Kitonum

@Carl Love thanks for your efforts. But can u do it  to suit  M15 cause that's all I've got.

@Carl Love 

Re the aside, maybe I didn't explain myself. Looking at the output of res[2], I want to extract the non-zero answers.
In the above expression, x[3]=6. For ease of reading, I want it to report "30=6x5" or "30=5+5+5+5+5+5".So it needs to map the third prime as a multiple of 6.

As another example, PF(44,10) yields x[1]=1,x[6]=1,x[10]=1. I want "44=2+13+29"

@Carl Love it would be more instructive for maple to report an error or display "undefined" rather than a definative answer like "false".

@Kitonum 

thanks for your interest.

But when i put in these values, unless i've cocked up, the tests for square and triangular number fail:

unprotect(D);
> d:=3515820*n;                             

          5.414603381 10^206543 
> B:= (1243419/585970)*d; D:= (367903/175791)*d; W:= (246821/83710)*d; Y:= (125739/106540)*d; b:= (815541/585970)*d;  w:= (17158/8371)*d; y:= (1813071/1171940)*d;
                                   

> B+D+W+Y+b+d+w+y;
                         7.760263432 10^206544 
> is(sqrt(W+B),integer);
                             false
> is(-3/2+(1/2)*sqrt(1+8*(D+Y)),integer);
                             false