@Kitonum for those of us unenlightened can you show how you derived your formula?

@Carl Love 

@Carl Love thanks.

yes, there are 15 throws (out of 36 states)  which satisfy the given sums (=5/12).

if the number pairs can be generated using combinat:-permute(1,1,2,2,3,3,4,4,5,5,6,6)

would you kindly write some code that will count the pairs which sum to a given number?

eg sum =7-> n=6;  sum=8 -> n=5

play_rank.mw
rank.xls
@Carl Love Sorry to keep bugging you.

When I imported this file into Maple it reported 0's (maybe because the numbers are formula generated). but when i copy-paste-values into another column =, the numbers are impoted but with rabbits ears.

@Carl Love Thanks again.

tested well, only slight problem to report. if S contains a duplicate, then the labeling is confused. eg in the above list replace 30 by 28 and you end up with two H's and no G's.

@Carl Love 

@Carl Love thanks, thats just what I wanted.

An extra Q: If the original set S corresponds to A,B,C...I, (ie A=3,B=4....) is it possible to map the final result back to the corresponding letters. in this case, [{3, 9, 35}, {4, 8, 28}, {5, 6, 30}] = [{A,F,I},{B,.......]

@Kitonum thanks for your efforts.

What about this set :{3, 4, 5, 6, 8, 9, 28, 30, 35}?

Using Evolver I got {5,6,30},{4,8,28}and {3,9,35} as the three groups close to each other as possible

@Carl Love good-o.

its a pity one can't put the character font (eg Bold,Brown Aerial,size=10) into it

@Carl Love how does one create this file with your mods? I tried Edit...Startup Code

@Markiyan Hirnyk try http://www.physics.csbsju.edu/stats/t-test.html

@Markiyan Hirnyk what about student's t tests? inference based on small samples.

http://www.math.wichita.edu/~richardson/mathematics/magic%20squares/even-ordermagicsquares.html

thanks Carl.

As a supplementary question, say you sample the last 10 episodes, and you find the questions were [A,B,C,D,E], [A,B,C,D,F],.... How could you determine if they were truely random selections. I guess there may be a significance test in Maple, but I don't know...

Carl, wonder if you can alter this code to catch the longest sequences <= n for a given AD and output them

for instance, 

I/P:

AD:=210,n:=11

O/P:

7: [47, 257, 467, 677, 887, 1097, 1307] 
10: [199, 409, 619, 829, 1039, 1249, 1459, 1669, 1879, 2089]