@Carl Love thanks for your input. Is there any way to refine the list further, so no player from either team features twice in each block of 3. 

eg

[[A,X],[B,Y],[C,Z],[B,X],[A,Z],[C,Y],[B,Z],[C,X],[A,Y]]

@mmcdara and @Kitonum 

But what I was really after was a listing of 'practical' permutations, w.r.t the convention: A or B or C on the left, X or Y or Z on the right.

This is an example of an order I don't want:

 [[A, X], [A, Y], [A, Z], [B, X], [B, Y], [B, Z], [C, X], [C, Y],[C, Z]]

player A isn't going to play 3 times in a row ....(nor is B or C)

Here are two valid ones, i'm sure theres more

 [[A,X],[B,Y],[C,Z],[A,Y],[B,Z],[C,X],[A,Z],[B,X],[C,Y]]
 [[A,X],[B,Y],[C,Z],[B,X],[A,Z],[C,Y],[B,Z],[C,X],[A,Y]]

what I want is a method to display them all.

@mmcdara Thank you sir.

@tomleslie the error message was not so cryptic (in retrospect). Thanks

@tomleslie I did overcomplicate it. After I posted I thought, there must be a way to dispense with the x's, but I thought it needed to be a function to use in Explore.

In fact, you can dispense with variable x altogether. In your code set x=l*sin(theta), then it will be only in terms of theta, l and w.

Thanks to Scot too.

@mmcdara The other way to get a is more direct, albeit taking longer. I initially did this but thought I could get 'a' from the physical properties of the material.

restart:
DIV := diff(y(x), x, x) = a*sqrt(1 + diff(y(x), x)^2):
RV  := y(0)=2.6, y(3)=2.1:
sol := rhs(dsolve({DIV, RV}, y(x)));
L   := Int(sqrt(1+diff(sol, x)^2), x=0..3);
a   := select(is, [solve(value(L)=3.6)], positive)[];

EDIT

Just used this method for the triangular sail. For L=4.33m, got a= -1.015016, but with your method +1.015016

Anyway, the sag was ~1.4m for this case

@brian bovril C is a scaling factor

@mmcdara Whats big c? "for instance, let C > 0, and denote..."

@vv Thats got it!  thanks vv.......

@Carl Love I could do ST[2] and get the result I wanted. I did give an upvote if it's any consolation.

@tomleslie 

@tomleslie I like this one liner, but can the input be stripped off its apostrophes?
2 instead of

`2`

'

@mmcdara Thanks.

edited: using numeral 2 rather than name ‘2’ using Carl Loves Table:

rhs(ST[ListTools:-Search(2, lhs~(ST))]):-mu; #doesnt work.
 

@Carl Love My actual function is a product of two Gaussians. Thus no closed-form solution afaik. For the sake of brevity, I supplied the above expression. To avoid this palava, it's a pity sum doesn't have an inbuilt step parameter like seq. Anyways the good news is, by cutting down the number of terms by 10, my calculation time has gone down by a factor of 20.  Thanks for your efforts.

@tomleslieChanging to this convention worked! inadvertent bug discovery...