Finding values of S where a square cannot be constructed

[bubokribuck]

Can't do this question :( please someone help

I have managed to do part(A) and the answer I've got is 22 (when S=200). However, I'm stuck at part(B) at the moment. Here's what I've done so far for (B).

I don't know how to work out the values of S for which a square cannot be constructed. Any suggestion or advice please? Thanks!NB: I'm not sure whether this question is classified as "precalculus" or "calculus" so if I've posted in the wrong place please let me know :)

 

[NascentOxygen]

I'm not sure whether I am on the right track, but ...

S = 20a + 11(b+c) +2d
  = 20a + 10(b+c) + b + c + 2d

So,  S - (2d + b + c) = 20a + 10(b + c)

Which can be interpreted as being a multiple of 10.