It could be proven that for n != 4 there is always 'NO' answer.
Is it right for each test?

e.g. in test 8 n != 4 and answer is 'YES'.
With absolute precision of calculations u will get 'NO'

I read your posts very attentievely, but I didn't understand what exactly you mean.

What's about test:

5
1 0.5
0.654508, 0.975528
0.0954915, 0.793893
0.0954915, 0.206107
0.654508, 0.0244717

I am sure the answer is YES