To put this simply,
At level 2,
We have
a) Nanny
b) Son
c) Wife
At level 1 lobby,
a) Maid
b) Butler
At level 1 room in lobby,
a) Cook
Out of the house,
a) Bodyguard
Logically, if we go by elimination process.. since Nanny is with
son and son is not asleep. (Coaxing != sleeping)
There is only Butler, Bodyguard, Wife, Cook and Maid.
1) Given that a strong fight ensued and only one person actually
fought.
We are left with Butler, Bodyguard and Cook, given that both the
maid and wife are not as strong.
Since Maid was at lobby at almost all times with Butler except
during when Butler visit the loo, Butler is already free of
guilt.
To caps it all off, Butler is having a bad stomach, which makes him
unfit to fight.
We're left with the cook and bodyguard. The bodyguard can easily
overcome John so there won't be a struggle and the cook has the
best chance of being undetected..
So there, solved.
While the pair at the lobby went to the dumb roof to see the cat,
the cook climbed up the stairs. The kitchen window is left open
because, the cook killed John but returned through the kitchen
window as he would be caught if he came through the lobby back to
his room. And since the maid is watching horrow show on TV. The
cook could have returned to his room undetected yet forgetting his
stupid window.
