This is a a variation of a classic (very old) riddle,
but I don't have a complete solution.
. . I don't know if there is one.
A local hair salon has three hair stylists.You have been told that one of them
is an excellent stylist, one is an average stylist and one is a very poor stylist,
though you do not know which is which.
Every morning, the three stylists style each other's hair.
No stylist styles her own hair, each one works on the hair of exactly one of the other two stylists
and who styles whom is randomly determined.
One day you walk into the salon to get your hair styled.
Which stylist should you select in order to look your very best?
I don't think we can choose the Excellent stylist every time.
When you walk in, choose the stylist with the worst hair.
. . You know that is not the Poor stylist.
So you have chosen either the Excellent or the Average stylist.