When dropped in System 1 the head of the UA points to
Merope while the tail of the UA points to System A
When dropped in System 2 the head of the UA points to
Merope while the tail of the UA points to System B
When dropped in System 3 the head of the UA points to
Merope while the tail of the UA points to System C
When dropped in System 4 the head of the UA points to
Merope while the tail of the UA points to System D
When dropped in System 5 the head of the UA points to
Merope while the tail of the UA points to System E
When dropped in System 6 the head of the UA points to
Merope while the tail of the UA points to System F
When dropped in System 7 the head of the UA points to
Merope while the tail of the UA points to System G
The common system is Merope. Logically, that is the information that the "pointing" mechanic gives us.
Continue this for all 400 billion systems in the galaxy and you will have the UA head pointing to 1 common system... Merope. The UA points to Merope.
Drop the UA ten times, and out of those 10 times, tell me how many times the head points to Merope.
http://i.imgur.com/e4P5pGF.png