Can anybody explain to me why the outer for-loop loops len(letter) times ?
Is it because each iteration through the outer for loop decides the final position of exactly one letter ?

My solution is similar except that I just kept the outer for loop going until the inner for loop resulted in no swaps at all.

The circuit is X3X4X2X1 with a right angle at X3, X4, X2. Read the description and don't worry too much:-)

If the towns that need to be visited are in this order : X3 -> X4 -> X2 -> X1 (because the friends are in this order)
what is the circuit here ? In particular how does the granny travel from X4 to X2 ?

Thanks for your feedback!