Challenge the king
A king has \(K\) servants. He ordered them to stand in a circle and numbered them from 1 to \(K\).
He gave to number 1 a sword and ordered him to kill the one next in number and pass the sword until only one left.
(1 kills 2 and passes to 3 and so on)
If the king has 34 servants, 67 servants and 102 servants, which servant will stay last in each of the possibilities?
The Answer will be the sum of all three