Question 16
Suppose there are 101 persons sitting around a round table in an arbitrary order. The $k$th person possesses $k$ pieces of cards, $k = 1, \dots, 101$. We call it a *transition* if one transits one of his cards to one of his adjacent persons. Find the minimum positive number $k$, such that whatever the order of the seating, there is a way of no more than $k$ transitions so that each person possesses 51 cards.