MathDB

11

people are sitting around a circle table, orderly (means that the distance between two adjacent persons is equal to others) and

11

cards with numbers

1

11

are given to them. Some may have no card and some may have more than

1

card. In each round, one [and only one] can give one of his cards with number

i

to his adjacent person if after and before the round, the locations of the cards with numbers

i-1,i,i+1

don’t make an acute-angled triangle. (Card with number

0

means the card with number

11

and card with number

12

means the card with number

1

!) Suppose that the cards are given to the persons regularly clockwise. (Mean that the number of the cards in the clockwise direction is increasing.) Prove that the cards can’t be gathered at one person.

Problem Statement