MathDB

A group of

100

students numbered

1

through

100

are playing the following game. The judge writes the numbers

1

2

\ldots

100

100

cards, places them on the table in an arbitrary order and turns them over. The students

1

100

enter the room one by one, and each of them flips

50

of the cards. If among the cards flipped by student

j

there is card

j

, he gains one point. The flipped cards are then turned over again. The students cannot communicate during the game nor can they see the cards flipped by other students. The group wins the game if each student gains a point. Is there a strategy giving the group more than

1

percent of chance to win?

Problem Statement