MathDB

a) Year 1872 Texas 3 gold miners found a peice of gold. They have a coin that with possibility of

\frac 12

it will come each side, and they want to give the piece of gold to one of themselves depending on how the coin will come. Design a fair method (It means that each of the 3 miners will win the piece of gold with possibility of

\frac 13

) for the miners. b) Year 2005, faculty of Mathematics, Sharif university of Technolgy Suppose

0<\alpha<1

and we want to find a way for people name

A

and

B

that the possibity of winning of

A

\alpha

. Is it possible to find this way? c) Year 2005 Ahvaz, Takhti Stadium Two soccer teams have a contest. And we want to choose each player's side with the coin, But we don't know that our coin is fair or not. Find a way to find that coin is fair or not? d) Year 2005,summer In the National mathematical Oympiad in Iran. Each student has a coin and must find a way that the possibility of coin being TAIL is

\alpha

or no. Find a way for the student.

Problem Statement