Question 54
Artur and Dinah will play in the match or odd match. Dinah chooses "par" and Arthur chooses "Odd". Then each writes a positive integer on a sheet of paper without the other seeing it. Emilio collects the two sheets, multiplies the numbers and declares Dinah winner if the result is even and Arthur is the winner if it is odd.
a) How should Dinah do so that she always wins the game? Emilio suggests a modification in the dispute. First he asks Arthur and Dinah to write only numbers that are not divisible by three. He collects the sheets, multiplies the two numbers, divides the result by three, and declares Dinah winner if the rest of the division equals 1 and Arthur is the winner if that remainder is equal to 2.
b) Shows that Dinah can no longer have a winning strategy.
c) Show that Arthur and Dinah have the same probability of winning.
a) How should Dinah do so that she always wins the game? Emilio suggests a modification in the dispute. First he asks Arthur and Dinah to write only numbers that are not divisible by three. He collects the sheets, multiplies the two numbers, divides the result by three, and declares Dinah winner if the rest of the division equals 1 and Arthur is the winner if that remainder is equal to 2.
b) Shows that Dinah can no longer have a winning strategy.
c) Show that Arthur and Dinah have the same probability of winning.