MathDB

Addison and Emerson are playing a card game with three rounds. Addison has the cards

1, 3

, and

5

, and Emerson has the cards

2, 4

, and

6

. In advance of the game, both designate each one of their cards to be played for either round one, two, or three. Cards cannot be played for multiple rounds. In each round, both show each other their designated card for that round, and the person with the higher-numbered card wins the round. The person who wins the most rounds wins the game. Let

m/n

be the probability that Emerson wins, where

m

and

n

are relatively prime positive integers. Find

m +n

.
Proposed by Ada Tsui

Problem Statement