Question 43

Challenge question #43 (30/01/2017)

Junior Question

Amy and Ben are playing a game. In this game, they are sent to seperate rooms where they cannot communicate with each other.

Each person then flips a coin, and records whether it is a head or a tail. Then, Amy writes down a guess of the result of Ben's flip, and Ben writes down a guess of the result of Amy's flip.

If at least one of the guesses are correct, they win the game, but if they both guess incorrectly, they lose the game.

Amy and Ben are allowed to strategise before entering the separate rooms. What strategy should they use to guarantee that they will win the game?

Hint

Senior Question

Solve the system of equations

$ab=$
 $1$
$bc=$
 $2$
$cd=$
 $3$
$de=$
 $4$
$ea=$
 $6$
Answer