Exercise $4$: $($homework$)$ Four siblings receive, as an inheritance, the contents

of a safe deposit box in a bank. Access is granted via an $8$ digits key. Since the

$4$ are greedy, the will executor must design a mechanism that forces the siblings

to cooperate in order to gain access to the safe.

$1.$ Explain an appropriate mechanism using the Chinese remainder theorem.

$2.$ If the key is $87654321,$ give the information that each sibling receives $($the

expected answer is $4$ pairs of positive integers$).$

Expected time to solve: $25$

Exercise $5$: $($homework$)$ If the four siblings from Exercise $4$ received the

following pairs of values:

$59,13,61,14,71,4,73,24.$

What is the key to the deposit box?. $($You may need to slightly modify class

$$GameChineseRemainderTheorem$2$ given in Blackboard in order to compute

the solution$).$

Expected time to solve: $30$