Chinese Remainder Theorem

[mat12]

I am trying to work on this problem..

A company wishes to permit only 2 people working together to be able to decode a message circulated
among a group of three people.The message is a number somewhere between
30 and 240.The company issues primes 13,19 and 23 to employees Alice,Bob and carol. The number will be given
mod these primes to each employee .If Alice gets a 6, Bob a 9, Carol a 8, then what was the message.

b)How could the company modify the scheme, so that all three people would have to be willing to share the information in order for it
to be decoded? similarly ,

c) How could the company modify the scheme so that only if r people out of n people are to be willing to share the information can it be decoded.

------ This is what I tried to do .........

x = 6mod13
x = 9mod19
x = 8mod23

M=5681
m1=13
m2=19
m3=23

But the question says only 2 people can work together.. How to proceed ?.
how to solve for a) and b)

Anyone can provide some help?..

Thank you

mat

[RobertuX]