Quiz

Actually, I had another idea on how to prove this:
Let's say the statements that they didn't do it are:
Lillian - a,
Judy - b,
David - c,
Theo - d,
Margaret - e.

Judy's dad is rich - f,
Margaret knows who - g,
David doesn't know Margaret - h,

Each variable can be equal to 1 if it's true or 0 if it's false. Then, based on their statements:

Lillian a+a+(1-d)=2
Judy b+f+g=2
David c+h+(1-d)=2
Theo d+(1-e)+d=2
Margaret e+(1-b)+(1-h)=2
a+b+c+d+e=4

From the first equation, a=1, d=1
From the fourth equation, e=1
From the third equation, c=1, h=1
Therefore, from the fifth equation, b=0
Judy is guilty.