Question 10
Arie, Bert, Caroline know only their own positive integers $a,b,c$, and are told $1/a+1/b+1/c=1$. They are asked: (one) Do you know $a+b+c$? (two) Do you know all three values? Arie answers no to both. Hearing this, Bert answers yes to one and no to two. Caroline hears everything. How does she answer?