Zero knowledge protocol - Information exchange

Question

I have a past exam paper question on zero-knowledge and I'm trying to figure out to understand properly.

My lecturer said if Bob says to Alice "you might know" it is a non-duplicate if it is a duplicate then Bob is "sure Alice doesn't know", therefore according to this idea, I excluded 3 months 4,5 and 6 as they have full duplicates for sub question (a). Then, if I'm correct I excluded 21 and 31 for sub question (b) as they are duplicates within the 2 remaining data sets so 3 numbers remain 26, 32 and 35. The answer for sub question (c) is 35 but I don't know 100% why is it so as it could be 26 also in my opinion.

Can someone more knowledgeable explain idea behind this? Zero knowledge question

PS: I use months and days in my explanation instead of tens and ones as it is easier to understand that way.

Answer 1

Some hints:

1. There are only two possibilities for the ones place where Alice would definitely know the answer? What are they? What are the candidates for the tens place?
2. After completing step $1$ you should have two possibilities for the tens place. Since Alice didn't know ahead of time that leaves three possibilities for $X$.
3. Two out of the three possibilities in step $2$ have the same ones place which would leave Alice still uncertain. She is not, therefore $X=?$