This was a fun and relatively simpler puzzler, and I was bombarded with correct answers. People with correct answers included Mahi Saraf, Deepak Jayaraman, Rishikant Kumar, Abhinav Jain, Pratik Poddar and Shivanshu.
I am taking the liberty of copying the solution from Rishikant.
The answer is 6.
Details:
12, 15 and 18 are the products
12 = 4*3 or 6*2
15 = 5*3
15 = 5*3
18 = 9*2 or 6*3
If student 1 or student 2 has 5 or 9 or 4, they know what the other person has when their turn comes. So either of them cannot have these numbers.
Student1 Student 2
2 6/9
2 6/9
3 4/5/6
6 2/3
6 2/3
If Student 1 cannot decide, then she has 2/3/6. If student 2 has 2 or 3 then, she knows student 1 has 6.
So Student 1 may have 2/3 and student 2 has 6.
Hope you all enjoyed the puzzle!
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