This was a relatively simple puzzle, and I received many correct answers – Santosh Kumar, Kamaljit Dhooria, Karan Sharma, Anisha Goyal, Mohit Khare, Abhinav Jain, Vijay Raghavan, Pratik Poddar, P R Kumar and Suman Saraf + his 10 year old daughter! If I have missed out anyone, apologies as I received a lot of correct answers. (Addendum – as suspected I missed out many – Ayush Tutakne from Manila, Sanjana from Washington DC, Vikas Vats from New Jersey and Ashwin Khandel)

Answer is 6,6,1. Like some other puzzles in the past, one needs to solve this through a process of elimination, beginning with a superset of all the possible ages based on the statement that the product of the ages is 36. (Copying solution from Pratik Poddar)

1, 1, 36

1, 2, 18

1, 3, 12

1, 4, 9

1, 6, 6

2, 2, 9

2, 3, 6

3, 3, 4

With the second hint, sum is a constant that both of them know about.

Sum is all the options:

1, 1, 36=38

1, 2, 18=21

1, 3, 12=16

1, 4, 9=14

1, 6, 6=13

2, 2, 9=13

2, 3, 6=11

3, 3, 4=10

Since even after the sum, the answer is not clear – the room number or the sum is 13.

Since there exists a “youngest” daughter, the ages of the daughters are 1, 6 and 6.

Hope you all enjoyed the puzzle.