This was a difficult puzzle, and I did not get any complete answer from anyone. Ofcourse, Alok Aggarwal, who contributed the puzzle, had an answer. I will replicate the answer I gave to Alok.
The answer is 8, i.e. within a maximum of 8 trials, you can figure out which is the lowest floor on which the egg can break. Here is the explanation:
– First identify one of the three 27 floor segments by trying from 27th and 54th respectively (if it breaks from 27th, then we do not need to try 54th, if it does not break even in the 54th, we know that it is the last segment)
– Then identity the segment of 9 floors within the identified 27, by trying 9 floors from the beginning of the segment, e.g. if the egg broke on 54th, we should try 27+9. i.e. 36th floor, and then 45th floor
– then identify the segment of 3
– finally identify the segment of 1
In each case one will need to make maximum of 2 tries, and hence 8.
Hope you all enjoyed the puzzle!