Apologies for skipping last weekend, I was traveling on work!
I got correct answers from three people – Pratik Poddar, Abhinav Jain and Suman Saraf. Well done!
Most people thought binary, i.e. have links of size 1, 2, 4, 8, ….while that will work, we need to recognise that the link opens on both side, and once opened, you gave a chain of the size of “1” from the opened link. Therefore for each opened link, you will have a chain of “1”. The optimal will be to cut the fourth and the eleventh link which will create the following parts:
This would mean 2 cuts are enough xxx|xxxxxx|xxxxxxxxxxxx (where | are the links we open)
Hope you all enjoyed the puzzle!