Got both problems Accepted.
11942: Lumberjack Sequencing - tried binary search and found it to be tedious to program and difficult to get right. Switched to linear search and it simplified the number of cases to be handled.
11461: Square numbers - interesting thing here is that we need to remember the length of the beards as we proceed. I was thinking of comparing diff(i - 1, i) with diff(i, i + 1), but again, need to remember the history. So, I kept the implementation simple by remembering the last diff and the current.
Small problems can teach us quite a bit.
Thanks to Alluri for solving the problems ahead of me and recommending them to me.