A problem which TRIZ does not help to solve

There is a problem which TRIZ apparently cannot solve. I don't want to name the problem and leave it to the reader as an exercise. The problem manifests itself in a dialogue taken place on February 16-17 on Facebook between me and one of my Facebook friends interested in TRIZ. The dialogue was triggered by the following question "the friend" posted on Facebook:

I decided to respond and a discussion ensued. Here is the discussion as it appeared on Facebook:

I remind the readers that the main purpose of presenting this discussion in the journal is to identify a problem which TRIZ does not help to solve. I am looking forward to receiving your suggestions as to what this problem is. The answers and my vision of the problem will be posted in the subsequent issues of the journal.