Apply the psychic powers you evidently think we posess to the problem. Your question didn't specify that it is old unanswered nodes that you are interested in. Perhaps if you elaborate on why you want to find such nodes, we may be able to suggest a search technique, or provide one if the pmdevils deem the cause sufficiently worthy.

That is fantastic from GrandFather. I want to take all nodes which are unanswered in the earlier days and try to bring a proper solution for the nodes which are unanswered. Just, I am taking that as a challenge.

This has been discussed before.
  unanswered questions
  Finding unanswered threads
  Unanswered post search?
  a bit more about unanswered nodes.

Read the Recently Active Threads Faqlet. In particular note:

The time period of the selection is controlled through the "<<" style links at the top of the page. By default the time period is now. The << links go back in time, with more <'s indicating further back, and likewise for >> links but going forward. If a datestamp link appears, then that is the date of the page displayed, which can be used for finding that set of nodes later.

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DWIM is Perl's answer to Gödel