1) How much water flows down the Mississippi (at, say, New Orleans)
in a year, approximately? Don't look anything up. Just estimate
whatever raw data you need.
-- Arno Penzias, when he was in charge of all research at Bell
Labs, liked to spring this question on members of the technical
staff. Woe betide the person who blurted out "I have no idea".
Arno would yell back "you must have SOME idea ... don't tell me
you have no idea ... FIGURE IT OUT."
-- Anybody with a US high-school education "should" be able to
answer this _without_ looking anything up. It just requires
strength of character, i.e. not giving up in the face of a
problem that seems hard. It also requires marshalling lots
of facts that may not, at first glance, have seemed relevant.
2) Find a second independent solution to the Mississippi problem.
-- Somehow knowledge of the first solution is a psychological
impediment to finding the second solution.
-- OTOH if you can reach the same conclusion by two different
avenues, it greatly increases the reliability of the result.
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