There is some evidence we can and in an easy way, by exploiting the effect of 'psychological distance'.
Instead of thinking about a problem solely in terms of here and now, we should project our mind to distant places and times, try to consider the problem from another person's standpoint and so on. How would the problem appear to an inhabitant of a planet billions of light years away?
Research reported in Scientific American suggest this technique may really help us to be more inventive and creative.
And how did the prisoner divide the rope?
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Interesting, confirms the efficacy of a systemic approach to problem solving - identifying the problem space within extraneous detail, and the possibility of getting the right mind set using any of the strategies investigated by Wakslak, Liberman, Trope looks useful
Suppose the quoted problem had been set as:
A prisoner was attempting to escape from a tower. He found a rope in his cell that was half as long enough to permit him to reach the ground safely and used it to escape. How could he have done this?
Looks likely that most people would have been able to get the answer straight off without the - 'in half' advice included to generate an erroneous assumption.
However, the second study looks seriously flawed by the choice of the location for the far group of problem setters. People living elsewhere in the US are likely to ignore advice, helpful or otherwise, given by Californians irrespective of their distance from this location. There may even be an inverse distance relationship involved.
This opinion is confirmed by my own research done by Googling 'How many Californians does it take to change/screw-in a light bulb?' - generally a useful test of social attitudes towards other groupings with respect to problem solving.