Sometimes a problem’s presentation hampers its solution. An illustration of this,
comes from the mathematician Gauss. When Gauss was an infant, the kindergarten the
teacher instructed the class to add up 1+2+3+4+5+6+7+8+9+10. Most of the children
started working this through. However, Little Gauss immediately shot his hand up
and gave the correct answer of 55, explaining that as 1+10 is 11 so 2+9 is 11 and
3+8 is 11 etc, there are five pairs of 11 and 5 x 11 is 55. Instead of attempting
to solve the problem sequentially as posed he had first reorganised the structure
of the problem.
Creative Exercise 11: Re-evaluating the problem
With some problems as above, a creative
solution can only occur after the elements or parts of the problem have been reorganised
into a different pattern. This requires you to juggle the parts in your mind's eye.
With this in mind, see if you can solve the following problem: A businessman brought
back four pieces of chain in solid gold from Africa, each consisting of three links.
He wanted to keep them as an investment, but his wife felt that - joined together
- the pieces would make a lovely necklace. She went to a jeweller and said, "I want
you to connect these pieces to make a necklace. How much will it cost?" The jeweller
laid the individual pieces of chain out in this pattern:
As long as you think of the segments of chain as four sides of a square or as segments
of a circle, you can't discover the solution. The moment you shift your focus and
regard one of those segments - not as an immutable structure - but as a stockpile
of individual links, you've made the necessary breakthrough. At the woman's suggestion,
the jeweller placed three segments in a triangular pattern, took apart the remaining
segment, and used those three links to close the three comers of the necklace.
Most
people will have to juggle the elements visually, drawing them in different arrangements
before arriving at the triangular pattern that leads to solution. This juggling of
the parts of a problem results in a reorganisation. But before that can happen, you
have to feel free to destroy the original pattern in which the problem was presented.
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He told the lady, "I charge £2.50 to break a link and £2.50 to melt it together again.
Since you have four corners, it will cost you £20." The lady said, "That's too much.
Actually you can do it for £15." The problem, then, is to construct a necklace, breaking
and joining only three links. How would you do it?
