Where does the leap of reason spring from?

I am singularly weak in mathematics. For some reason the type of intelligence that is needed to be adept at mathematics has eluded me totally till now. When I sometimes see some math puzzles and the solutions that are given to them, I am amazed at the 'leap of reason' at certain crucial steps, and to my limited understanding, such leaps of reason are simply divine! I am amazed how one could think of a step like that? Even more astounding to me is, how on earth could one conceive of a problem like that! Take the 'Mindbender' Puzzle that figured in the Bangalore Times section of The Times of India today (28th September 2010):

My brother Julian is a little simple. I recently asked him to buy some ribbon for my daughter's pretty pink bonnet. He went to the haberdashery shop for the required length and accidentally interchanged the feet and inches. When I measured the resulting ribbon, I only had 5/8th of the length I required. How much ribbon did I originally ask for?

 I thought of trying my hand at the problem - specially now that I had a 'partial understanding of the way the world works', so I started off this way:

         1st Step : Since he got 5/8th of the length, that implies he lost 1 - 5/8 = 3/8 of the length.

         2nd Step: What number when multiplied by 1/12 (since 1 feet = 12 inches) causes a loss of 3/8 ?

         3rd Step:  So if the number is 'p' then (p)*(1/12) = 3/8
                          or p/12 = 3/8
                          or p = 36/8 or 4.5
          So is the answer 4 feet plus 0.5 feet or 4 feet and 6 inches?
Let us check: 
            Is 4 feet six inches 5/8ths the length of 6 feet 4 inches?
                    4 feet 6 inches is 54 inches and 6 feet 4 inches is 76 inches
                     So what is 54/78 ?
                      That is 9/13 and not equal to 5/8
                     Since I did not get the correct answer I QUIT !

     I decided to see the solution. Here it is :

    1st Step: Label what I asked for as A feet and B inches.  (Now who could think of that?)
    2nd Step: So I had to ask for (12xA + B)  but asked (12xB + A) (o.k. This is simple)
    3rd Step:Which means that :
                  (5/8)x(12xA + B) =  (12xB +A)             (o.k. This is also quite easy)
    4th Step: Simplifying the above equation gives :
                          A in feet = (91/52) x B                    (This too is simple)

   5th Step: As B is the number of inches, it can only be between 1 and 12 and must give A as a whole  number of Feet 

   6th Step: Which means that B is a number such that it should give 13 in the denominator as 91 is only divisible by 13 to give 7.

          ( In my understanding these 2 steps are an 'inspired' leap of reason)


  7th Step: And the number which cancels 52 to give 13 in the denominator is 4 .

  8th Step: So we have the Answer that B is 4 and A is 7.

     SO I HAD ASKED MY BROTHER TO GET ME 7 FEET 4 INCHES OF RIBBON AND HE BOUGHT 4 FEET 7 INCHES (A clear exposition helps).

If I were given such a problem in my high school examination, after my feebly attempted steps, I would have lapsed into a reverie - 'How old is the daughter? Is she sexy? Could she be of a friendly type or would she be moody? Is there a chance that she has a bobbed hair? O.K., if I meet her you know what I'll tell her? I'll tell her that...' and so on I would go along for a whole quarter of an hour before realizing I was in an examination and had to get on with the other questions.

Which explains why I got just 35% marks, which is just the marks required to pass the examination, evidently given by a sympathetic examiner to ensure that I pass, maybe responding to a directive from the state government, to ensure that a particular percentage of students pass the examination to bring a good name to the government that it is doing well in the field of education.

                       xxx