On a recent visit to the Professor Simon Greathead at Colney Hatch, he expounded to me on
the simple nature of division.
"It is a lamentably little known fact," he explained, "that the more
complex can always be reduced to the less so. Take, for example, the issue of
division: The fraction 16/64 can be reduced by noting that the central 6/6 is equal to 1,
and can therefore be cancelled out, leaving just 1/4."
I pointed out that this was necessarily a special case.
"Not at all!" the Professor protested. "Again, consider 19/95.
Simply cancel out the 9/9, and one is left with 1/5, the correct ratio."
I saw that it would be no use to argue the matter with the man, and passed on to the next
inmate. The reader might find it an interesting puzzle, however, to look for the
three-digit solutions. That is, what fractions abc/cde (where a, b, c, d, e are all
single digits) are equal to ab/de? To avoid degenerate solutions, we require that
none of the five digits be zero, though they need not be distinct. There are not
many solutions..
Answer
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