This
week we talked about some social problems, for
example, life with, or without, computers, which works better, how many hours of work do we prefer to have every week
as well as does technological change automatically improve lives. I have learnt
the effect of automation/computerization. A sound case in point is that in
1940s, a car cost 35 hours but now it costs 19 hours only. Also, I have known
the effect of hardware on working lives, for instance, storing information gets
smaller, cheaper, faster by the decade.
The
thing that challenged me was the problem-solving handout on products of sums.
For instance, the list of positive integers that add up to 1 is (1),
and the product of this list (if you allow unary products) is also 1. There are
two lists of positive integers that add up to 2, and they yield two different
products: (2) (with product 2), and (1,1) (with product 1). There are several
lists of positive integers that add up to 3, and they yield several different
products: (3) (with product 3), (2,1) (with product 2), and (1,1,1) (with
product 1). And the question says: If n is a positive integer, what is the
maximum product that can be formed of a list of positive integers that sum to
n?
In order to
work out this question, we should understand the problem first of all and write
all the lists of numbers that add to n, take their product. Then organize the
list, carry out and verify and finally look back.