My SLOG For Week #10

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.