3.1 What do we mean by a ‘problem’? 81
Of course, you could do the whole thing by
guesswork, but you might get it all wrong and,
more to the point, you cannot be confident
that you will have got it right.
In the sense we are using the word in this
book, a ‘problem’ means a situation where we
need to find a solution from a set of initial
conditions. In the following chapters we shall
look at different sorts of problem, different
kinds of information, and how we can put
them together to find solutions to the
problems. These chapters will lead you through
the types of problem-solving exercises you will
encounter in thinking skills examinations and
give some indications about how you might
4 The following questions are based on a
very simple situation, but require clear
thinking to solve. Some are easier than
others.
A drawer contains eight blue socks and
eight black socks. It is dark and you
cannot tell the difference between the
two colours.
a What is the smallest number you will
have to take out to ensure that you have
a matching pair?
b What is the largest number you can take
out and still not have a matching pair?
c What is the smallest number you can
take out to be sure that you have one of
each colour?
d What is the largest number you can take
out and still have all of one colour?
e What is the smallest number you can
take out to be sure you have a blue pair?Answers and comments are on pages 315–16.1 Imagine you are going to book tickets for
a concert. List the pieces of information
you need and the processes you need to
go through in order to book the tickets and
get to the concert. In what order should
you do them? First list the main things,
then try to break each down into smaller
parts.
2 Consider something you might want to buy,
such as a car, mobile phone or computer.
Make a list of the pieces of information
you would need in order to make a
decision on which make or model to buy.
3 Find a mileage chart that gives the
distances between various towns (these
can be found in most road atlases or on
the internet). Pick a base town and four
other towns. Consider making a journey
that starts at the base town, takes in the
other four and ends at the base town. In
what order should you visit the towns to
minimise the journey?End-of-chapter assignments
approach such problems. However, learning to
solve problems is a generally useful life skill
and also, we hope, fun!Summary
• In this chapter we have looked at what a
problem is and how the word can be used
in different ways.
• We have seen how information is used to
contribute to the solution of a problem.
• We have looked at how various methods
of using information can lead to effective
solutions.