Thinking Skills: Critical Thinking and Problem Solving

5.1 Combining skills – using imagination 205

Combining skills –

using imagination

5.1

Unit 5 Advanced problem solving

The next four chapters deal with more
advanced problems. In some cases these are
just harder or longer examples based on the
skills you have already learned. In other cases,
slightly more advanced use of mathematics is
required. This does not go beyond algebra and
probability at relatively simple levels but, if
you are not confident with this, you can first
look at Chapter 6.1, which may help you in
using these mathematical techniques. The
problems may involve the use of several
different skills in one question, require extra
stages of intermediate result or require more
imagination in developing methods of
solution. The examples in this unit, some of
which are longer and harder than those you
are likely to encounter in AS Level thinking
skills tests, will help you to improve your skills

and make the standard questions seem easier.

They will be particularly useful for those

candidates taking higher-level tests, including

A2 Level and some university admissions tests.

The end-of-chapter assignments include a

question from an A Level Thinking Skills paper

and show the progressive nature of such

questions, where either additional material is

introduced or the conditions of the question

are changed. Further examples showing the

nature and difficulty of actual A Level

questions can be found in past papers.

The problem below is an example of one

requiring imagination; although data

extraction and processing skills are needed,

the main difficulty is in finding a method by

which to solve the problem.

Activity

Grunfling is an activity held in Bolandia,

where competitors have to contort their faces

into the most extreme shapes. Several

Bolandian villages have a grunfling

competition each year. Each village puts up a

champion grunfler who demonstrates his or

her skills, then the villages vote one by one.

(They are not allowed to vote for their own

grunfler.) Each village awards 8 votes to their

favourite, 4 to the second, 2 to the third and

1 to the fourth. Clearly, tactical voting is

important, so the order of voting is changed

every year. This year, the villages vote in

order from most northerly to most southerly.

The results before the last two villages have

voted are shown (in voting order). Who still

stands a chance of winning?

Fartown 6

Waterton 5

Blackport 6

Longwood 24

Gigglesford 12

White Stones 9

Martinsville 24

South Peak 4

Riverton 13

Runcastle 17