238 Unit 6 Problem solving: further techniques
• In this unit we have seen how various
diagrams may be used to represent and
solve problems in categorisation, logic and
searching.
• We have looked at using sketched maps
and graphs to clarify and simplify quite
complicated problems.• More advanced Venn and Carroll diagrams
have been introduced for problems
involving three levels of categorisation.Summary
2 Draw a Venn diagram for three categories
to sort the numbers from 1 to 39
according to whether they are even,
multiples of three or square numbers.
Write each number in the appropriate part
of the diagram.
3 The island of Nonga has two ferry ports:
Waigura and Nooli. All ferries from Waigura
go to Dulais on a neighbouring island.
Some ferries from Nooli also go to Dulais.
Some of the ferries that serve Dulais
are fast hydrofoil services; those going
elsewhere are slow steamboats.
Which of the following statements can
safely be concluded from the information
given above?
A No hydrofoils go to Dulais from Nooli.
B All hydrofoils going to Dulais leave
from Waigura.
C Some hydrofoils from Nooli go to
places other than Dulais.
D Some steamboats from Waigura go
to Dulais.
E All hydrofoils from Waigura go to
Dulais.1 Winston is organising a dinner to raise
money for his football team. The hall he
has hired is a square room measuring
15 metres by 15 metres. The tables are
rectangular. Each one measures 2 metres
by 80 centimetres and can seat up to eight
people, as indicated in this diagram:To fit as many people as possible into
the hall, Winston plans to put the tables
together, end to end, to create parallel
rows. He can use as many tables as he
can fit in, but he has to make sure there
is a gap of at least 1.5 metres between
the edge of any table and the edge of
the room, and also a gap of at least 1.5
metres between rows of tables.
What is the maximum number of people
that could sit down to eat at Winston’s
dinner?A 190 B 192 C 228 D 240 E 288End-of-chapter assignments