Thinking Skills: Critical Thinking and Problem Solving

118 Unit 3 Problem solving: basic skills

assistant to count the bags. However, the

assistant, not being very bright, counted

the total number of pieces of fruit instead.

George was about to send him back to

repeat it when he realised that the number

that the assistant had given him was not

only sufficient information for him to work

out how many bags there were of each, but

was also the maximum such number. How

many bags of pears and bananas were

there?

3    Kuldip told me she had 12 coins in her

pocket, all either 1¢, 2¢ or 5¢, with a

different number of each denomination.

There were more 2¢ than 1¢ coins and

more 5¢ than 2¢ coins. She asked me

how much money she had in her pocket

altogether. I told her that I did not have

enough information to answer.

Which of the following additional pieces

of information would enable me to know

how much money she had in his pocket?

A She had three 2¢ coins.

B The total amount of money was a

multiple of 10¢.

C 5¢ coins amounted to^34 of the total

value.

D She had two more 5¢ coins than 1¢

and 2¢ together.

Answers and comments are on pages 321–2.

1    I have made a dice out of a sheet of

cardboard in the form of an octahedron,

which has eight faces as shown below.

I now want to number the faces from

1 to 8. The numbers on opposite faces

must add up to 9, so when I number a face

1, the opposite face must be 8.

If I start with number 1 and work up,

how many faces can I number before I am

left with no choice about where to put the

numbers?

2    (Harder task) George stocks bags of

pears and bananas in his shop. Each

bag contains either five pears or three

bananas. He wanted to know how many to

order to keep his stocks up, so he sent his

End-of-chapter assignments