Copyright © University of Cambridge. All rights reserved.

'It's a Tie' printed from http://nrich.maths.org/

Show menu

Kaia's father always wore a white shirt and coloured tie for work. He didn't like deciding which tie to wear so he would put his hand in the drawer and wear the first tie that he pulled out. Each evening the tie would go back in the drawer.

One Friday morning, Kaia said, "Do you like that tie? You usually wear it at least twice a week."
"I do not," replied her father, "I have eight ties and I only work five days a week. I certainly don't wear any tie more than once a week."
"You have worn that tie twice a week in at least five of the ten weeks you have been taking me to school," Kaia insisted.
"Impossible! Prove it!" challenged her father.

Do you think Kaia or her father was right? Why?

That weekend Kaia did an experiment. She made the following drawings of his ties and created the chart shown below.

eight different ties labelled A-H
Week no. Monday Tuesday Wednesday Thursday Friday
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20

How might Kaia use the drawings and chart to prove her father wrong?
Try doing an experiment yourself to find out which ties might be chosen.
What did the result of your experiment show?