‘What do you think of this, Chief?’ asked the deputy, handing him a newspaper clipping. ‘Looks like a swindle to me!’ The clipping read:

SUPERCYCLES A BICYCLE FOR $20!
Make the most of this opportunity! You can obtain a $100 bicycle for just $20. Write for free application.

‘And here is what I received when I wrote in,’ said the deputy, a little shame-facedly. He handed over four coupons worth $20 each.

‘I sell these to my friends,’ he said, ‘and the $80 I receive plus my $20 buys me a bicycle.’

‘Hmmm,’ said the Chief. ‘So the firm gets its money. What about your friends?’

‘Well, they each get four more coupons from the shop. They sell them to their friends, and so each receives a bicycle for $20 too.’

‘So they don’t lose out either,’ muttered the Chief. ‘But there must be a catch somewhere.’

Can you see where it is?

Hint 1

Work through a few steps of the deal. Look at the number of friends at each step.

Solution

This is a form of ‘pyramid selling’. The same principle underlies the common ‘chain letter’, where you are asked to send money to the author, and to send ten copies of the letter to your friends. It is easy to see that it is a swindle.

To see this, we need to look at the number of new people involved at each step. We get the following table:

Step   Number of people    1                    1    2                    4    3                   16    4                   64    5                  256    6                 1024    7                 4096    8               16,384             . . . . . . . .

The number of people involved increases very rapidly. At some stage people have paid for coupons which they cannot sell.

Extensions

1. Pyramid selling is illegal in many countries. Find out how it works, and why it has been made illegal.

2. If you have ever received a chain letter, look at its format, and determine how many people need to be involved at each step.  Do you think it is a swindle?

Hint 1

 

Solution

Extensions