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 Post subject: How to find the nth term?Posted: Sun Feb 13, 2011 9:28 am

Joined: Thu Apr 08, 2010 10:28 pm
Posts: 95
Location: London
Please could anyone help me on following questions.

1) For 2 people there is 1 handshake
For 3 people there is 3 handshakes
Can you predict the number of handshakes for 10,15,20 people?
Can you work out a formula ?

2) 3 monkeys and their partners are invited to a party.When they reach the
party everyone shakes hands with everyone except their own partners.
How many handshakes were there?

How many hands shakes would there be for 4 monkeys and their partners?
5 monkeys?
Can you predict the number of handshakes for 10,15,20 monkeys and their
partners?

Can you work out a formula?

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 Post subject: Re: How to find the nth term?Posted: Sun Feb 13, 2011 10:55 am

Joined: Thu Jan 03, 2008 8:26 am
Posts: 1330
Location: Watford, Herts
Tulip wrote:
1) For 2 people there is 1 handshake
For 3 people there is 3 handshakes
Can you predict the number of handshakes for 10,15,20 people?
Can you work out a formula ?

2) 3 monkeys and their partners are invited to a party.When they reach the
party everyone shakes hands with everyone except their own partners.
How many handshakes were there?

How many hands shakes would there be for 4 monkeys and their partners?
5 monkeys?
Can you predict the number of handshakes for 10,15,20 monkeys and their
partners?

1) If there are N people, each one shakes hands with the remaining N-1 people. There are 2 people in each handshake, so divide by 2, giving N*(N-1)/2.

2) There are 2N monkeys, each shaking hands with 2N-2 monkeys. Again divide by the number of monkeys in each handshake (2), giving 2N*(2N-2)/2 = 2N*(N-1).

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 Post subject: Re: How to find the nth term?Posted: Sun Feb 13, 2011 1:30 pm

Joined: Thu Apr 08, 2010 10:28 pm
Posts: 95
Location: London
Sorry WP could you please explain me the formula little bit more
and the 2nd question is starting with 3 monkeys and their partners.
Is it easier if we draw a table first and then find the formula for these
questions? Thank you.

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 Post subject: Re: How to find the nth term?Posted: Sun Feb 13, 2011 5:58 pm

Joined: Thu Jan 03, 2008 8:26 am
Posts: 1330
Location: Watford, Herts
It often helps to work out a few specific examples until you notice a pattern. Suppose there are 3 people: A, B and C. Then

A shakes hands with B
A shakes hands with C
B shakes hands with A
B shakes hands with C
C shakes hands with A
C shakes hands with A

That's 6 handshakes (each of the 3 people shook hands with the 2 others), but we've counted each handshake twice (once for each person involved), so divide by 2, giving 3.

If there are 10 people, each of them shakes hands with the 9 others, making 90. Again we've counted each handshake twice, so divide by 2, giving 45.

In general, there are N people, and each one shakes hands with the remaining N-1 people, giving a total of N*(N-1). There are 2 people in each handshake, so divide by 2, giving N*(N-1)/2.

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 Post subject: Re: How to find the nth term?Posted: Mon Feb 14, 2011 2:33 pm

Joined: Thu Apr 08, 2010 10:28 pm
Posts: 95
Location: London
Brilliant explanation WP thank you very much...!!!

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