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**espeon****Real Member**- Registered: 2006-02-05
- Posts: 2,586

In the mission club4 people join. if each person handshakes everyone once how many hand shakes all together?

The following week 6 more join. Now how many handshakes?

At the end of the month 100 people altogetherare in the mission club. Now how many hand shakes altogether?

My friend said that he took a week trying to figure it out, and in the end he managed to get 100 people to shake each others hand.

I thought he was mad!!!!!

But he was right, but there is a more simple way...

Good luck and try not to get 100 people.

Presenting the Prinny dance.

Take this dood! Huh doood!!! HUH DOOOOD!?!? DOOD HUH!!!!!! DOOOOOOOOOOOOOOOOOOOOOOOOOD!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,631

2 people = 1 handshake

3 people = 3 handshakes

4 people = 6 handshakes

5 people = 10 handshakes

each new person must shake hands with every person already there, so if a 6th person arrives, he must shake hands with the 5 already there

6 people = 10+5 = 15 handshakes

And yes, there is "shortcut", and it is ...

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Triangular numbers!

The nth triangular number is given by n(n+1)/2, and x people will have the (x-1)th triangular number of handshakes.

So, the answers are 6 and 15, as MathsIsFun said, and 100 people will shake hands 100*101/2 = 5050 times. I think.

Why did the vector cross the road?

It wanted to be normal.

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**espeon****Real Member**- Registered: 2006-02-05
- Posts: 2,586

You got the first one right...4+6people is the hint on the second one, and I am not going to tell you the last one...:lol:

Presenting the Prinny dance.

Take this dood! Huh doood!!! HUH DOOOOD!?!? DOOD HUH!!!!!! DOOOOOOOOOOOOOOOOOOOOOOOOOD!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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**mathsyperson****Moderator**- Registered: 2005-06-22
- Posts: 4,900

Grr and double-grr. Two stupid mistakes there.

OK then, so in the second week there are 4+6 = 10 people in the club, so they need the 9th triangular number, which is 9*10/2 = 45.

When there are 100 people, they need the 99th triangular number, which is 99*100/2 = 4950.

Is that better?

Why did the vector cross the road?

It wanted to be normal.

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**espeon****Real Member**- Registered: 2006-02-05
- Posts: 2,586

Right!

Presenting the Prinny dance.

Take this dood! Huh doood!!! HUH DOOOOD!?!? DOOD HUH!!!!!! DOOOOOOOOOOOOOOOOOOOOOOOOOD!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!

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