Math Is Fun Forum
  Discussion about math, puzzles, games and fun.   Useful symbols: √ ∞ ≠ ≤ ≥ ≈ ⇒ ∈ Δ θ ∴ ∑ ∫ π -

Login

Username

Password

Not registered yet?

#1 2006-02-10 06:56:21

espeon
Real Member

Offline

Here is a puzzle...you may find it tricky

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.faintfaintfainttongue


Presenting the Prinny dance.
Take this dood! Huh doood!!! HUH DOOOOD!?!? DOOD HUH!!!!!! DOOOOOOOOOOOOOOOOOOOOOOOOOD!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 

#2 2006-02-10 09:00:03

MathsIsFun
Administrator

Offline

Re: Here is a puzzle...you may find it tricky

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
 

#3 2006-02-10 09:02:35

mathsyperson
Moderator

Offline

Re: Here is a puzzle...you may find it tricky

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. smile


Why did the vector cross the road?
It wanted to be normal.
 

#4 2006-02-12 03:40:47

espeon
Real Member

Offline

Re: Here is a puzzle...you may find it tricky

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!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 

#5 2006-02-12 05:11:26

mathsyperson
Moderator

Offline

Re: Here is a puzzle...you may find it tricky

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.
 

#6 2006-02-12 21:20:46

espeon
Real Member

Offline

Re: Here is a puzzle...you may find it tricky

Right!


Presenting the Prinny dance.
Take this dood! Huh doood!!! HUH DOOOOD!?!? DOOD HUH!!!!!! DOOOOOOOOOOOOOOOOOOOOOOOOOD!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
 

Board footer

Powered by FluxBB