Math Is Fun Forum

momofmathkid

Member

Registered: 2008-01-14

Posts: 32

problem needing a mathematical formula

My child brought home this "challenge" question from school.  It's beyond me...sad, I know.  Can anyone help me so I can help her?  She figured out the answer (we think it's right), but doesn't know how to put it into a mathematical formula.  Here it is:

If 10 people meet at a party, and each person shakes hands of everyone else exactly once, how many handshakes are there in all?  Try to find out the mathematical fomula, or rule, to solve this for "n" people.  For example, if you were to input 2 and get 6 back, the formula would be n=3 or n=3n.  Help the mom, please!

luca-deltodesco

Member

Registered: 2006-05-05

Posts: 1,470

Re: problem needing a mathematical formula

work through it step by step.

10 people.

so person number 1, has to shake hands with the other 9 people. 9 handshakes
person number 2, also has to shake hands with the other 9 people, however the shake between person 1 and 2 is already taken into account. so only an extra 8 handshakes occur.
person number 3 similarly, an extra 7 handshakes and so on.

so we get the number of handshakes is 9+8+7+6+5+4+3+2+1
this is equal to the sum of the integers 1 to (n-1) where n is the number of people, this is equal to ½n(n-1)
so for example, for 4 people the number of handshakes is 6.
so for 10 people it is ½*10*9 = 45 handshakes

Last edited by luca-deltodesco (2008-01-14 11:23:11)

---

The Beginning Of All Things To End.
The End Of All Things To Come.

momofmathkid

Member

Registered: 2008-01-14

Posts: 32

Re: problem needing a mathematical formula

Many thanks!!  She had 44, but she sees how she missed the one at the end!  Yea!!  Mom:)

NullRoot

Member

Registered: 2007-11-19

Posts: 162

Re: problem needing a mathematical formula

A classic, Mom. It's all about observing patterns. The first person needs to shake hands with everyone but himself. The second only needs to shake hands with everyone but #1 (already done that) and himself. So the first person will shake n-1, the next shakes n-2 and so on. You should try drawing diagrams and keeping track of the number of handshakes. If you're familiar with factoring you should notice that the formula generalises itself nicely with there being a specific number of n's.

Sorry if it's not specific enough but I'm not sure if you want answers or hints so I'll play it safe.

---

Trillian: Five to one against and falling. Four to one against and falling… Three to one, two, one. Probability factor of one to one. We have normality. I repeat, we have normality. Anything you still can’t cope with is therefore your own problem.

LuisRodg

Real Member

Registered: 2007-10-23

Posts: 322

Re: problem needing a mathematical formula

In reply to luca-deltodesco:

Although i believe this is out of the scope of this mom's question. I have one for myself.

You said that it represents the sum of integers from a to n-1 which is (n(n+1))/2

However, I remember that the sigma summation from k=1 to n of k is equal to (n(n+1))/2 just like you said but the thing is that the defition is from 1 to n while u said it from 1 to n-1 and still same formula?

Would you care to explain?

John E. Franklin

Member

Registered: 2005-08-29

Posts: 3,588

Re: problem needing a mathematical formula

That's because he uses a minus sign in his pairs; n and n-1, see?
½n(n-1)
Because the n is n-1+1.

---

igloo myrtilles fourmis