# 1st Day at school

powergirl

## Main Question or Discussion Point

It was Cheryl's first day at school. The teacher suggested that it would be a good idea for each child to meet every other child in the class. The teacher said, "When you meet, please shake hands and introduce yourself by name."

If there were 15 children in the class, how many total handshakes were there?
:uhh:

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$$\sum_{i=1}^{15}i$$

powergirl
No.....Slightly wrong

Hootenanny
Staff Emeritus
Gold Member
14.............

powergirl
14...................?

It's not 120?

Hootenanny
Staff Emeritus
Gold Member
I thought it was only Cheryl's first day, therefore all the other children would already know each other.

If not the answer must be 210.

powergirl
no.......sorry

Lol I thought way too fast... 105!

powergirl
Ya..Now it's Correct........

Hootenanny
Staff Emeritus
Gold Member
hmm, could someone explain this one to me?

Hey dontdistrbmycircles :)

powergirl
may I do that?

Sure, the first boy shakes 14 hands right? Then the next shakes 13 until you get to 1, my original sum should have read $$\sum_{i=1}^{14}i$$ :P

Keeps going down one because the same person does not shake the same person's hand twice.

powergirl
Ya right....
The class has 15 children. The first

child shakes hands with the other 14

children. The second child has already

shaken hands with the first child, and so

has to shake hands with only the other 13

children. In this manner, the

second-last child has to shake hands with

only one child, and the last child has

already met all the children. Thus, the

number of handshakes is

14 + 13 + ........ + 2 + 1 = 105.

If there were 15 children in the class,

then there were 105 total handshakes.

Hootenanny
Staff Emeritus