Handshakes

A Maths Starter of The Day

If all the students in this room shook hands with each other, how many handshakes would there be altogether?

 

 

 

 

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    Answers

    If there was only one student in the room there would be no one to shake hands with.

    If there were only two students in the room, there would be one handshake.

    If there were three students, let's call them Ann, Bee and Cindy then:

    Ann would shake hands with Bee
    Ann would shake hands with Cindy
    Bee would shake hands with Cindy

    ...so there would be three handshakes.

    Here's a table showing these results:

    No. of Students

    		  

    No. of Handshakes
    . . .

    1

    		  

    0

    2

    		  

    1

    3

    		  

    3

    4

    		  

    6

    5

    		  

    10

    6

    		  

    15

    7

    		  

    21

    8

    		  

    28

    9

    		  

    36

    10

    		  

    45

    11

    		  

    55

    12

    		  

    66

    13

    		  

    78

    14

    		  

    91

    15

    		  

    105

    16

    		  

    120

    17

    		  

    136

    18

    		  

    153

    19

    		  

    171

    20

    		  

    190

    21

    		  

    210

    22

    		  

    231

    23

    		  

    253

    24

    		  

    276

    25

    		  

    300

    26

    		  

    325

    27

    		  

    351

    28

    		  

    378

    29

    		  

    406

    30

    		  

    435

    31

    		  

    465

    32

    		  

    496

    Can you find a formula?

    If instead of handshakes, each student in the room gave every other student a present, how many presents would be given?