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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?