If all the students in this room shook hands with each other, how many handshakes would there be altogether?
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Topics: Starter  Investigations  Number  Problem Solving
Solving the classical #handshakes problem in a #maths lesson with a difference. #GirlsInSTEM pic.twitter.com/cWQKcSf4AC
— MSY_STEAM (@MSY_STEAM) October 10, 2017
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Previous Day  This starter is for 8 November  Next Day
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 for the number of handshakes given the number of students?
Edward and Lucy invite four couples to dinner. Each person shakes hands only with the people that he or she has not met before. Edward then asks his wife and eight guests how many hands they shook, and he receives nine different answers. How many people did Lucy shake hands with?
Bellos, Alex. Can You Solve My Problems?: a Casebook of Ingenious, Perplexing and Totally Satisfying Puzzles. Guardian Books, 2017.
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