# Shake, Rattle and Roll

At an annual conference 20 people attended. At the start of the conference, each person shook hands with every other person, how many handshakes took place in total?

### 2 guesses to Shake, Rattle and Roll

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• Paul

Imagine a line of 20 world leaders. President Obama arrives first and starts the line. He’s followed by Dave Cameron and they shake hands (one). Nic Sarkozy saunters up and shakes Barack’s and Dave’s hands (1+2=three). Angie Merkel goosesteps up and shakes Barack’s, Dave’s and Nic’s hands (3+3=six). Don Tusk waltzes in and shakes with all four leaders present (6+4=ten) and so on. Finally, Fel Calderon flamencos in and shakes all nineteen other leaders’ hands after the 171 previous shakes totaling 190 greetings between the twenty world leaders.

• Dude

You’re correct, Paul!

190 is correct: The first person shook hands with 19 others, the second had already shook hands with the first and therefore shook 18 hands, etc: 19+18+17+16+15+14+13+12+11+10+9+8+7+6+5+4+3+2+1 = 190.