A probability problem by awesome happywinks
Probability
Level
2
At a party everyone shook hands with everyone else There were 66 handshakes How many people went to the party?
12
16
17
14
21
11
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1 solution
In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1 + 2 + 3 + ... + n. Since this sum is n ( n + 1 ) / 2, we need to solve the equation n ( n + 1 ) / 2 = 66. This is the quadratic equation n2 + n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party. This should be used for bigger numbers
Since 66 is a small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.