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  1. #1
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    arithmetic problem

    At a party , each person shakes hands with every other person . the total number of hand shakes was 66. how many persons are present at the party ?

    A 6 b 11 c 12 d 18 e 33
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  2. #2
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    Quote Originally Posted by sri340 View Post
    At a party , each person shakes hands with every other person . the total number of hand shakes was 66. how many persons are present at the party ?

    A 6 b 11 c 12 d 18 e 33
    Line up half of the people with the other half of the people facing them.

    One line has \frac{x}{2} people, so \frac{x}{2} handshakes can take place.

    Each person can shake hands with (x-1) other people,

    hence there are (x-1)\frac{x}{2} handshakes possible

    (x-1)\frac{x}{2}=66

    (x-1)x=132

    the factors of 132 that differ by 1 are 11 and 12, hence x=12, x-1=11.

    12 people are at the party.
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