At the party everyone clink with everyone. Together, they clink 406 times. How many people were at the party?

Correct result:

On party was:  29 people


(n2)=406 n(n1)/2=406n>0  n2n812=0n>0  n=29 people\dbinom{ n}{ 2} = 406 \ \\ n(n-1)/2 = 406 \wedge n>0 \ \\ \ \\ n^2-n-812=0 \wedge n>0 \ \\ \ \\ n = 29 \ \text{people}

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