in a party every person shakes hands with every other person. if there are 105 hands shakes, find the number of person in the party.	Pick one
A) 14  B) 12  C) 13  D) 15  E) 16
<gadget id="calculator">105 * 2</gadget>
<output>210</output>

<gadget id="calculator">210 * 4</gadget>
<output>840</output>

<gadget id="calculator">840 + 1</gadget>
<output>841</output>

<gadget id="calculator">841 ** (1/2)</gadget>
<output>29</output>

<gadget id="calculator">29 + 1</gadget>
<output>30</output>

<gadget id="calculator">30 / 2</gadget>
<output>15</output>

<result>D</result>
in a party every person shakes hands with every other person. if there are 105 hands shakes, find the number of person in the party.
divide(add(sqrt(add(multiply(multiply(105, const_2), const_4), const_1)), const_1), const_2)
"let n be the number of persons in the party . number of hands shake = 105 ; total number of hands shake is given by nc 2 . now , according to the question , nc 2 = 105 ; or , n ! / [ 2 ! * ( n - 2 ) ! ] = 105 ; or , n * ( n - 1 ) / 2 = 105 ; or , n 2 - n = 210 ; or , n 2 - n - 210 = 0 ; or , n = 15 , - 14 ; but , we can not take negative value of n . so , n = 15 i . e . number of persons in the party = 15 . option d"