Question
Sun March 15, 2015 By: Godson Babuji

In a society for children, each child gives gift to every other child. If the total number of gifts is 132, find the number of children.

Expert Reply
Prasenjit Paul
Sun March 15, 2015
L e t space t h e space n u m b e r space o f space c h i l d r e n space b e space apostrophe n apostrophe 2 cross times to the power of n C subscript 2 equals 132 rightwards double arrow 2 cross times fraction numerator n left parenthesis n minus 1 right parenthesis over denominator 2 end fraction equals 132 rightwards double arrow n squared minus n minus 132 equals 0 rightwards double arrow n squared minus 12 n plus 11 n minus 132 equals 0 rightwards double arrow n left parenthesis n minus 12 right parenthesis plus 11 left parenthesis n minus 12 right parenthesis equals 0 rightwards double arrow left parenthesis n minus 12 right parenthesis left parenthesis n plus 11 right parenthesis equals 0 therefore n equals 12 space N u m b e r space o f space c h i l d r e n space i s space 12.
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