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March 29, 2017

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At a party, there were 105 handshakes. If each person shook hands exactly once with every other person, how many people were at the party?

  • 7th grade - ,

    If there are N folks, then
    n-1 + N-2 + n-3 +....1 handshakes
    take 4 people:
    3+2+1= 6 handshakes.

    10 people is
    9+8+7+6+5+4+3+2+1= 45

    14= 13+12+11+ 10 + number above
    = 13+12+11+10+45= 91
    you want 105, so try
    15= 14+ 91

  • math - ,

    So the answer is 15? But still I don't get how you solve it

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