Really super hard maths question!
If you answer this you are smart:At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party? 
post to me to find out!
post to me to find out!(edited 9 years ago)
Original post by SkilledGamer
If you answer this you are smart:At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party? post to me to find out!
post to me to find out!isn't 11?
yes because:In general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n.
Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66.
This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.
Since 66 is a relatively small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.
Since this sum is n(n+1)/2, we need to solve the equation n(n+1)/2 = 66.
This is the quadratic equation n2+ n -132 = 0. Solving for n, we obtain 11 as the answer and deduce that there were 12 people at the party.
Since 66 is a relatively small number, you can also solve this problem with a hand calculator. Add 1 + 2 = + 3 = +... etc. until the total is 66. The last number that you entered (11) is n.
Original post by TeeEm
isn't 11?
I followed you
Original post by SkilledGamer
If you answer this you are smart:At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party? post to me to find out!
post to me to find out!11 as 11+10+9... Is 66
Posted from TSR Mobile
Original post by SkilledGamer
If you answer this you are smart:At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party? post to me to find out!
post to me to find out!I would have said 12.
does n^2 -n -132 solve to give -11 and 12?
(edited 9 years ago)
Original post by SkilledGamer
I followed you
thanks
Not really hard I would say, it's just basic graph theory.
n(n-1)/2=66
n^2-n-132=0
(n-12)(n+11)=0
n=12
n(n-1)/2=66
n^2-n-132=0
(n-12)(n+11)=0
n=12
Original post by Tai_wuz_here
I would have said 12.
Agreed
Original post by samb1234
Actually it should probably be 12
Posted from TSR Mobile
Original post by samb1234
problems with my keyboard, it was 12
1+2+3+4+5+6+7+8+9+10+11 = 66
so must be 12 people as someone had 11 handshakes.
so must be 12 people as someone had 11 handshakes.
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