**Maths Handshake Puzzle - 4 September**

At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?

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At a party, everyone shook hands with everybody else. There were 66 handshakes. How many people were at the party?

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12 People:

ReplyDelete#12 shakes w/ #1-11 (11 shakes)

#11 shakes w/ #1-10 (10 shakes)

#10 shakes w/ #1-9 (9 shakes)...

11+10+9+8+7+6+5+4+3+2+1+0=66 total handshakes

correct

Deletecorrect nC2 = 66 , and n comes out to be 12.

Deleten*(n-1) = 66*2 and 12 satisfies this relation

ans: 13 members

ReplyDeletefor ex: if 4 mems are there then 6 shakes... i.e. (n-1*(n))/2 so here n-1*n/2=66, then n is 13

This comment has been removed by the author.

ReplyDelete((13-1)*13))/2 = 78

ReplyDelete((12-1)*12))/2 = 66

Still going with 12 :)

Also, check the parentheses: ((n-1)(n))/2

As written, (n-1*(n))/2 simplifies to (n-n)/2, and thence to, well, 0.

nc2= n*(n-1)/2=66

ReplyDeleten=12

the answer is 12 people.

12

ReplyDelete11

ReplyDelete1+2+3+....+(n-1) = 66; total persons = n

ReplyDeleten(n-1)/2=66 => n(n-1) = 132 => n = 12

Explaination: If there are n people, the first person

will shake hand with n-1 persons, the second with n-2, the third with n-3, and the (n-1)th person with n-(n-1)=1

person; ie, the last person. Hence, total handshakes are (n-1)+(n-2)+(n-3)+....+3+2+1

12 for sure..

ReplyDelete132

ReplyDelete12 people....

ReplyDeletecoz,

n = total persons

totally 66 handshakes,

2 persons = 1 handshake

and each person shakes hand with n - 1 persons

==> Half of ( n(n-1) ) = 66

==> n(n-1)/2 = 66

==> n = 12 or -11

==> n = 12

where do does half came?

Delete12, it's so simple

ReplyDeleteHere's the script i made, just save as anything.bat, 14 here, :

ReplyDelete@echo off

set people=1

set handshakes=0

set cnt=0

:LOOP

set /A people+=1

set /A cnt+=1

set /A handshakes+=%cnt%

echo.handshakes:%handshakes%

if "%handshakes%" NEQ "66" Goto :LOOP

echo.Handshakes:%handshakes%

echo.People:%people%

pause > nul

exit /b

12

ReplyDeleteIn 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.

it's just nC2=66

ReplyDeleteso n=12

This comment has been removed by the author.

ReplyDelete(X-1)+(X-2)+(X-3)+......+{X-(X-1)}=66

ReplyDeleteSo X=12

It's basically 11+10+9+8+7+6+5+4+3+2+1+0 which equals 66

ReplyDeleteThe answer is 12. Cmon people it was so easy.

22

ReplyDeleteIn general, with n+1 people, the number of handshakes is the sum of the first n consecutive numbers: 1+2+3+ ... + n.

ReplyDeleteSince 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.

so the answer is 12.

12 people. Number of shakes=n*(n-1) where n is number of people

ReplyDelete33 because 33x2=66

ReplyDelete