**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?

**For Solution :**Click Here

This Blog is a collection of brain teasers, puzzles (maths,fun,brain etc), riddles,Questions, Quiz.

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

Subscribe to:
Post Comments (Atom)

Difficulty Level 3/5
(803)
Logic Puzzles
(534)
Difficulty Level 4/5
(532)
Picture Puzzles
(384)
Maths Puzzles
(372)
Riddles
(369)
Difficulty Level 2/5
(360)
Trick Teasers
(300)
Popular Puzzles
(232)
Rebus Puzzles
(168)
Humor Puzzles
(161)
Series Puzzles
(138)
Interview Puzzle
(131)
What Word Am I
(103)
Difficulty Level 1/5
(90)
Equation Puzzles
(85)
Trivia
(79)
Mystery Puzzles
(76)
Who Am I
(60)
Difficulty level 5/5
(59)
Murder Mystery Puzzles
(45)
Algebra
(41)
Probability Puzzles
(40)
Square Count
(40)
Cipher Puzzles
(38)
IAS-EXAMS
(35)
Science Puzzles
(34)
MatchSticks-Riddles
(28)
Situation Puzzles
(28)
Puzzles of Age
(23)
statement
(19)
Google Interview Puzzle
(18)
Read Between Lines Puzzles
(18)
Microsoft Interview Puzzles
(16)
Odd One Out
(15)
Time Distance Problem
(14)
Relationship Puzzles
(12)
Cards
(11)
Story Puzzles
(11)
Paradox Puzzles
(9)
Classic
(6)
Directional Puzzles
(6)
Best Of 2011
(5)
clever
(5)
Analytical
(4)
Brain-Twister
(4)
Mind Games
(4)
chess
(4)
What Does This Text Mean
(3)
CHALLENGING
(2)
Double Meaning
(2)
Acronym
(1)
Measure
(1)
Suduko
(1)
Video Riddle
(1)
coin-Puzzles
(1)
m
(1)
pop
(1)
triv
(1)

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

ReplyDeleteThere weee 12 people at the party.

ReplyDeleteIf one person shakes hands to every one,therefore the number of shakes will be 11.

The second person will next shake to the ten people for the total shakes of 10.

The third person will shake to 9 people with 9 shakes.

The fourth person will shake to 8 people with 8 shakes.

Now the number of shakes will be decreasing by 1 as we have seen from the first shakes of the first person to everyone. Therefore the last shake will be done by two people for 1 shake.

Now the total shakes will be equals to 11+10+9+8+7+6+5+4+3+2+1=66.