The Handshake
Handshakes are used traditionally as greetings, but they are also used to seal an agreement when a business transaction has been mutually accepted. A handshake is sometimes used to characterize the personality of an individual. A firm handshake is interpreted to indicate an assertive person or an extroverted personality, whereas a less firm or limp handshake is viewed as a sign of weakness and lack of confidence. Some diseases, such as influenza, can be spread by shaking hands with an infected individual and then touching one’s face. (See Hygiene)
With two people (A and B), there is one handshake
(A with B).
With three people (A, B, and C), there are three handshakes
(A with B and C; B with C).
With four people (A, B, C, and D), there are six handshakes
(A with B, C, and D; B with C and D; C with D).
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.
12.
if there are n+1 people.
no. of handshakes=n
n*(n+1)/2=66
This is a simple problem that can be solved using standard combination formula
nCr = n!/r! (n-r)!
So in order to get 66 handshakes C(n , 2):
n(n-1)/2 = 66
n(n-1)=132
n^2 – n=132
Since n is the number of people in the party, it should be a whole number and the value that satisfies the equation is 12
Hence there were 12 people in the party
Your Answer
More puzzles to try-
How many times a day do all three hands of analog watch overlaps?
There is a perfectly accurate analog watch with hour, minute, and second hands. How many times a day do all three ...Read More »Help your pain
I have seven letters and am something you eat. My only anagram can help your pain. If you remove my ...Read More »I will Make it Lighter
I am weightless, but you can see me. Put me in a bucket, and I\’ll make it lighter. What am ...Read More »Famuous Pi to Square Puzzle
Take a piece of paper and draw a Pi as shown in the figure. Now cut it from the given ...Read More »Who Kidnapped Him
There is a family that live in a round house. The two parents go out for a movie and leave ...Read More »Word with different meaning
A word begins with the letter \’I\’. By prefixing \’A\’, becomes another word that is pronounced the same, what is ...Read More »Number Of Races Puzzle
In order to complete the racing competition, the London racetrack has to submit its top and the most famous three ...Read More »Two guys in the desert puzzle
Two men are in a desert. They both have packs on. One of the guys is dead. The guy who ...Read More »Distance travelled by Tyres
John always keeps a spare tyre in his car. To make full use of all the five tyres, he changes ...Read More »Highest mountain on Earth
Before Mount Everest was discovered, what was the highest mountain on Earth?Read More »What does it mean?
What does it mean?Read More »The Astronaut’s Pee
An astronaut orbiting in a space capsule at normal atmospheric pressure ejects 100 grams of water into the vacuum of ...Read More »Ping pong ball stuck into the pipe puzzle
Your last good ping-pong ball fell down into a narrow metal pipe embedded in concrete one foot deep. How can ...Read More »twice of ten is 22
Prove that twice of ten is the same as twice of eleven.Read More »Cuboid Shaped block
A cuboid shaped wooden block has 6 cm length, 4 cm breadth and 1 cm height. Two faces measuring 4 ...Read More »Initializing an array in constant time
Consider the following array operations. Init(N,d) initializes an array of N elements so that each element has value d. Once ...Read More »What letter is missing From the center
Avoiding The Train
A man was walking along a railway track when he spotted an express train speeding towards him. To avoid it, ...Read More »In British Columbia you cannot take a picture of a man with a wooden leg. Why not?
In British Columbia you cannot take a picture of a man with a wooden leg. Why not? Hint: TimeRead More »Man on Admiral
A man walks into a restaurant and the the waiter says good day Admiral. Why did the waiter call the ...Read More »