# If every person at a party shakes the hand of every other person and there were 105 handshakes in all How many persons were present at the party?

The answer is 15 people. Each shook hands with 14 others, and there are half that many handshakes (pairs).

The total number of pairs (distinct handshakes) within the group is defined by the formula T = [n!/(n-2)!] /2

Given T = 105

we get n!/(n-2)!=210 which implies n(n-1)=210 on solving we get n=15

### If each of seven persons in a group shakes hands with each of the other six persons then a total of forty-two handshakes occurs?

The answer is 21 handshakes because the first person shakes hands with the other 6 people. The second person shakes hands with 5 people because they already shook hands with the first person. The third person shakes hands with 4 people because they already shook hands with the first and second person. The fourth person shakes hands with 3 people because they already shook hands with the first, second, and third. The fifth person shakes…

### At the end of a banquet 5 people shake hands with each other How many handshakes will there be in total?

Each person shakes hands with every other person at the end of the banquet. When person 1 shakes hands with person 2 that constitutes one handshake even though 2 people are involved. So the answer is 10 total handshakes because the 1st person will have 4 total handshakes(because he can't shake hands with himself, he has 4 and not 5 total handshakes), and then the 2nd person will have 3 total handshakes (you wouldn't say…

### If each OF seven persons in a group shakes hands with each of the other six persons then a total of forty two handshakes occurs?

The correct answer is 21. The first person shakes hands with the other 6 people. The second person shakes hands with 5 people because they already shook hands with the first person. The third person shakes hands with 4 people because they already shook hands with the first and second person. The fourth person shakes hands with 3 people because they already shook hands with the first, second, and third. The fifth person shakes hands…

### There are five people in a room Each person shakes the hand of every other person exactly once How many handshakes are exchanged?

Everyone shakes hands with 4 other people. Since there are 5 people in the room this would suggest there are 5*4 = 20 handshakes. However, you would then be double counting handshakes: A shaking hands with B and B shaking hands with A is, in reality, only one handshake. Thus there are 5*4/2 = 10 handshakes in all.

### Examples of hard riddles or quizzes?

if there are 2 people in a room and each one shakes hands once with every other person in the room, how many hand shakes are there?... answer( 1 handshake) pretty easy isn't it? if there are 3 people in a room and everyone shakes hands with everyone else, how many hand shakes are there? answer( three handshakes) now how many handshakes will there be for 5 people in a room? its your time to…

### In a party everyone shakes hand with each other. If total number of handshakes is 780 how many people were there?

There were 40 people at the party. Let n be the number of people at the party. Each person shakes hands with every other person, so each person shakes hands with (n - 1) people, a possible total of n(n - 1) handshakes. But when person A shakes hands with person B, B also shakes hands with A, so each handshake would be counted twice. → number_of_handshakes = n(n - 1)/2 total number of handshakes…

### How many handshakes will there be in total if 10 people shake hands with each other?

"Each other" leaves this very open-ended; that depends on if A shakes with B or A shakes with B & C, OR if A shakes with all the other nine, etc. I would say the answer would have to be one of two: 10 or 100. If each person chooses only one to shake with, it would be ten. IF each person shakes with everyone there, all ten, it would be 100. Since this question…

### How many people are there if everyone shakes hands and there are 66 handshakes?

Assuming that each person shakes hands with every other person, there are 12 people. Let n be the number of people. Then each person shakes hands with (n-1) people and if you ask every person how many hand shakes they made and total them you will get a total of n(n-1) handshakes. However, each handshake involves two people and has been counted twice - once by each person that shook hands - thus number of…

### When ten people in a room shake hands with everyone else how many handshakes will there be in total?

### In a room there are N number of people if everyone shakes hands how many handshakes are made?

Depends what you mean, if you mean if everyone shakes hands just once then N-1 handshakes are made. If you mean if everyone shakes hands with everyone else then the answer is (N-1)+(N-2)+....+2+1 (we dont include N as they're not going to shake their own hand, obviously) written as Σn-1i=1 i, this is a arithmetic progression and so the total number of handshakes will be equal to (1+(n-1))(n-1)/2

### How many handshakes if 8 people shook hands at a party?

Assuming that each person makes a shaking partnership just once and no one shakes there own hand,Consider the situation. The eight people are in a line. The first person goes down the line shaking hands with everyone else so he shakes hands 7 times. He then sits down. The second person shakes hands with everyone left in line, six handshakes, and sits down, He has no need to shake ands with the sitting man as…

### At a party 28 handshakes were exchanged How many people were present at the party?

The underlying assumption is that each person shakes the hand of each other person. If there are "n" people, each will shake the hands of "n-1" other people. To avoid counting double, the result has to be divided by 2. Therefor, the number of handshakes is equal to n(n-1)/2. Trying this out for several values of "n" should be faster than using the quadratic formula. (If you use the quadratic formula, you will probably get…

### If 7 girls shake hands only once how many handshakes does that make?

The question is ambiguous: If each girl shakes one other person's hand once, then there are seven (7) handshakes. If each girl shakes each other girl's hand once, then there are 7 x 6 x 0.5 = 21 handshakes (each girl x each other girl x cancelling out the doubles). Another way to look at this one: If each girl shakes each of the other girl's hand once, there would be 42 shakes (each girl…

### 15 friends at a party and all kisses each other then how many kisses?

This is a variation on the handshake problem which say if there are n people at a party and every one shakes hands with every other one, how many handshakes are there? It is well know that kisses in fact are cleaner than handshakes which to tend to pass diseases. So thanks for a cleaner version of this classic math problem! n(n-1)/2 is the formula for the number of handshakes OR kisses for n people…

### There are six people in a room each person shakes hands with another person once until they all shake hands fifteen handshakes occur Explain how the fifteen handshakes resulted?

Start out with small cases and you will see the pattern. At that point, you might even guess what the formula is. So let's ay the room has only A and B---two people. there is one handshake (A with B). Three people (A, B, and C), there are three handshakes (A with B and C; B with C). Now, let's try four people (A, B, C, and D), there are six handshakes (A with B…

### What does it mean when someone squeezes your hand during a handshake?

Don't get too thrilled over the different types of hand shakes. Some people will give a firm handshake; others will give weak handshakes(my father always use to say you can tell what type of person you are dealing with by the way they shake hands ... he was right!) Some people give gentle handshakes and may squeeze the hand a little. This is affectionate, but doesn't mean they love you, but care about you. There…

### How many handshakes do 1000 people make?

Making the totally unrealistic assumptions that each person shakes the hand of every other person once and only once the answer is 499500. However, it is totally unlikely that any sane person would keep track of how many of the 999 possible partners he or she had shaken hands with. Furthermore, even if the time taken to shake one person's hand and move on to the next person is only ten seconds, it will take…

### There are 8 people they all shake hands how many hand shakes are there?

There are 28 handshakes if everyone shakes hands with everyone else. It is an arithmetic progression and can be solved with the equation Sn=(1+(n-1))(n-1)/2 where Sn is the total sum of handshakes for n people. NB: I have used n-1 instead of n in the equation for the sum of an arithmetic progression, because you're not really going to shake hands with yourself, so you don't include the nth term, in this case 8. Alternatively…

### At a meeting every person shook hands with every other person exactly 1 time and there were a total of 28 handshakes then find the number of people at the meeting?

8 Explanation: The general formula for the number of handshakes is n(n-1)/2 where we have n people shaking hands with n-1 other people. so 28=n(n-1)/2 or 56=n^2-n the solution to this comes from solving n^2-n-56=0 so this factors as (x-8)(x+7) and the answer is 8 To understand this formula think of a small number, like 3 people Each person can shake hands with 2 other people. Let us call the people A, B, and C…

### 12 members were present at a board meeting each member shook hands with all of the other members before and after the meeting how many hand shakes were there?

66. Each of the 12 members shook hands with the 11 other people. That would make 12*11 hand shakes. BUT, the A shaking B's hand is the same event as B shaking A's hand so all these handshakes are double-counted. The actual number is half that ie 33. If you are more familiar with combinatorial mathematics, the answer is the number of combinations of two obejects from 12, which is 12C2 = 12*11/(2*1)

### If in a party everyone shakes everyone else and the total handshakes are 66 How many people are in the party?

Answer : 12 people. The 1st person can't shake hands with him/herself so has 11 handshakes, the 2nd person has 10 ....and so on. The total is 11 + 10 + ....+ 3 + 2 + 1 = 66. Another way is to use the formula to sum a range of consecutive integers from 1 to n. The Sum = ½n(n - 1) In this case, we can put, ½n(n - 1) = 66 then…