[Guest]

Four couples, including Mr and Mrs Wilson, were invited to a party. Mr Wilson was getting late in his office, so he asked is wife to proceed to the party and he would follow soon. When he reached the party, all other - 7 members including his wife were already enjoying the party. He shook hands with a few people, and sat at the bar. Getting a bit curious, he asked the bartender, how many people, his wife has shaken hands with? The bartender told him, hmmm, I can give you a hint - "all possible number of hand shakes have been performed in this party". Mr Wilson said "O, now I know. Thanks". The question is, how did Mr Wilson know the number of hand shakes performed by his wife from this simple clue? No tricks, pure mathematics. Struggle, the first hint will appear tomorrow, followed by a few more.

[Guest]

We need to know how couple handshakes are counted. If one member of a couple shakes hands with another member of a couple, is that suffiecient, or do both members of two couples have to shake hands with both of the other couple? And does a couple have to shake hands with itself? I would assume the last answer is no. I will try to answer with both cases of the other question.

If every member must shake hands with every other member except their own spouse, then Mr and Mrs Wilson each shook the hands of the 6 other members.

If handshakes are per couple and not per member, then each couple shakes only 3 hands. Since Mr Wilson shook hands with "a few" people, and "a few" means more than 2, then he shook 3 people's hands and Mrs Wilson did not shake any hands.

[Guest]

1. There is nothing like a "couple handshake". Each individul'a handshakes are counted separately. Of course, 2 persons shaking hands with each other will be counted as one handshake.

2. Obviously, one would not shake hands with oneself, or one's spouse.

3. Each one has a choice, whom to shake hands with.

4. There is no such rule that one has to shake hands with all others.

We need to know how couple handshakes are counted. If one member of a couple shakes hands with another member of a couple, is that suffiecient, or do both members of two couples have to shake hands with both of the other couple? And does a couple have to shake hands with itself? I would assume the last answer is no. I will try to answer with both cases of the other question.

If every member must shake hands with every other member except their own spouse, then Mr and Mrs Wilson each shook the hands of the 6 other members.

If handshakes are per couple and not per member, then each couple shakes only 3 hands. Since Mr Wilson shook hands with "a few" people, and "a few" means more than 2, then he shook 3 people's hands and Mrs Wilson did not shake any hands.

[Guest]

Hmmm.

Since Mr Wilson only shook a "few" hands, the bartender must be suggesting that all possible handshakes prior to Mr Wilson's arrival had taken place. Since there are 7 people at the party up to that point, and Mrs Wilson is one of them, she must have shaken 6 other hands.

Suspect the tale is meant to mislead us into calculating all handshakes and wondering whether to include Mr Wilson.

[Guest]

Hmmm.

Since Mr Wilson only shook a "few" hands, the bartender must be suggesting that all possible handshakes prior to Mr Wilson's arrival had taken place. Since there are 7 people at the party up to that point, and Mrs Wilson is one of them, she must have shaken 6 other hands.

Suspect the tale is meant to mislead us into calculating all handshakes and wondering whether to include Mr Wilson.

Notice - the bartender did not say "all possible handshakes have taken place', he said "all possible NUMBER of handshakes have taken place". Also remember, no one will shake hands with oneself or one's spouse.

Edited May 18, 2011 by Mukul Verma

[Guest]

Ahha

7, since it is possible for the bartender to shake hands as well.

[Guest]

Before Mr Wilson came, there were 7 people including mrs wilson.

Other than Mrs Wilson, ^ people were there and

1.) I can shake hand with 1 person in 4 ways. (My right-his right, my right- his left like that) den the answer is 24 (excluding bar tender), 28 (including bartender).

if only opposite hand shake is allowed then 12 & 14 respectively.

2.)But the question is "how many people, his wife has shaken hands with?" SO THE ANSWER WILL BE 6 (EXCLUDING BAR TENDER) & 7 (INCLUDING BARTENDER)

[Guest]

There can be only 7 possibilities:

0 handshakes

1

2

3

4

5

6

Whoever does 6 handshakes, his/her spuse can only do 0 hanshakes ( as all others have shook hands with the person who did 6 handshakes so only the spouse can do 0)

Whoever did 5 handshakes, his/her spouse can do only 1 handshake (as all others have shook hands with the person who did 6 as well as the person who did 5, so only 5's spouse can do 1)

Similarly, whoever did 4, the spouse did 2

3's spouse did 3

So Mr. Wilson knows how many his wife did as he knows how many he did. No absolute answer in my opinion but Mr. Wilson would know for sure. Am I right?

[Guest]

There are 7 people at the party + the bartender (assuming that the bartneder is not part of a couple)

She did not shake her own hand. She shakes hands with the 3 couples (6) and with the bartender (1) this makes 7 hand shakes.

When husband comes to the party she shakes his hand (1) to satisfy "all possible number of hand shakes have been performed in this party"

She shakes the hands of 8 people while at the party.

Edited May 18, 2011 by kkehoe5

[Guest]

I have to change my answer to 1.

Seeing as how this is a small party these couples are all friends and know each other well, they would greet each other with hugs and kisses on the cheek. I assume she has visited the bar for a drink where she introduced herself with a friendly handshake and ordered her favorite drink. furthermore, judging by the clues in the OP I can deduce that she ordered a martini with 3 olives and wore a black dress.

[BobbyGo]

0.

His wife is the bartender.

The bar has a strict "No Touching the Customers" policy for all of their employees.

Either that or 6 (each of the other three couples).

[Guest]

It says "Four couples, including Mr and Mrs Wilson, were invited to a party." since the host of the party would not invite themselves to their own party there is more than 8 total people at the party.

But later it says "When he reached the party, all other - 7 members including his wife were already enjoying the party" so there is a contradiction that needs to be resolved before this can be solved

[Guest]

Please clarify the difference between "all possible handshakes" and "all possible NUMBER of handshakes" since the answer we are looking for is not the number of handshakes with Mrs. Wilson, but the number of people with whom she has shaken hands.

[k-man]

Please clarify the difference between "all possible handshakes" and "all possible NUMBER of handshakes" since the answer we are looking for is not the number of handshakes with Mrs. Wilson, but the number of people with whom she has shaken hands.

I think it means that every number of handshakes possible given the number of people was performed. Somebody did 0 handshakes, somebody did 1, etc up to 6, which is the maximum possible # of handshakes given the rules of the puzzle.

Based on this understanding I believe amitgols got the correct answer in post #8.

Please use spoilers, amitgols, and welcome to the den!

[Guest]

I believe it would be 7 handshakes.

6, 2 for each couple, and 1 for the bartender.

[Guest]

It seems there must be trick involved.

Either the bartender is one of the 4 couples for a total of 8 individuals at the party, or the bartender and the party host are one of two separate individuals apart from the 4 couples, and, by not being 'members' of the couples, provide a count of 9 or 10+ party-goers.

As Mr Wilson did not shake hands with each other party-goer, it would be impossible for all possible number of hand shakes to have been performed in the party, unless one was speaking of the number as the number of different combinations or permutations, and, each individual handshake given, counted apart from a handshake received.

[Molly Mae]

Four couples, including Mr and Mrs Wilson, were invited to a party. Mr Wilson was getting late in his office, so he asked is wife to proceed to the party and he would follow soon. When he reached the party, all other - 7 members including his wife were already enjoying the party. He shook hands with a few people, and sat at the bar. Getting a bit curious, he asked the bartender, how many people, his wife has shaken hands with? The bartender told him, hmmm, I can give you a hint - "all possible number of hand shakes have been performed in this party". Mr Wilson said "O, now I know. Thanks". The question is, how did Mr Wilson know the number of hand shakes performed by his wife from this simple clue? No tricks, pure mathematics. Struggle, the first hint will appear tomorrow, followed by a few more.

Logical deduction.

[Auramyna]

I think the question needs to be clarified as it is not clear what it is asking. Does all possible NUMBER mean 0,1,2,3,4,5,6,7? How many people she has shaken hands with depends on whether you include the bartender and/or the husband, and if we say that all possible numbers are accounted for, then one person shook hands with 0 people, so that brings the answer down by one number.

It seems too easy, that she has shaken hands with 6 people (as the OP said not with her own husband) plus or minus the bartender and the person who shook 0 people's hands. It is meant to be a brainteaser so there must be more to it than that. And so I think the question is not clear. Look at bonanova's signature, I can't recall the words but something to do with the question needing to be defined as the starting point of a good brainteaser.

The hardest part of this brainteaser is working out the ambiguous question.

[Guest]

9 - she shook hands with the other 7 invitees, her husband, the bartender, and herself.

The "all possible number of hand shakes have been performed in this party" cannot mean all combinations, ie: 1 person shook 0 hands, 1 person shook 1 hand, as there is no information to differentiate between who shook how many - given the information provided. Additionally, it is impossible, because 8 handshakes is possible. And if 1 person shook 8 hands, then nobody shook 0 hands.

If that was the intent, then I would say 0, his wife must be a double amputee and could not shake hands with anybody. She is the 0. There would be no '8' because its not possible to shake hands with a person with no hands. The husband (of course) is an idiot for asking.

Edited May 18, 2011 by Cheesner

[Guest]

Great amitgol, you got it right. 7 possible number of handshakes can be performed - 0, 1, ..., 6. As amitgol has deduced from the clue given by the bartender, sum of the number of handshakes performed by each couple is always 6 - (0,6), (1,5), (2,4), and (3,3). Thus if one knows the number of handshakes performed by him/her, one can easily find out the number of handshakes performed by one's spouse. Pure logic, please dont look for tricks. And yes, the bar has a "dont touch the customer" policy, specially in view of the recent incidence involving the head of a premiere finance organization, so bartender shaking hands with the guests is ruled out.

Watchout for the next challenge.

[Guest]

Great amitgol, you got it right. 7 possible number of handshakes can be performed - 0, 1, ..., 6. As amitgol has deduced from the clue given by the bartender, sum of the number of handshakes performed by each couple is always 6 - (0,6), (1,5), (2,4), and (3,3). Thus if one knows the number of handshakes performed by him/her, one can easily find out the number of handshakes performed by one's spouse. Pure logic, please dont look for tricks. And yes, the bar has a "dont touch the customer" policy, specially in view of the recent incidence involving the head of a premiere finance organization, so bartender shaking hands with the guests is ruled out.

Watchout for the next challenge.

IF thats the answer, I think the story needs some fine tuning. Still don't see the logic and why if the husband shakes 2 hands his wife can only do 4. Thats not the maximum number of handshakes by my reading.

[k-man]

IF thats the answer, I think the story needs some fine tuning. Still don't see the logic and why if the husband shakes 2 hands his wife can only do 4. Thats not the maximum number of handshakes by my reading.

I agree with you that the puzzle could've been worded better and some ambiguity could be resolved, but nonetheless, there were some clarifications made later that made the puzzle solvable.

It was clarified that husband and wife do not shake hands. So, among 8 people made up from 4 couples, the maximum number of handshakes one person can perform is 6 and the minimum is 0. The logic of coupling (6,0), (5,1), (4,2) and (3,3) is this:

Let's call the person who shook 6 hands Amy. Amy shook hands with everybody except her spouse, so everybody except Amy's spouse shook at least one hand - Amy's hand. This leaves only Amy's spouse as the person who shook 0 hands.

Let's call the person who shook 5 hands Bill. Bill shook hands with everybody except Amy's spouse and his own spouse. Now, everybody except Amy's and Bill spouses shook at least 2 hands - Amy's and Bill's. This leaves Bill's spouse as the only person who shook 1 hand - Amy's.

The same can be continued further to couple 4 with 2 and 3 with 3. So if one knows how many hands he/she had shaken, one can deduce how many hands one's spouse had shaken.

P.S. Given that the both the OP and amitgol didn't use spoilers I didn't use one either.

[Guest]

All possible shake hands is 0,1,2,3,4,5,6

0: one person did not shake with anyone,

6: shake hands with every one except wife or husband.

Therefore, 0 and 6 must be couple.

1->0 if counted he shake hands with 6

5->4 if counted he shake hands with 6

Therefore 1,5 is also couple.

Same reason

2,4 is couple.

Therefore

3 is not only lonely, his wife

Four couples, including Mr and Mrs Wilson, were invited to a party. Mr Wilson was getting late in his office, so he asked is wife to proceed to the party and he would follow soon. When he reached the party, all other - 7 members including his wife were already enjoying the party. He shook hands with a few people, and sat at the bar. Getting a bit curious, he asked the bartender, how many people, his wife has shaken hands with? The bartender told him, hmmm, I can give you a hint - "all possible number of hand shakes have been performed in this party". Mr Wilson said "O, now I know. Thanks". The question is, how did Mr Wilson know the number of hand shakes performed by his wife from this simple clue? No tricks, pure mathematics. Struggle, the first hint will appear tomorrow, followed by a few more.