[Guest]

Ken and Barbie go out to dinner. They invite 3 other couples. When everyone arrives they greet each other and some even shake hands with one another. However, no one shook hands with his or her own spouse. At the end of the dinner, Ken asks all the attendees "How many people did you shake hands with?" They all reply with a number. The numbers are: 0, 1, 2, 3, 4, 5, 6. How many people did Barbie shake hands with?

Please notify me if this one is already taken. I tried searching w/ multiple keywords but found nothing. Thanks. =)

Edited March 28, 2009 by jdbeautiful

[Guest]

was it really that hard?

[Guest]

6

[Guest]

6

nope sorry.

[Guest]

0. Since barbie is a plastic doll she cant really shake anyones hand

[Guest]

3

[Guest]

Ok, I'm kinda anxious, could anyone really smart come and figure it out, cause I can't?...

[Guest]

Both Barbie and Ken shook 3 hands

[Guest]

Both Barbie and Ken shook 3 hands

this

[Guest]

Both Barbie and Ken shook 3 hands

Yes to both of you. WELL DONE! If you would like you can elaborate how you found the answer for the others.

[Guest]

There's not enough info to determine a final answer. Only SOME people shook hands and we don't know who did and who did not. We need to add an assumption or two to get to an answer. For example, we could assume that Barbie shook hands with 6 people, excluding herself and Ken. But that's a maximum possibility. If, however, we assume that she, as the host, greeted everyone with a smile and a hug, she will have, effectively, shaken hands with nobody. No additional information was provided to narrow the possibilities.

Ken and Barbie go out to dinner. They invite 3 other couples. When everyone arrives they greet each other and some even shake hands with one another. However, no one shook hands with his or her own spouse. At the end of the dinner, Ken asks all the attendees "How many people did you shake hands with?" They all reply with a number. The numbers are: 0, 1, 2, 3, 4, 5, 6. How many people did Barbie shake hands with?

Please notify me if this one is already taken. I tried searching w/ multiple keywords but found nothing. Thanks. =)

Edited March 28, 2009 by andrewz12

[Guest]

actually, to be completely truthful with you - the statement really only tells you how many peoples hands that KEN shook, and not necessarily Barbie. By plotting out the following:

ABCD

abcd

and drawing lines from each letter (uppercase represents the males, lower the females) - we see that two people shook hands with three people. Ken's answer not being given in the list of numbers, tells us that Ken shook hands with 3 people (seven people answered, so the eighth person (second one with 3 handshakes) is Ken). The way that my chart ended up was that D and d (representing Ken and Barbie respectively) each shook hands with 3 people. The configuration was as follows:

A=6 a=0

B=5 b=1

C=4 c=2

D=3 d=3

However, had I drawn lines differently - d could have been 2, and c could have been 3. Really, d (barbie) could have been anything. Ken is the only one who's number of handshakes is definite. Plot it out yourself and see what I mean.

[Guest]

There's not enough info to determine a final answer. Only SOME people shook hands and we don't know who did and who did not. We need to add an assumption or two to get to an answer. For example, we could assume that Barbie shook hands with 6 people, excluding herself and Ken. But that's a maximum possibility. If, however, we assume that she, as the host, greeted everyone with a smile and a hug, she will have, effectively, shaken hands with nobody. No additional information was provided to narrow the possibilities.

I'm sorry to say it, but this puzzle is solvable without any additional help. Keep trying.

[Guest]

actually, to be completely truthful with you - the statement really only tells you how many peoples hands that KEN shook, and not necessarily Barbie. By plotting out the following:

ABCD

abcd

and drawing lines from each letter (uppercase represents the males, lower the females) - we see that two people shook hands with three people. Ken's answer not being given in the list of numbers, tells us that Ken shook hands with 3 people (seven people answered, so the eighth person (second one with 3 handshakes) is Ken). The way that my chart ended up was that D and d (representing Ken and Barbie respectively) each shook hands with 3 people. The configuration was as follows:

A=6 a=0

B=5 b=1

C=4 c=2

D=3 d=3

However, had I drawn lines differently - d could have been 2, and c could have been 3. Really, d (barbie) could have been anything. Ken is the only one who's number of handshakes is definite. Plot it out yourself and see what I mean.

Umm... I guess your answer makes sense...somehow. Still a little bit confusing but I guess you could think about it like that. I had another solution in mind though.

[Guest]

Umm... I guess your answer makes sense...somehow. Still a little bit confusing but I guess you could think about it like that. I had another solution in mind though.

well the connecting lines represent the handshakes, and they can be drawn in several different combinations - so long as the connecting lines meet the criteria of the statement. So given the possibility of several combinations where barbie doesn't have 3 connecting lines, the puzzle is not properly constrained.

had you asked:

"how many people did Ken shake hands with" (rather than ask about barbie)

or changed the wording to read:

"Barbie did not answer" (implies Ken did answer)

"Ken shook hands with the same amount of people Barbie did" (puzzle then provides a definite answer for barbie, since it provides a definite answer for Ken)

those all provide a means to arrive at one and only one answer.

---------

I'm curious as to your logic though?

Edited March 28, 2009 by spikejones

[Guest]

you know what... I'm sorry... I just realized that it will only be one combination. disregard all my previous statements about different combinations. there was enough information here to gather a proper answer - and it is based directly off Halmos's Handshake Puzzle:

http://docs.law.gwu.edu/facweb/jsiegel/Per...shakeanswer.htm

so... my apologies.

now I wonder where the edit button got off to?

[Guest]

lol im a barbie girl in a barbie world i pee out plastic its fantastic lmao XXXXXXXXXXXXXXD

[Guest]

lol im a barbie girl in a barbie world i pee out plastic its fantastic lmao XXXXXXXXXXXXXXD

please don't post just to increase post count.

[Guest]

well, i solved by using a graph representation. A graph with 8 nodes, grouped into 4 sets of two nodes that are never adjacent. Each node is a person, and i added edges between two nodes if the corresponding people shook hands. I don't know which node is which person, but starting by adding 6 edges to any node, all the others are determined in a unique way. At the end there will be a pair of node with three edges each. They must be Barbie and Ken, because Ken is the only one who didn't say how many people he shook hands with, and all the other nodes have a different number of edges incident to them, from 0 to 6.

[plasmid]

Here's my explanation of the answer

There are 8 people at the party. If no one shook hands with their spouse (or of course themself), each person could shake hands with at most 6 people. Somebody did shake hands with six people, let's give that person a name: "Alan". Since Alan shook hands with six people (everyone else at the party except for his spouse), we know that his spouse is the only person who could possibly have not shaken hands with anyone else, let's call her "Brenda" and she's the person who shook zero hands.

Now someone shook 5 hands - meaning he shook hands with everyone except for his spouse, himself, and Brenda (who shook no hands); I'll call him Carl. Now, Alan has shaken hands with everyone I haven't named yet, and Carl has shaken hands with everyone I haven't named yet except for his wife, we know that the only person who could have shaken only one hand is Carl's wife, who I'll call Debbie.

Hopefully you see that this same line of reasoning will apply to the next couple -- I'll call Evan the person who shook 4 hands and Francine the person who shook 2 hands.

Finally, that leaves us with Ken and Barbie (whose names clearly should have been Greg and Harriet : ) We know that they each shook three hands: with Alan (who shook hands with everyone except Brenda), Carl (who shook hands with everyone except Brenda and Debbie), and Evan (who shook hands with everyone except Brenda, Debbie, and Francine).