### Brain Teasers

# Fred and Ethel

Fred and Ethel go to the golf course. They meet 3 other couples there, and everybody gets introduced. After introductions, Fred asks everyone how many hands they shook. He gets seven different answers. Presume that no one shook their partner's hand

How many hands did Ethel shake?

How many hands did Ethel shake?

### Answer

3Since no one shakes his own hand or his spouse's, the most handshakes is 6. Since there are seven different answers, then the given answers are 0 through 6. If Mr A shook 6 hands, Mrs A had to be the one who shook no hands. Similarly, if Mr B shook 5 hands, then Mrs B could only have shaken 1 hand; and Mr and Mrs C shook 4 and 2 hands respectively; and Mr and Mrs D would have shaken 3 hands each. Since only one person could have given an answer of 3, then Fred had to be Mr D, meaning that Ethel was Mrs D. This means that Ethel shook 3 hands.

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## Comments

surely some mistake!!

If they met 3 couples, that is six other people and Ethel shook each ones hand then that must be six hands, the only hand see didn't shake was her partners. So 8 people all together, minus herself and her partner = six!

If they met 3 couples, that is six other people and Ethel shook each ones hand then that must be six hands, the only hand see didn't shake was her partners. So 8 people all together, minus herself and her partner = six!

There is some information missing from the question. You need to be told that people do not shake hands with those people they have already met and that either Fred or Ethel have previously met at least one of each of the couples. The answer is then correct.

I agree with the last two comments. It doesn't make any sense with the information given.

No, I think the teaser and answer is exactly right as stated.

If Fred got seven different answers, and no one shook

hands with his/her spouse, then the most hands anyone

could have shaken is six, so the seven answers must be 0 through 6.

The person shaking 6 hands shook hands with everyone but his/her spouse,

so must be partnered with the person shaking 0 hands.

Likewise, the person shaking 5 hands must have shaken with everyone

but his/her spouse and the person shaking 0, so must be partnered with

the person shaking 1 (who only shook with #6). Similarly, #4 and #2 (who shook with #5 and #6) must

be partners. The only person left to be Ethel is #3.

Both Fred and Ethel must have shaken three hands, with #4, #5, and #6.

Clever!

If Fred got seven different answers, and no one shook

hands with his/her spouse, then the most hands anyone

could have shaken is six, so the seven answers must be 0 through 6.

The person shaking 6 hands shook hands with everyone but his/her spouse,

so must be partnered with the person shaking 0 hands.

Likewise, the person shaking 5 hands must have shaken with everyone

but his/her spouse and the person shaking 0, so must be partnered with

the person shaking 1 (who only shook with #6). Similarly, #4 and #2 (who shook with #5 and #6) must

be partners. The only person left to be Ethel is #3.

Both Fred and Ethel must have shaken three hands, with #4, #5, and #6.

Clever!

Nice, just enough info to be able to work it out, without being obvious. Mind you, I did start off wondering if one of the 'couples' was a man and his dog!! Got me thinking.

dewtell, how do we know specifically that Ethel is #3? What if Fred & Ethel were the #0 and #6 couple? Or the #2 and #4 couple?

The short answer to na-iem's question is that

that is the way the answer was constructed: we

identified the seven other people by the

number of hands they reported to Fred, so clearly

none of them can be Fred. Once we determine

that two of the people answering Fred must be

married to each other, neither of them can

be Ethel (barring some sort of group marriage).

Another way of looking at it is that if

a member of the #0 and #6 couple asked the

same question, he or she would not have

gotten seven distinct answers (because both

Fred and Ethel shook three hands).

that is the way the answer was constructed: we

identified the seven other people by the

number of hands they reported to Fred, so clearly

none of them can be Fred. Once we determine

that two of the people answering Fred must be

married to each other, neither of them can

be Ethel (barring some sort of group marriage).

Another way of looking at it is that if

a member of the #0 and #6 couple asked the

same question, he or she would not have

gotten seven distinct answers (because both

Fred and Ethel shook three hands).

Yes, the teaser is perfectly alright. The only thing missing was an explanation of the answer but that has also been given by Dewtell. Good one!

No this teaser is missing vital information that closes a BIG loop-hole..here is what's missing:

"no one is allowed to shake anyone else's hand more than once"

Without that, the 7 different answers could be anything from 0 to inifinity...or the physical limits of human handshaking whichever comes first LOL.

Other than that, good teaser. Maybe I'll submit the one with 5 couples handshaking at a party. I'll be sure and word it correctly so that there are no loopholes.

"no one is allowed to shake anyone else's hand more than once"

Without that, the 7 different answers could be anything from 0 to inifinity...or the physical limits of human handshaking whichever comes first LOL.

Other than that, good teaser. Maybe I'll submit the one with 5 couples handshaking at a party. I'll be sure and word it correctly so that there are no loopholes.

Oh, and please don't say that it's ASSUMED that no one shakes hands with anyone else more than once. These types of teasers need to be clear because you never know when the answer involes a loophole...so close all loopholes. Again, good teaser though. I actually got this one.

I'm not sure I understand why the person who shook 6 hands MUST be partnered with the person who shook 0 hands. Maybe the person who shook only one hand is partnered with someone who doesn't shake hands at all for whatever reason. Why not 0-1, 2-3, 4-5, 6 and Fred?

Sorry to seem thick, but I am not seeing it.

Sorry to seem thick, but I am not seeing it.

Never mind. Drew a diagram and saw it.

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