Give Me a Hand
A professor and their spouse are at a party. At the party there are four more couples (overall five couples).
During the party couples shake hands with the following rules:
a. One does not shake hands with oneself.
b. One does not shake his/her spouse’s hand.
At the end of the party the professor asked all the other guests at the party (including their spouse) how many different people they shook hands with. Each person tells him a different answer (meaning, if one person said “five,” no one else said “five”).
With how many people did the professor shake hands?
Communicated by Michael Geike (who heard it in college in 1999).
feel free to share but so slammed I have almost no time to do more now
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yes. –s
Was there also supposed to be the direction of no one shook hands with the same person more than once??
It can be the same.
Can the number of hands that the professor shakes be the same as another guest’s, or does it need to be different?
We (my class) would love a solution emailed to us….thanks!
glad you’re enjoying it
there’s the AMS grad blog: http://mathgradblog.williams.edu/
another is the math less traveled: http://mathlesstraveled.com/
Tried emailing you but your address didn’t work.
maybe why do math: http://www.whydomath.org/index.html
Hello! This is my 1st comment here so I just wanted to give a quick shout out and say I genuinely enjoy reading through your blog posts.
Can you recommend any other blogs/websites/forums
that go over the same subjects? Thanks!
I want a riddle to make model on it can anyone help?????????????
Heyyy coach Jackson!!! We love you!!!! #AlgebraIsCool
I’ll send a hint
I would like an email on what the solution is please.
Rage: nope — your second answer is right (sjm1 AT williams.edu)
5..
anonymous: please include name/email: correct (sjm1 AT williams.edu)
Nope — sjm1 AT williams.edu
Has to be 5.
sergio — correct; email me at sjm1 AT williams.edu
Ravi: correct (sjm1 AT williams.edu)
quiz genious: correct, not posting as it’s the soln (sjm1 AT williams.edu to chat)
quiz genious: correct, but why? (sjm1 AT williams.edu)
[email protected]: correct answer but can’t tell if logic is write as didn’t provide details — email me at sjm1 AT williams.edu to chat further /s
nope — I’ll email you a hint. //s
I started with drawing 5 couples
If the first person shakes one hand, the second two etc and you put a ring on every person that shakes a hand and on the person that get his hand shook
Then my answer is that the professor and his spouse both only shook hands with two people.
ok
please sent me a hint to my email dont get it
I’ll send a hint //s
i’m not getting how to solve the problem:(
there is a unique answer
There’s nothing unique about the professor from any other person there. The answer could be several answers.
Nope. Try doing small cases first (2 couples, 3 couples) and try and find a pattern.
32. he and the other guests all have 2 hands. he shakes both hands from all people with one hand and again with another
he gets her answer as well as the other 8, but doesn’t know which answer is hers.
Did the professor asked his spouse that how many different people she shook hands with?
Or only the 4 other couples?
no — there are only 10 people ./s
no (sjm1 AT williams.edu)
He shook hands with 8 people. right?
Did he shake hands with 16 people?
Neveron: are you asking or are you telling me for your response? The number you sent *is* correct. sjm1 AT williams.edu
No, a bit higher.
Is it 2? /:
It is not 10. He is not single.
Ten. He is single
Nope, not 10. Also, he’s not single /s
the answer os ten. FIVE couples, ten people, ten hand shake. He is single.
no — try doing special cases (just 2 couples, just 3 couples, …)
the answer is 2
anonymous: email me at sjm1 AT williams.edu
person 1 shook 1 person
person 2 shook 2 people
person 3 :3, person 4:4 and so on until person 8 shook 8 people
nope. try special cases: 2 couples, then 3 then 4 //s
he shook hands with 0 people.
This is a bit hard to follow. Try having just 2 couples, and go through all the possibilities of who shook 0 hands. Then do the same with 3 couples, then 4….
Ok so let me get this straight, with two couples there are 3 answers-0,1,2, So if one of them says 0 then its safe to not count them so there are only 3 people that interchanged handshakes,if the proffesors wife says 0 then the proffesor shook two hands but if the other couples spouse says 0 then the professor only shook one hand….
With three couples the same thing happens, if the professors wife says 0 then he shook 4 hands but if someone else said 0 then he only shook 3 hands.
With four couples he either shakes 6 hands or he shakes five hands.
and so on and so fourth……
no, a bit higher — try doing just 2 couples, then just 3, then just 4. look for a pattern. //s
Is 1 the correct answer
nope — try smaller cases (just 2 couples, then just 3, then just 4). //s
Is it 2?
There’s a unique answer. The number of hands he shakes doesn’t depend on the order. It only depends on the restrictions of the problem (that one shaked exactly 0, one exactly 1, …).
if there is five couples it depends in the order the profesor starts shaking hands if he goes
1st he would shake 8 hands
2nd he would shake 7 hands
3rd he would shake 6 hands
4th he would shake 5 hands
If he is the last coulpe to shake hands he would only have 4 hands he has not shake
no one left until the problem was solved.//s
did anybody leave the party?
nope — try doing just 4 people, then just 6, then just 8….
if im not mistaken, the answer is zero
send your soln to me ([email protected]) and I’ll take a look at it. //s
I think I have it, but is the final answer just one answer or is it a depended of how others responds. In my solution I proved that the above is possibe however, the answer may vary.
no, lower. try doing just 2 couples, then just 3 couples….
Is it 9?
No, not 3. try special cases — try just 2 couples, then 3, then 4….
is the answer 3?
It’s not zero. Email me at [email protected] if you want a hint.
0
lower than 8. email me ([email protected]) for a hint
8
I’m not sure, as you haven’t provided enough details. Do the case of 2 couples (4 people) very carefully. The person knows that among the three remaining people (which includes his spouse), one shook 0 hands, one shook 1 hand, and one shook 2 hands. You will see that the person ended up shaking 2 hands (as did his spouse). If you do three couples, you’ll find he shook 3 hands, NOT 4. One way to attack this is to ask: whom shook the maximum number of hands? You’ll find it isn’t the spouse, and then the person who shook 0 hands is the spouse of the one who shook the maximum.
I don’t see how it can’t be that he shook hands with 8 people. I first did 2 couples (4 people) results in 2 handshakes, 3 couples 4 handshakes, 4 couples 6 handshakes. The pattern I see is that the number of handshakes is always 2 less than the total number of people. This would make sense given that the professor doesn’t shake with himself or his spouse thus 10 people 8 handshakes. What am I missing? Is your definition of a couple different than 2 people?
try doing smaller cases first — imagine there are just 4 people total, then 6, ….
5??? I really dont know.
yes, the prof can (and in fact MUST) say the same as someone else
I have a question about this:
Can Professor say same number than someone else said or can his spouse?
Cause with 2 couples there is only 2 possible amount of shakes, cause u can shake only with 0, 1 or 2 peoples and if someone shakes “0”, no-one cant shake 2 anymore. So with this function there is always 2 less ansrews that peoples.
I think it must be zero, because everyone else would take the answers 1, 2, 3, 4, 5, 6, 7, and 8. The trouble is, I don’t know if anyone else said zero. I’m a 6th grade teacher posting this for my students, so if I don’t figure it out, I’m sure one of them will!
I think it must be zero, because everyone else would take the answers 1, 2, 3, 4, 5, 6, 7, and 8. The trouble is, I don’t know if anyone else said zero. I’m a 6th grade teacher posting this for my students, so if I don’t figure it out, I’m sure one of them will!
he doesn’t have to — he cannot shake his own or his spouse’s hand
Does he have to shake hand to all except self and spouse?
No, it isn’t 7. try doing just 2 couples, then 3, and see if you can detect a pattern.
I’m having internet trouble tonight and can’t send email. Email me at [email protected] and let me know which riddle.
is the answer 7
i want to know the answer
If you shake someone’s hand, your shake count goes up by 1, as does theirs; it does not matter how many people either of you have shaken.
Im confused if he shakes a hand does it accumulate with the numbers he has shaken? So, he shakes hands with some who has shook five hands does that count as six? If i had to guess 4 as he doesnt shake the hands of spouses?
Nope. start with two couples, then do three couples….
6?
Try special cases. Imagine there are just 4 people total. Then try 6 people….
ths riddle is tricky send me a clue
correct again, not posting as it is the soln
Richard: not posting your solution as it is correct; well done!
it’s possible. it’s not 9 answers for 10 people.
Is it possible? There would be 10 people if you exclude yourself and your spouse you leave 8 potential people to shake hands with. Assuming you only shake hands with each person once you have the answers to the question 0-8 which is only 9 answers for 10 people so one person would either have to shake hands with the same person twice to enable 10 different answers or two people have to give the same answer. Unless you allow polygamy
yes — don’t shake the same hands twice ..s
Can I assume that they don’t shake the same hand twice?
I’ll email you as I don’t want someone to see the hints by mistake.
Hi, i send you the message about helping me with some riddles for example this one, fruitful problem, bridge over troubled students, and a peeny for your thoughts.
Please repley.
Just email me at [email protected] for hints / solns
Nope. The professor did not shake hands with 8. If you want a hint, let me know.
oh…and we need some answers before June 3rd…if possible!!!!
We know you don’t print answers, but we need to know if we are right….
The professor shook hands with everyone but himself and his spouse which would mean he shook hands with eight people!
Yes????