One of those hand shaking problems

[ashi_mashi]

Hi agian...
I have one of those hand shaking problems..it says:
There are 14 couples. There is some shaking of hands. No one shakes hand of their date. No one shakes hands more than once with anyone person. A boy asks each person how many times they shook hands. Each person gave him a different answer. How many times did the boy's date shake hands?Now, i thought it well through and i got the idea that assuming that everyone shook hands, then the total number of hand shakings would be "26+25+24+...+13+13+12..+1+0". (I drew a little sketch ) I thought that since there are two 13's (i'm not 100% sure, but I'm pretty sure;)) then, the boy has to be one of those 13's. And the problem is kinda solved...but, the TOTAL number that everyone shakes hands is the same, that is 26...so, i guess it can't be solved this way...anyway, I'm a little confused...i guess there is another way to solve it, or maybe i shouldn't assume that everyone shakes hands.

Thanks agian.

 

[honestrosewater]

You've gotten it right, with the reasonable assumption that no one shakes their own hand. There are 28 people. The boy asks 27 different people and gets 27 different responses. By the rules, no one can shake hands with more than 26 people, so the responses ranged from 0-26. The person who shook hands with 26 people shook hands with everyone except him/herself and the person who shook hands with 0 people. So {0, 26} must be a couple. By the same reasoning, the rest of the couples are {1, 25}, {2, 24}, ... {13, 13}. Also, by the time you get to 13, 13 has already shaken hands with 14-26, and 0-12 are already paired with their dates, so the boy must be 13's date.

 

[tacman]

It seems like you have a good start to solving this problem, but you're right, assuming that everyone shakes hands may not be the best approach. Instead, try to think about the problem in terms of the total number of handshakes and how many times each person shakes hands. For example, if each person shook hands with 13 other people, then the total number of handshakes would be 14 * 13 = 182, which is much higher than the total number of handshakes you calculated.

Another approach you could take is to think about the relationship between the boy's date and the number of handshakes they had. Since no one shakes hands with their date, the boy's date must have shaken hands with every other person in the room. So, if we subtract the number of handshakes the boy's date had from the total number of handshakes, we can find the number of handshakes between the other 13 couples. From there, you can try to figure out the number of handshakes each person had and see if that leads you to a solution.

Don't get discouraged, problem-solving can be tricky sometimes, but keep thinking and trying different approaches and you'll eventually find the solution. Good luck!