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Title: The marital friends party Post by: Exploited on October 08, 2007, 11:10:41 am We was having a big party. Only martial couples (wife + husband) was invited (there were NO single guests). Total of 60 martial couples attended to the party (that was a huge party indeed!). Of course I was a part of a martial couple too - I was with my wife there.
At the start of the party all guests was shaking hands between each other (of course a husband will not shake hands with his own wife - they shake hands with other married couple!). At the end of the party I made a quick survey. I asked everybody "With how many people you shaked hands today?"... Amazingly, but every guest gave me different answer - it came that there was no two people who shaked hands with other guests the same times (for example if guest X shaked hands 23 times today - then no other guest Y shaked hands the same 23 times)! What a co-incidence... nevermind - lets go to my question for you: How many times my wife shaked hands with guests on the party? Title: Re: The marital friends party Post by: keaglez on October 11, 2007, 10:51:41 am Zero??
Title: Re: The marital friends party Post by: Exploited on October 11, 2007, 11:12:23 am it is not zero, but how did you calculated that number? :)
Title: Re: The marital friends party Post by: keaglez on October 11, 2007, 11:29:48 am LOL, i guess if there are 120 people (60 couple), and every of them are not shaked hand with his/her wife/husband so the maximum is one people can shake 119 people hand.. Well, there are 120 people and no one same, so 119 people will shake 1 until 119 hand... So the 0 is the last possibilities for the 120th people...
Title: Re: The marital friends party Post by: Exploited on October 11, 2007, 11:04:46 pm Let's start from the situation with 4 people:
me wife \ | M1 F1 Check it out and you will see that it is the only solution: M1 - shaked hands 0 times My Wife - shaked hands 1 time F1 - shaked hands 2 times => all guests shaked hands different amount of times & no man shaked hands with his wife This is the only possible solution (try it out)... However I will leave you with the two couples example... now it's your turn to give me the answer for N=60 :))) Title: Re: The marital friends party Post by: BlinK_ on October 11, 2007, 11:47:26 pm I think its 118.
She shook hands with everybody except herself and exp. Title: Re: The marital friends party Post by: keaglez on October 11, 2007, 11:51:40 pm LOL, i forgot that... ;D
Title: Re: The marital friends party Post by: Exploited on October 12, 2007, 07:00:38 am Blink_ not true...
Try to extend the problem with 2,3,4 couples and then make it for N couples recursively Title: Re: The marital friends party Post by: Exploited on October 24, 2007, 09:53:14 am ok it's hard to represent it in text mode, but it happens that if you add one man and woman additional - your wife will shake hands one more time
=> if we have 1 couple she shake hands 1 time, 2 couples - 2 times, "n" couples - "n" times => my wife shaked hands 60 times total :) |