I have 6 friends and during a certain vacation, i met them during several dinners. I found that I dined with all the 6 on 1 day, with every 5 of them on 2 days, with every 4 of them on 3 days, with every 3 of them on 4 days, and with every 2 of them on 5 days. Further every friend was absent at 7 dinners. How many dinners did I have alone?

I have 6 friends and during a certain vacation, i met them during several dinners. I found that I dined with all the 6 on 1 day, with every 5 of them on 2 days, with every 4 of them on 3 days, with every 3 of them on 4 days, and with every 2 of them on 5 days. Further every friend was absent at 7 dinners, and every friend was present at 7 dinners. How many dinners did I have alone?

Actually (Very sorry), i missed a  line of information last time.

Teachers, please answer it, this might well come in iit!

This Qn is given in a book. Answer given at the end is 1. But how does this answer come? My answer is coming 34.

Intresting question...i think teacher's should come forward to answer this.

Yeah... but where are they? 

That's not given...

FASCINATING.... no one to answer!!!! 

given the total no of dinners a friend is absent ,list down the no of cases :

    CASE:                                                      NO OF DINNERS IN WHICH A PARTICULAR FRND IS ABSENT:

1.when all 6 r invited                                   0

2.when 5 r invited                                         1

3.4 r invited                                                    5 choose 4,ie     5

4.3 r invited                                                     5 choose3,ie 10

5.2 r invited                                                      5 choose 2,ie 10

Sum of all these +(no of dinners alone) =no of dinners in wich a frnd is absent  THEN U CAN SOLVE

Chenglu

Fine, I see no wrong in ur working, but why are the other data given?

Well, I think I've found out a small error in ur working, u've assumed that this combination i.e. 6Co occurs only once... My dear u've to prove it first...