Combinatorics
I have six friends and during a certain vacation I met them during several dinners. I found that I dined with all the six exactly on one day; with every five of them on 2 days;with every four on 3 days ; with every three on 4 days ;with every 2 on 5 days.
Further every friend was present at 7 dinners and every friend was absent at 7 dinners. How many dinners did I have alone?
The answer is 1.
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