I-have-6-friends-and-during-a-vacation-I-met-them-during-several-dinners-I-found-that-I-dined-with-all-the-6-exactly-on-1-day-with-every-5-of-them-on-2-days-with-every-4-of-them-on-3-days-with-eve

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Question Number 21686 by Tinkutara last updated on 30/Sep/17

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

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