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

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

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

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