question: 12 people, once a week to a restaurant. Three tables, 4 people per table. Ask any two to sit at least once in the same seat. Q. How many weeks does it take for a dinner party?Answer: 4 weeks. Analysis:1, first of all, consider 8 people, to a restaurant once a week. Two tables, 4 people per table. Ask any two to sit at least once at the same table. Q. How many weeks does it take for a dinner party?
Solution: 8 persons per two groups, then the total has C (8,2) = 28 combinations;
Four people per table, then 4 people per two people a group, a total of C (4,2) = 6 combinations;
Each meal has 2 tables, so it can be concluded that there are 6*2=12 combinations are equivalent, that is, a week of dinner can solve the combination of 12 combinations;
So a dinner party will take at least 28/12≈3 weeks. to encode 8 people, the three-time meal will be seated in the following way:
(1234), (5678);
(1456), (2378);
(1478), (2356). Meet the requirements.
2, the original question, according to the above ideas can have:
Solution: 12 persons per two groups, C (12,2) = 66;
Four persons per table, 4 persons per two persons a group, C (4,2) = 6;
Each meal has 3 tables, 6*3=18 combination equivalent;
So a dinner party will take at least 66/18≈4 weeks.
A combination problem
