组合覆盖问题

（原标题：概率问题） 
来源: 馨尹 于 06-12-17 00:56:20
 已知13个数字中任选3个数字的组合是286组，13个数字中任选6个数字的组合是1716组，请问选6个数字的组合中最少几组就可以包含所有选3的组合？  

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Deuss:

35个可以，不知能否更少

split 13 elements into 7 groups: [1,2],[3,4]...[11,12],[13].

form size 6 groups by picking all 3-combinations from these 7, (add any one additional element if [13] is used). There are C(7,3)=35 of them.