共享秘密
Sharing a Secret
题目详情
有 5 个人想把一份秘密文件存放进保险箱。他们希望未来只有多数人（>=3）在场时才能打开保险箱。为此，他们打算在保险箱上装若干把锁，而且必须把所有锁都打开才能取出文件。每把锁可以有多把钥匙，但每把钥匙只能开一把锁。最少需要多少把锁？每个人需要携带多少把钥匙？
A group of 5 people want to keep their secret document in a safe. They want to make sure that in the future, only a majority (>=3) of people can open the safe. To accomplish this they want to put some locks on the safe, whereby each of the locks have to be opened to access the safe. Each lock can have multiple keys; but each key only opens one lock. How many locks are required at minimum? How many keys will each member carry?
解析
对于任意 2 人组成的小组，都必须存在一把锁，使得这两个人都没有这把锁的钥匙。这样一来，这把锁的钥匙就要分发给该 2 人小组之外的另外 3 个人。
因此，至少需要 把锁。每把锁有 3 把钥匙，对应唯一的 3 人子集。因此，每位成员应携带的钥匙数为
Original Explanation
For each group of 2 people, there must be a lock which none of them have a key to. But the key of such a lock will be given to the remaining 3 people of the group. Thus, we must have at least 5C2 = 10 Locks. Each lock has 3 keys, which is given to unique 3-member subgroup. So each member should have 10*3/5 =