多数人才能开保险箱
Sharing a Secret
题目详情
5 个人要把秘密文件放入保险箱。希望未来只有当多数（至少 3 人）共同合作时才能打开保险箱。
保险箱上可装多把锁：每把锁必须被打开才能取出文件。每把锁可以配多把钥匙，但每把钥匙只能开一把锁。
问：最少需要多少把锁？每个人需要带多少把钥匙？
提示：对任意 2 人小团体，必须存在一把他们都没有钥匙的锁。
A group of 5 people want to keep their secret document in a safe. They want to make sure that in future, only a majority (>=3) can open the safe. So they want to put some locks on the safe, 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 the minimum? How many keys will each member carry?
Hint
For each group of 2 ppl, there must be a lock which none of them have a key to.
解析
最少需要 10 把锁，每人携带 6 把钥匙。
理由：任意 2 人不应能开箱，因此对每个 2 人组都必须有一把锁不给他们钥匙，只给剩余 3 人钥匙。这样的 2 人组共有 个，因此至少 10 把锁。
每把锁给 3 把钥匙（给某个 3 人组），总钥匙数为 ，平均到 5 人每人 6 把。
Original Explanation
10 locks, 6 Keys.
Solution
For each group of 2 ppl, 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 ppl of group. Thus, we must have atleast 5C2 = 10 Locks. Each lock has 3 keys, which is given to unique 3-member subgroup. So each member should have 10*3/5 = 6 keys.