MathDB

Let

m,n

be positive integers with

1 \le n < m

. A box is locked with several padlocks which must all be opened to open the box, and which all have different keys. The keys are distributed among

m

people. Suppose that among these people, no

n

can open the box, but any

n+1

can open it. Find the smallest possible number

l

of locks and then the total number of keys for which this is possible.

Problem Statement