B. 4011. Assoc City has 2007 inhabitants. They like joining clubs. The following two resolutions are passed to regulate club life: (1) every club must have exactly 101 members, and (2) no two clubs may have exactly the same set of members. In the senate of the city, each club is represented by a member, and it is against the law for two clubs to have the same representative. The committee of law are planning to impose a limitation on the number of clubs, so that however they are formed according to the rules above, it should always be possible to delegate representatives. What is the maximum number of clubs that may be allowed by the committee?
Solution (in Hungarian)