BALTIC-WAY 2004 Problem 13

The 25 member states of the European Union set up a committee with the following rules: (1) the committee should meet daily; (2) at each meeting, at least one member state should be represented; (3) at any two different meetings, a different set of member states should be represented; and (4) at the $n$ 'th meeting, for every $k<n$, the set of states represented should include at least one state that was represented at the k'th meeting. For how many days can the committee have its meetings?