Question 109
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 $k \lt n$, 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?
(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 $k \lt n$, 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?