A 10-member society has to pay $30 \mathrm{Ft}$ each for a common goal. Everyone only has paper money (in denominations of 20, 50, 100, and 500 Ft). What is the minimum amount of money the society has in total, if everyone can pay the 30 Ft and no one ends up owing anyone else?
Since there is no 30 Ft note, everyone has money left, at least 20 Ft. Thus, everyone originally had at least 50 Ft, which totals 500 Ft. Those who have a 50 Ft note can only pay if there are also people in the group who pay with 20 Ft notes. Such a person must have at least 80 Ft, as they will receive at least 50 Ft back. A single such person is only sufficient if they have at least 180 Ft, in which case the group has at least 630 Ft. Two such people are also sufficient if they each have 80 Ft, since their 8 20 Ft notes are just enough for the other eight people who pay with 50 Ft notes. In this case, the group originally had a total of 560 Ft. In any other case, there is at least this much money together, since everyone has at least 50 Ft, but at least two people have at least 80 Ft.