|The Olympic emblem consists of five overlapping rings
containing nine regions. In order to contribute to a pension fund
for the retiring International Olympic Committee people are asked
to deposit money into each region.
The guidelines allow the delegate to take all the money in any one of the rings. Place the numbers 1, 2, ... 9 in the nine regions so that the amount in each ring is the same. How many different ways can you find to do this? (Problem from University of Sydney Mathematics Enrichment Groups 1999)