Sunday Times Teaser 2601 – Olympic Economics
by Danny Roth
Published: 29 July 2012 (link)
George and Martha are organising a large sports meeting. Usually a gold medal (costing £36) is given to each winner, silver (£17) to each runner-up, and bronze (£11) to each third. In a minority of events, such as tennis and boxing, both losing semi-finalists get a bronze medal. However, George and Martha are going to economise by having third place play-offs in such events, thus reducing the medals needed by an odd number. George noticed that the total cost of the medals is now a four-figure palindrome, and Martha commented that the same would have been true under the previous system.
How many events are there?