Treebeard's Stumper 22 September 2000

Olympic Number Rings

With our Catalina trip, and school underway, it’s been hard to find time to follow the Olympic Games. My favorites are the track and field events and the odd events like air gun shooting. Here’s another odd Olympic challenge. The Olympic logo consists of five overlapping rings that form nine separate areas, four of them shared between different rings. The stumper is to place the numbers 1 to 9 in these nine areas so that each complete ring has the same sum. This should be easy with these small numbers! How many different solutions are there?

I've numbered the 9 regions in order from left to right, but this numbering does not work for the stumper. The top-left ring has a sum of 1 + 2 = 3, and the top-middle ring has a sum of 4 + 5 + 6 = 15. The challenge is to arrange the digits so that each ring has the same sum!

Answer

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