Olympic Oops!

Megan and I have been watching the Vancouver 2010 Olympics, wishing we were in Canada! We both hope to attend an Olympics someday. Megan suggested we have a party to celebrate the accomplishments of all the athletes and participate in the international spirit of the Olympics.

Megan created an Olympic rings decoration and was about to put it up when I ran into her. Megan was left holding the blue ring, but the yellow, black, green, and red rings had come apart and rolled to various spots of the living room. I quickly apologized and helped her put the rings back together. We were careful to put the colors in the proper order.  After we had fixed the rings and hung them on the wall, Megan wondered how many different ways there are to arrange the colors while keeping the same formation for the Olympic rings.

• Determine how many arrangements can be made.
• Explain how you solved this problem, what was the pattern you found or show up what you did to solve the problem.

Bonus: Generalize your results above for other combinations (if you noticed a pattern, how would it extend to the 6th, 7th, 10th, and 100th rings?).

Tips:

1.   Start with less rings and add a ring at a time. So you see a pattern?
2.   Do not make the mistake of thinking there are 5 rings and 5 places for the rings to go in so there must be 25 arrangements, this would not be correct. There are more arrangements than 25.

 

What is the relevance of the Olympic rings?

The original flag also carried the Olympic motto, "Citius, Altius, Fortius," Latin for "Faster, Higher, Stronger."  The Olympic rings are the official symbol of the Olympic Movement. There are five interlacing rings of the colors blue, yellow, black, green, and red. The rings are set upon a white background.

Baron Pierre de Coubertin designed the Olympic emblem in 1913. The Olympic rings represent the union of the areas - the Americas, Africa, Asia, Oceania and Europe and the meeting of athletes throughout the world at the Olympic Games. Contrary to a popular misconception, the colors themselves do not represent any single continent. The colors were chosen because at least one of these colors is found in the flag of every nation.