# Before The Lottery Case Study

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GOLD MEDAL PROBLEMS

page 13

GM-12.

GOING IN CIRCLES In the olden days before the “Lottery” or the “Big Spin”, there lived a very compassionate queen. She was very, very kind and very, very rich. In fact, she decided to share her wealth with some lucky people. Once every year she would invite some of her subjects to a banquet dinner and choose one lucky winner who would be granted one wish. The chairs were numbered consecutively starting with number 1 and set up in order around a large circular table as shown at right.

11 10 9 8 7

12

1 2 3 4 5

6

After dessert, the court jester entered and, starting with chair number 1, followed this rule: he eliminated every other person in a clockwise rotation until only one person was left. That person would be the lucky winner of the year and could ask the Queen for one wish. For example, if twelve people were invited and seated around the table, the jester would eliminate them in the following order: 2, 4, 6, 8, 10, 12, 3, 7, 11, 5, 1 This would leave person number 9 the winner. Your Task: • • • When 12 people are invited, show why the lucky winner will be person number 9. Find the lucky winner for at least 20 different-sized groups of people. Describe any patterns you find. Using the patterns you found, tell where you would sit in order to be the lucky winner if you were one of 270 people invited to dinner. Explain why you think your answer makes