# 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

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Speedi lives at the corner of Chestnut and Mason and drives to school, which is located at the corner of Jackson and Grant, every morning. She usually drives down Mason, then turns left on Jackson. However, after going 12 blocks, she’s late for school! See if you can find a shorter route. The streets in downtown San Francisco are set up in a grid with Columbus Avenue running diagonally between them, as shown on the map at right. Columbus directly meets the intersection of Chestnut and Taylor, as well as the intersection of Washington and Montgomery. One-way streets are shown with arrows. Kearny is unusual as it only allows traffic that heads toward

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As a treat, one mom offered to bake some cookies. While waiting for them to cool, all three students fell asleep. After a while, Latisha woke up, ate her equal share of cookies and went back to sleep. A little while later, Susan woke up, ate what she thought was her equal share and fell asleep again. Then Hieu woke up, ate what she thought was her equal share, and went back to sleep. Later, all three kids woke up and discovered 8 cookies left. How many cookies were baked originally? The next day, four students got together to study. Another mom baked cookies. Again the four students fell asleep. As before, they woke up one at a time and each ate her equal share. When they all awakened, they discovered 81 cookies remained. How many cookies were baked originally? Your Task: • • • Solve both problems. Compare the original cookie numbers to the final numbers of cookies left. What is their relationship? What would happen if there were 5 students? As before, each student ate her equal share of what was left. When they all awakened, how many cookies remained? How many cookies were baked originally? Explain how this problem would work for any number of