103 A long time ago, there lived a very compassionate queen. She was very, very kind
and very, very rich. She decided to share her wealth with some lucky people.
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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 #1 and set up in order around a large circular
table.
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After dessert, the court jester entered and, starting with chair # 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 be able to ask the Queen for one wish.
For example, if twelve people were invited and seated around the table as shown in the diagram above right,
the jester would eliminate them in the following order:
2, 4, 6, 8, 10, 12, 3, 7, 11, 5, 1
This would leave person #9 the winner.
Winner
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a. When 7 people are invited, show why the lucky winner will be #7
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Group
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b. Copy and complete the table at right that shows the lucky winner for each size of
group from 1 to 18. (Note that if there is only one person, that person automatically
wins.) For which group sizes would person number #1 win? When would person number
#2 win? Describe any patterns you find in your table.
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c. 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 how your pattern helped
you find your answer.
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