HIGHLINE SCHOOL DISTRICT |
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MATH OLYMPIAD |
April 7, 2001 | ||

The Great Escape | |||

There is a legend about a secret spy, Spavadio, from the village
of Cransvania. As he tried to leave the town of Yuglost,
Spavadio was stopped by a guard at the gate. In order to pass
through the gate, he had to give the guard one-third of his
gold coins. Spavadio was then stopped by the guard at the entrance
to the roadway. He had to give that guard one-half of the coins
he had left. Spavadio continued walking along the roadway until he
was stopped by a guard at the bridge. The guard demanded one-fourth of
Spavadio's remaining coins. Finally Spavadio reached the border.
He gave the guard at the border two-thirds of his coins, and crossed
the border. According to the legend, Spavadio had 7 coins left,
exactly enough to buy a horse he could ride to Cransvania.

How many coins did Spavadio have before he was stopped by the first
guard?

`Your response should be made on the response sheet. You may use both
sides of the sheet. Be sure to describe any patterns or different ways
to solve this problem, and your strategy for solving it.`