National Countdown Round - The Problems
May 12, 2008

Here are a few questions from the 2008 National Countdown Round. Enjoy! (Congratulations to all of our National competitors!)

A line with slope m is tangent to a circle with its center at the origin. If the line is tangent at (3, 4), what is the value of m? Express your answer as a common fraction.

Sonia takes at most three tests on any one school day, and at most seven tests in any five consecutive school days. (A Friday and the following Monday are considered consecutive school days.) What is the least number of consecutive school days in which Sonia could take 20 tests?
A set of distinct positive integers has a total of 11 digits, and all the digits are 1s. What is the smallest possible sum of the integers in the set?
The solutions to this week's problems will be posted on Monday, May 19, 2008.

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