Monthly Archives: February 2012

Millionth Term

What is the millionth term in the sequence ? Source: mathcontest.olemiss.edu 2/27/2012 SOLUTION A simpler problem: What is the term? To get a good understanding the problem we list some of the terms and their position as follows. Alternatively we can list … Continue reading

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Call Letters

In the United States of America, radio and television stations have three or four letter identification call letters. East of the Mississippi River, the call letters begin with W as in WCBI and WGN. If W is not used except … Continue reading

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Coloring Book Covers

A bookbinder must bind 12 identical books using red, green, or blue covers. In how many ways can this be done? Source: http://www.mathcircles.org SOLUTION Suppose there are only 3 books. How many ways can we bind the books using red, … Continue reading

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Factorial Series

Observe the series: . Find the sum of this series if . Source: mathcontest.olemiss.edu 2/13/2012 SOLUTION Use a calculator to calculate the partial sum Calculate the partial sum as follows Factor Use the calculator Use the distributive property of multiplication … Continue reading

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Circling Around

Suppose that the circles in the figure below are tangent to one another. The radius of the circle centered at  is one unit, and the radius of the circle centered at  is two units. What are the radii of the … Continue reading

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1995 Remainder

When an integer is divided by , the remainder is . When the same integer is divided by , what will be the remainder? Source: mathcontest.olemiss.edu 2/6/2012 SOLUTION Let be the integer. By definition of division remainder, there exists a … Continue reading

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