Monthly Archives: June 2011

Average is Twelve

The average (mean) of five numbers is twelve. When the smallest of these five numbers is removed, the average of the remaining four numbers is sixteen. What is the value of the number that was removed from the original five … Continue reading

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123456

If all 720 permutations of the digits 1 through 6 are arranged in numerical order from least to greatest, what is the 409th permutation? Note that 123456 is the first permutation, 123465 is the second, and so on. Source: mathcontest.olemiss.edu … Continue reading

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Sum Four Digit Primes

represent different digits. represent four different four-digit prime numbers. Determine the sum of all four four-digit prime numbers . Source: mathcontest.olemiss.edu 10/22/2007 SOLUTION Since the prime numbers end in  , these digits must be 1, 3, 7, or 9 for … Continue reading

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Ends in 75

Determine how many positive whole numbers exist that meet all of the following conditions: 1. Greater than one thousand 2. Less than ten thousand 3. End in seventy-five 4. Divisible by seventy-five. Source: mathcontest.olemiss.edu 10/15/2007 SOLUTION Condition 1 and 2 … Continue reading

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B x DE = ABC

are consecutive digits. are also consecutive digits.  are all different digits. If , find the sum of . (Note: are not necessarily consecutive digits. Source: mathcontest.olemiss.edu 10/29/2007 SOLUTION Let . Then,  . Let , then . Since is in the tens … Continue reading

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Negative Powers

Determine the sum of two to the negative one power plus two to the negative two power plus two to the negative three power all the way to two to the negative nineteen power. Express your answer as a simplified … Continue reading

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Convex Polygon

A convex polygon can be defined as a polygon with all its interior angles less than 180 degrees. Also, all diagonals lie entirely inside a convex polygon. If a convex polygon has 324 diagonals, how many sides does this polygon … Continue reading

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Powerful Twelve

What is the greatest multiple of that contains each digit once and only once? Source: mathcontest.olemiss.edu 7/2/2007 SOLUTION We list a few multiples of to see what their ending pattern looks like: All multiples of end in . Multiples ending in zero We … Continue reading

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Chord and Diameter

The given semicircle has a diameter of 8 inches (segment ). Chord is half the length and parallel to diameter . Find the distance from the midpoint of chord to the midpoint of diameter . Source: mathcontest.olemiss.edu 1/21/2008 SOLUTION Let … Continue reading

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Past Political Life

In 1999, while collecting information on an important politician figure, I found that his age at death was one thirty-ninth of the year of his birth. How old was the politician in 1921? Source: mathcontest.olemiss.edu 2/11/2008 SOLUTION Let be the … Continue reading

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