Monthly Archives: November 2010

Double Sequence

In a given sequence, the 7th term of the sequence is 8 and the 9th term of the sequence is 24.  In this sequence, it is important to note that each term after the second term is twice the sum … Continue reading

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Middle Three Digits

A five-digit perfect square in the form of has a thousands digit , hundreds digit , and tens digit . If is less than or equal to and is less than or equal to , what is the sum of … Continue reading

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Squared Expression

Find the sum of the following expression: Source: mathcontest.olemiss.edu 4/19/2010  SOLUTION Recall that . Let’s rewrite the squared expression using this identity as follows. Adding the left-hand and right-hand side of the above equations yields Recall that the sum of … Continue reading

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EDUCATION

In how many arrangements of the letters in the nine-letter word EDUCATION are the vowels in alphabetical order? Source: mathcontest.olemiss.edu 11/15/2010 SOLUTION The five vowels in alphabetical order are aeiou. An example of an arrangement is where the four dashes are … Continue reading

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10,000,000,000

Considering the integers from to , answer the following two questions: 1.  Is the number of integers that include the digit greater or less than the number of integers that do not include the digit ?  2.  What is the … Continue reading

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Nine-Digit Binary

How many nine-digit binary numbers do not have any consecutive zeros?  (Please note that the leftmost digit must be a one to be nine-digits). Source: mathcontest.olemiss.edu 11/8/2010 Solution by Process of Elimination STEP 1 Try something simpler first: five-digit binary … Continue reading

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Two Scoops of Ice Cream

On a very hot day, you decide to go to your favorite Ice Cream Parlor for an ice cream cone. Since it is especially hot, you decide to order a two-scoop cone. There are 14 different flavors of ice cream: … Continue reading

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Triangles and Cubes

How many distinct triangles can be constructed by connecting three different vertices of a cube? Source: mathcontest.olemiss.edu 11/1/2010 Solution STEP 1 Try something simpler first. Consider a square in a plane (it doesn’t look square because we look at it … Continue reading

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Seven Factorial!

The factorial of a positive integer, is denoted by and represents the product of all positive integers less than or equal to .  For example, .  Find the number of positive, odd factors of Source: mathcontest.olemiss.edu 5/3/2010 Solution By definition, … Continue reading

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