Monthly Archives: September 2011

Seven Boxes

There are 7 boxes each written with letter to ( for the first box, for the 2nd and so on). You have 7 balls each with letter to ( for the first ball, for the 2nd and so on). You … Continue reading

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Consecutive N

The sum of consecutive positive integers is 1998. If is odd, what is the greatest possible value for ? Source: mathcontest.olemiss.edu 9/26/2011 SOLUTION Before tackling this problem we should revisit two formulas related to the sum of consecutive positive integers. Let where … Continue reading

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Three Circles

In the figure below, 3 equal circles have been drawn so that each one passes through the centers of the other two. Is the area of overlap of the three triangles more or less than a quarter of the area … Continue reading

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Petal

The hex sign below is made up entirely of circles 1 inch in radius. Can you calculate the area of each of the petal-shaped areas? Source: Julia Robinson Mathematics Festival SOLUTION The above figure displays a petal in close-up. Since … Continue reading

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Ring

In the figure below, segment , which is 1 inch long, is tangent to the inner of two concentric circles at and intersects the outer circle at . What is the area of the annular region between the circles? SOLUTION Let … Continue reading

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Two Squares

The figure below shows two squares. The sides of the smaller square are 3”, those of the larger square, 4”. Point is the corner of the large square and the center of the small square. The length of is 1” … Continue reading

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Forty-Five

The sum of two numbers is 45. The sum of their quotient and the quotient’s reciprocal is 2.05. What is the product of the two numbers? Source: mathcontest.olemiss.edu 9/19/2011 SOLUTION Let and be the two numbers.         (1)         (2) … Continue reading

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Coffee Anyone

In a neighborhood café there are 10 seats in a row at the counter. In the morning, customers enter the café for their morning coffee. They don’t really want to have a conversation, so they prefer not to sit next … Continue reading

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Regions in a Square

In the figure below, quadrilateral  is a square, and is the midpoint of the side . How do the areas of regions I, II, III, and IV compare? Another way to think about this is to consider the question, What are … Continue reading

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35 Only Once

How many four digit numbers contain the digit pattern 35 at least once and only once? Source: mathcontest.olemiss.edu 9/12/2011 SOLUTION This problem is similar to the problem titled “Eighty-Five Four Digits” dated 11/12/2007. Case 1: 35XY X: ten choices from … Continue reading

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