Monthly Archives: October 2011

101st Group

101st Group Group the consecutive counting numbers as follows: (1), (2, 3), (4, 5, 6), (7, 8, 9, 10), . . Notice that there is one number in the first group, two numbers in the second group, three in the … Continue reading

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Tessellated Arcs

The tessellated figure below consists of 3 equal arcs in an equilateral triangle. Each side measures 2 inches. What is the area of the region labeled ? Source: Julia Robinson Mathematics Festival SOLUTION Draw altitude to side . Because is … Continue reading

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Inscribed Hexagon

Regular hexagons are inscribed in and circumscribed outside a circle, as shown below. If the smaller hexagon has an area of 3 square inches, what is the area of the larger hexagon? Source: Julia Robinson Mathematics Festival SOLUTION Regular hexagons … Continue reading

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Overlapping Circles

A circle of radius 15 inches intersects another circle, radius 20 inches, at right angle (see below). What is the difference of the areas of the non-overlapping portions? Source: Julia Robinson Mathematics Festival SOLUTION Let be the area of the … Continue reading

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Dividing Prime

Pick any prime number greater than three. Find one less than the square of that prime number. What is the greatest positive integer that must be a divisor of the result? Source: mathcontest.olemiss.edu 10/10/2011 SOLUTION Let be a prime number … Continue reading

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Reversing X

Let be a two-digit positive integer. If you find the sum of and the number obtained by reversing the digits of you get a perfect square. What are all of the possible values of ? Source: mathcontest.olemiss.edu 10/3/2011 SOLUTION If … Continue reading

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TENNESSEE

A 4-letter word can be made from the letters of the word . For example, , and so on. Each word is an ordering of four letters. Find the number of such distinguishable orderings. Source: submitted by Jimel Mariano 9/25/2011 SOLUTION … Continue reading

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