# 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

## 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

## 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

## 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

## 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