# Monthly Archives: March 2011

## Seven Seas

Although the Pacific Ocean, Baltic Sea, and Arctic Sea represent three bodies of water, when added together, their sum yields seven Cs. Using the nine digits {0, 2, 3, 4, 5, 6, 7, 8, 9} substitute a different digit for … Continue reading

## Median to 16

A median of a triangle is a line segment joining a vertex to the midpoint of the opposite side. You are given a triangle with side lengths of 11 cm, 13 cm, and 16 cm. Determine the length of the … Continue reading

## 615

You are given two positive integers, , such that . Find the sum of x and y. Source: mathcontest.olemisss.edu 11/30/2009 SOLUTION Since the first factor is positive, the second factor must be negative. Prime factorization: . There are three possibilities: … Continue reading

## Inscribed in a Circle

An equilateral triangle and regular hexagon are inscribed in the same circle. Find the ratio of the area of the triangle to that of the hexagon. Source: mathcontest.olemiss.edu 12/7/2009 SOLUTION First, rotate the equilateral triangle around center of the circle … Continue reading

## Big Chocolate Bar

You purchase a very large, rectangular chocolate bar at the candy store. The bar is arranged in a 4 x 8 rectangular pattern consisting of thirty-two 1 x 1 small squares. What is the minimum number of breaks needed to … Continue reading

## Greatest Integer X

If [X] represents the greatest integer function, then [X] represents the greatest integer less than or equal to X. Find the value of X if the product of X and [X] equals 200. Source: mathcontest.olemiss.edu 1/112010 SOLUTION If , then … Continue reading

## Consecutive Counting Groups

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 third, etc. What is the sum of the … Continue reading

## Special Six-Digit

There exists a special six-digit number such that when this number is multiplied by four, its digits are reversed. Determine this special six-digit number. Note: digits can be used more than once. Source: mathcontest.olemiss.edu 1/25/2010 SOLUTION Let be the special … Continue reading

## Newton’s Angle

Newton’s Angle Sir Issac Newton was examining an angle formed by two segments joined on a piece of paper. After using a protractor, he determined the measure (in degrees) of the angle to be one-fifth of the square root of … Continue reading

## Bernoulli Battalions

The country of Bernoulli has a standing army of 809,957 soldiers. It has a trained reserve of 3,149,796 soldiers. Both the active and reserve forces are organized into battalions. All battalions are of the same size (standing army or reserve), … Continue reading