# Monthly Archives: March 2011

## Shades of Gray

A square whose sides are each 10 cm and a right triangle with sides of 20, 21, and 29 cm overlap so that the vertex of the right angle of the triangle is at the center of the square. What … Continue reading

## The Deep Hole

If it takes a man one and a half hours to dig a hole two meters long, two meters wide, and two meters deep, how long would it take the same man to dig a hole six meters long, six … Continue reading

## Sum of Consecutive Numbers

How many positive integers from to inclusive can be written as the sum of two or more consecutive positive integers? (Different examples and : and ) Source: mathcontest.olemiss.edu 3/7/2011 SOLUTION Sum of two consecutive numbers There are numbers from … Continue reading

## Endless Root

Find the value of X in the given equation. Source: mathcontest.olemiss.edu 10/5/2009 SOLUTION The left-hand side of the equation looks pretty daunting. Let’s simplify by writing it as follows: . If , the answer is obviously . Since . Guess … Continue reading

## Water Tank

There are 2 inlet pipes for a large water tank and one drain pipe. Alone at full force, the first inlet pipe can fill the tank in 10 hours. The second inlet pipe can fill the tank in eight hours. … Continue reading

## A+b+c+d

Given , find the value of . Source: mathcontest.olemiss.edu 12/11/2006 SOLUTION Find b+c+d Add all the following four equations ———————————– Subtract from both sides . (1) Find a Add the following three equations ——————- Substitute for … Continue reading

## Three Prime Factors

Determine the three prime factors of the sum of two to the twenty-second power and one or . Source: mathcontest.olemiss.edu 2/28/2011 SOLUTION This problem is similar to the problem titled “Twenty-two Power”, mathcontest.olemiss.edu 4/11/2011. List of prime numbers 2 3 … Continue reading

## The Monuments

A circular park has a 5 km diameter. The National monument is located by entering the park from the northern most point and proceeding due south for 1 km. Starting at the National monument and going due west you would … Continue reading