# Monthly Archives: November 2011

## Green Marbles

You walk up to a black jar containing fewer than 20 marbles. If you reach into the jar and randomly remove two marbles out of the jar without replacing the marbles, you have a 50 percent chance of getting two … Continue reading

## Digit Exchange

A three-digit number increases by nine if you exchange the second and third digits. The same three-digit number increases by if you exchange the first and second digits. By how much will the number increase if you exchange the first … Continue reading

## 75 to 25

Find the sum of the reciprocals of two real numbers, given that these numbers have a sum of 75 and a product of 25. Source: mathcontest.olemiss.edu 11/7/2011 SOLUTION This problem is similar to the problem titled “25 and 75” dated … Continue reading

## 615

Given that and are integers, find all possible solutions, i.e. pairs of such that the sum of the square of x and 615 is equal to two raised to the nth power or . Source: mathcontest.olemiss.edu 10/31/2011 SOLUTION implies that … Continue reading