# Monthly Archives: May 2011

## Peace

If each letter in the equation represents a unique digit, determine the values that represent , and . Source: mathcontest.olemiss.edu 3/24/2008 SOLUTION This problem is similar to the problem titled “Seven Seas” dated 10/1/2007.    U  S  S R         … Continue reading

## Perfect Cube 735

What is the smallest positive integer by which you can multiply 735 so that the product is a perfect cube? Source: mathcontest.olemiss.edu 4/14/2008 SOLUTION Example of a perfect cube: . . To make 735 a perfect cube all we have … Continue reading

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## Algebraic Expansion

If you expand the polynomial , the resulting polynomial  has three terms whose coefficients are 1, 2, and 1.  Find the sum of the coefficients of the terms in the expansion of  . Source: mathcontest.olemiss.edu 5/5/2008 SOLUTION We use the “area” model … Continue reading

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## Powerful Powers

Using the values of  above, find the value of . Source: mathcontest.olemiss.edu 6/9/2008 SOLUTION Let . Then, . Answer: 4.

## Increasing Values

A number is considered increasing if each digit is greater than the digit to its left. For example, 146 is increasing because 6 is greater than 4, and 4 is greater than 1. How many increasing numbers exist that are … Continue reading

## Thirty-two Power of Two

Find the sum of the prime factors of . Source: mathcontest.olemiss.edu 6/23/2008 SOLUTION  is the largest known Fermat prime. Therefore, The sum of the prime factors is Answer: 65819.

## Find T and M

in the following equation represent positive whole numbers where M represents the hundred’s digit of a six-digit number. Find the values of . Source: mathcontest.olemiss.edu 10/6/2008 SOLUTION Since is a perfect square, we will check the 10 choices of to see … Continue reading

## 10000!

Determine the tens digit for the expression: . Source: mathcontest.olemiss.edu 10/13/2008 SOLUTION Since the values of , etc. are multiples of , these factorial numbers do not contribute to the tens digit of the bigger sum . Rather, the tens … Continue reading