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

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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.

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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

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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.

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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

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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

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25 and 75

The sum of two different positive numbers is 75 while the product of the same two numbers is 25.  Find the sum of the reciprocals of these two numbers. Source: mathcontest.olemiss.edu 10/20/2008 SOLUTION Let and be two different positive numbers … Continue reading

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Three Digit Forty-Eight

There are two different positive three-digit integers that are exactly forty-eight times the sum of their digits.  Find both three-digit positive integers that satisfy this condition. Source: mathcontest.olemiss.edu 10/27/2008 SOLUTION This problem is similar to the problem titled “11 Times” … Continue reading

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