# Monthly Archives: April 2011

## Multiples of Eleven

You are given a special set of numbers that contains all three-digit positive integers that are palindromes.  What is the probability that any thee-digit palindrome is also a multiple of eleven? Source: mathcontext.olemiss.edu 3/2/2009 SOLUTION Examples of 3-digit positive integers … Continue reading

## Last Digit

What would the units (ones) digit be for the value of 3 raised to the 9999th power? Source: mathcontest.olemiss.edu 3/30/2009 SOLUTION The pattern of the units digit is 1, 3, 9, 7 and it repeats in groups of 4. If … Continue reading

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## Divisible Perfect Squares

How many different numbers between 2 to 100 satisfy all three of the following conditions: 1.  The number is not a prime number. 2.  The number is not divisible by a perfect square greater than one. 3.  The double of … Continue reading

## Square or Cube

Find all positive integral solutions of and to . Remember, x and y are positive integers. Source: mathcontest.olemiss.edu 9/21/2009 SOLUTION Since and are positive, must be positive in order to make the above product positive. This implies that . Also, … Continue reading

## Four Different Numbers

The sum of four positive integers is 68.  The product of the same four integers is 50141.  The sum of the squares of the same four integers is 1420.  What are the values of the four positive integers? Source: mathcontest.olemiss.edu … Continue reading

## Divisibility Rules

A nine-digit number consists of each digit from 1 to 9 and the nine-digit number is divisible by 9.  If you remove the rightmost digit, the remaining eight-digit number will be divisible by eight.  If you remove the next rightmost … Continue reading

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## Twenty-two Power

When simplified, the numerical value of has three prime factors.  Determine these three different prime factors of . Source: mathcontest.olemiss.edu 4/11/2011 SOLUTION This problem is similar to the problem titled “Three Prime Factors”, mathcontest.olemiss.edu 2/28/2011. Answer: 5, 397, 2113.

## How Many Camels

A Camel merchant willed his 17 camels to his three sons. In the merchant’s will, the camels were to be divided among them as follows: The eldest son was to receive half of the camels; The middle son was to … Continue reading