# Monthly Archives: December 2010

## Open Lockers

A school with 3400 students has 3400 lockers, all of which are closed. The 3400 students start down the hall one at a time. The first student opens every locker. The second student closes all the lockers that are multiples … Continue reading

## Wheat Hens

On a certain farm, on average, 64 hens lay 768 eggs in 64 days. On that same farm, on average, 46 hens eat 46 kilograms of wheat in 46 days. On this farm, on average, the consumption of how much … Continue reading

## Dividing by Perfect Squares

The number 174636000 is divisible by how many positive perfect squares? Source: mathcontest.olemiss.edu 7/21/2008 SOLUTION 174636000 = 2⁵ × 3⁴ × 5³ × 7² × 11 Initial perfect squares: 6 divisors From the above prime factorization, we find the following … Continue reading

## Sum of All Primes

The object of this puzzle is to find two different prime number addends that sum to another prime number which is less than 10000. The catch is that each addend must contain digits that are all prime numbers. The prime … Continue reading

## Sum Billions

Determine the sum of all ten-digit numbers. Please provide the exact value! In other words, find the sum of all whole numbers from 1000000000 to 9999999999. Source: mathcontest.olemiss.edu 4/21/2008 SOLUTION We need to recall the formula used to calculate the … Continue reading

## X Greater than Y

The vertices of a rectangle lie on the coordinate plane at the coordinates (1,1), (5,1), (1,7), and (5,7). If a point is randomly selected within the rectangle, what is the probability that the x-coordinate of the point is greater than … Continue reading

## Without Sevens

How many seven-digit numbers contain the digit seven at least once? Source: mathcontest.olemiss.edu 8/13/2007 SOLUTION The range of seven-digit numbers is 1000000 to 9999999. It is easier to find the answer indirectly by first calculating the count of numbers that … Continue reading

## Up and Down Numbers

An up and down number is a five-digit number such that the first three digits are in ascending order and the last three digits are in descending order. For example, 12321 and 35741 are pointed numbers while 45454 and 67891 … Continue reading

## Fifty-one Factorial

When calculated, fifty-one factorial (51!) is quite a large number. If you calculate 51! answer the following two questions: 1. With what digit does 51! end (what is the ones digit – the rightmost digit)? 2. Beginning at the rightmost … Continue reading

## Four Digit List

The digits 1, 2, 3, and 4 can be arranged to form many different four-digit numbers. If these numbers are listed from least to greatest, in what position is 3214? (Note: the least value is in the first position; the … Continue reading