# Monthly Archives: February 2011

## Simplify Powers

If , find the value of the expression . Source: mathcontest.olemiss.edu 6/15/2009 SOLUTION . Answer: .

## Factorials Cubed

Determine the unit’s digit (one’s digit) of the sum of the expression: . Source: mathcontest.olemiss.edu 9/1/2008 SOLUTION All the factorials greater than or equal to 5! end in zero and all the factorials cubed greater than or equal to also … Continue reading

## Faster Than A Speeding Train

Two trains are traveling towards each other on separate, parallel tracks. Each train is traveling at a constant rate of 60 miles per hour and each train is 1/6 of a mile long. How much time will elapse between the … Continue reading

## X, Y, and Z

You are given real numbers where . Find the value of . Source: mathcontest.olemiss.edu 2/21/2011 SOLUTION Finding Solving the equation yields . . Finding Solving the equation yields . . Sum of Subtracting from both sides of the above equation yields Right-hand … Continue reading

## Four Thousand Digits

The number 12345678901234567890123…890 is four thousand digits long. First, you remove all of the digits in odd numbered places starting at the leftmost place. Next, you remove the digits in the odd numbered places in the remaining 2000 digits. You … Continue reading

## Tennis Anyone

Three tennis balls snugly fit in a cylindrical can (perfect right cylinder). The balls touch the side, top and bottom of the plastic can. What is the ratio of the volume of the balls to the volume of the space … Continue reading

## 199 Numbers

Group the consecutive counting numbers as follows: (1), (2, 3), (4, 5, 6), (7, 8, 9, 10), . . . Note there is one number in the first group, two in the second group, three in the third, etc. Determine … Continue reading

## Last Monday

You are looking at a calendar and notice that the sum of the date of the last Monday of last month and the date of the first Thursday of next month is 38. If both dates are in the same … Continue reading

## Minus Preceding Term

You are given this special sequence of numbers: 1, 3, 2, . . . where each term beginning with the third term, is determined by the term preceding it minus the term preceding that one. In other words, the third … Continue reading

## Four Digit Evens and Odds

This four-digit puzzler has three parts. You must submit the answer to part 3! 1. How many four-digit whole numbers are there such that the thousand’s digit is odd, the hundred’s digit is even, and all four digits are different? … Continue reading