# Monthly Archives: September 2012

## Building Blocks (Level 3)

Your friend builds a tower using at most blocks of each side length. For instance, if is then your friend selected blocks from a pile with edges of length , and so on. Also, the largest block in your friend’s … Continue reading

## Less Than 500

A three-digit number is drawn at random from all possible 3-digit numbers formed by the digits , and . What is the probability that the number drawn is an even number less than containing NO digits more than once? Source: … Continue reading

## Building Blocks (Level 2)

Now you have only cubes, of edge length . For simplicity we’ll suppose they go in increasing order, so is the smallest and is the biggest. There may be ties (or they may even be all the same size). You … Continue reading

## Seven Digit Pair

You write down all of the seven-digit numbers that can be formed using each of the digits exactly once (such as ). Your task is to find pairs so that is a multiple of but does not equal . How … Continue reading

## Triple ABC

Triple ABC How many ordered triples of positive integers satisfy ? Source: mathcontest.olemiss.edu 9/10/2012 SOLUTION This problem is similar to the problem “XYZ=4000” posted on 11/5/2014, nevertheless a different solution is offered here. Let be a positive integer and its … Continue reading

## Building Blocks (Level 1)

You have an unlimited supply of cubes. Each cube’s side length is a number of the form , where is any nonnegative integer. That is, there are cubes with edges of length unit, units, units, units, units, and so on. … Continue reading

## Eight Knights

Eight dashing knights are in love with [the] kingdom’s princess. Starting on January , the first knight visits the princess every day. The second night visits the princess on January and every second day thereafter. The third knight visits the … Continue reading