So are alternate solutions that use technology cheating? Does the creator of the solution demonstrate less skill when solving a problem in a way that the author of the problem did not think of? In some cases the answer seems to be clearly yes. I do not want my children using a calculator when they are trying to learn their math facts. However, in other cases I am not so sure.

Here is this problem and the alternate solution. You can be the judge if it is “cheating” or not.

Problem: What are three three-digit numbers where the second number is twice the first and the third number is three times the first. In addition, the three numbers together use every digit from 1-9 just once.

Solution via Java (this program actually found four different solutions):

import java.util.*;

public class FindNum

{

public static void main(String[] args)

{

for(int x=100; x<1000/3; x++)

{

int y = x*2;

int z = x*3;

//Throw each digit into a set

//Note: Sets ignore duplicate valules

Set<Integer> digitSet = new TreeSet<Integer>();

digitSet.add(x/100);

digitSet.add(x/10%10);

digitSet.add(x%10);

digitSet.add(y/100);

digitSet.add(y/10%10);

digitSet.add(y%10);

digitSet.add(z/100);

digitSet.add(z/10%10);

digitSet.add(z%10);

//if there are nine digits in the set and no

//zero, we win!

if(digitSet.size()==9&&!digitSet.contains(0))

{

System.out.println(x);

System.out.println(y);

System.out.println(z);

System.out.println();

}

}

}

}