Kata 3 – Magic Numbers

This kata comes from the website of one of my old lecturers. It was an interesting problems to tackle and there are a lot of different ways to approach it.

159 * 48 = 7632 contains each of the numbers 1-9. The program finds and displays all the other simple multiplications that also contain each of the numbers 1-9.

I started by creating an algorithm that generated a string containing all the numbers I wanted. This was exceptionally tricky to do. So my algorithm just starts counting from 123456789. Each number is checked that it contains only one of each number. Because I’m using only 9 digit numbers there isn’t any need to validate any further than that. If the number is valid it’s passed through to another checker that systematically changes the number into a simple multiplication equation. If the equation is valid I win.

The application takes a ridiculously long time to run. After completion I thought of a way to potentially half the run time but I didn’t implement it because I’ve been obsessing about this for far too long.

This was done largely using TDD but I actually wrote the test in Obj C and then transferred the program to C# because of a memory problem I was having in XCode.

 static void Main(string[] args)  
string equationString;
List createdStrings = new List();
//create an array of strings ///159 * 48 = 7632
for (int i = 123456789; i <= 987654321; i++){
equationString = i.ToString();
//validate strings with the checker
if (equationCharacterChecker(equationString)){
if (equationChecker(equationString)){
public static bool equationCharacterChecker(string equation) {
SortedSet setOfEquationCharacters = new SortedSet();
setOfEquationCharacters.Add("1"); setOfEquationCharacters.Add("2"); setOfEquationCharacters.Add("3");
setOfEquationCharacters.Add("4"); setOfEquationCharacters.Add("5"); setOfEquationCharacters.Add("6");
setOfEquationCharacters.Add("7"); setOfEquationCharacters.Add("8"); setOfEquationCharacters.Add("9");
string character;
for (int i = 0; i < equation.Count(); i++)
character = equation[i].ToString();
if (setOfEquationCharacters.Contains(character)){
} else {
return false;
return true;
//159 * 48 = 7632
public static bool equationChecker(string equation) {
int length = equation.Length;
for (int m = 1; m < equation.Length-2; m++){
for (int e = m+1; e < equation.Length-1; e++){
int multiplicand = Convert.ToInt32(equation.Substring(0, m));
int multiplier = Convert.ToInt32(equation.Substring(m, e-m));
int product = Convert.ToInt32(equation.Substring(e));
if (multiplicand * multiplier == product) {
Console.Write(multiplicand + " * " + multiplier + " = " + product + "\n");
return true;
return false;

Author: D

I'm a student developer living in the UK. I'm on a 1 year placement and am due to finish the final semester of a Computer Games Programming degree in 2015.

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