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## Friday, January 7, 2011

### Programmatic solution for a real time numerology belief

Three years back, I got a call from one of my friend. During the call he conveyed that he bought a new motor bike and asked my help to get the registration number for his motorbike. You may ponder how I am going to help to him in this regard.
Actually he was looking for an exclusive four digit registration number for his motor vehicle based on numerology with the following conditions.
1. The recursive sum of all the four digits should be 1.
2. Four digits of the number should be in ascending order. i.e., First number should be less than second, second less than third and third less than fourth.

To be honest, I was puzzled when he stated the above conditions. I asked him to give some time to find out those exclusive numbers. When I thought of this problem, I felt why didn’t automate this task by writing a program!! Hence this blog post!!

I usually do coding by divide and conquer approach. i.e., Split the entire problem into small logical units, and then integrate those small logical units to create the final one. Here in this case the following are the logical units.
1. Module to find those exclusive vehicle registration numbers.
2. Module to find the recursive sum of a number
3. Module to check whether the digits of the given number are in ascending order are not.

When you look sharper at the logical unit 2, it can be divided further into a small logical unit.
1. Module to find those exclusive vehicle registration numbers.
2. Module to find the recursive sum of digits of a number
a. Module to find the sum of digits of a number
3. Module to check whether the digits of the given number are in ascending order are not.

That’s it. All things were nicely setup to create a program which solves my friend’s vehicle registration number numerology problem. Still one thing is missing the logical flow of program. Before sitting in front of the system and start coding, It is highly recommended to manually work out the program logic in a paper. If you follow this approach, you can develop the program with free of bugs :P So What is the logic to solve this problem ??

Here is the logic!!
1. Traverse from 1000 to 9999
2. For each no check whether the digits are in ascending order.If the digits are in ascending order, then check whether the recursive sum of the digits of the number is 1 or not. If the recursive sum is 1, My friend got the solution for his problem.

The Source Code for this problem in C#

```using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;

namespace VehicleRegNo
{
class Program
{

// Module to find the exclusive four digit Vehicle Reg Nos Which statisfies the following conditions
// 1.Four digits of the number should be in ascending order.
//      i.e., First number should be less than second, second less than third and third less than fourth.
// 2.The recursive sum of all the four digits should be 1.
private static int[] GetExclusiveVehicleRegNos()
{
// Dynamic integer list to store the exclusive vehicle reg nos
List exclusiveVehicleRegNosList = new List();

// Range of all four digit numbers is 1000 to 9999
int count = 0;
for (int i = 1000; i < 9999; i++)
{
if (IsDigitsInAscendingOrder(i))
{
if (FindRecursiveSumOfDigits(i) == 1)
{
count++;
}

}
}

// Convert to list into an integer array and return
return exclusiveVehicleRegNosList.ToArray();
}

// Module to find the recursive sum of digits in a number
private static int FindRecursiveSumOfDigits(int number)
{
// Find recursive sum till the sum become a single digit.
// Eg:- 9999 => 9 + 9 + 9 + 9 = 36 => 3 + 6 = 9
int sum = FindSumOfDigits(number);
while (sum > 9)
{
sum = FindSumOfDigits(sum);
}
return sum;
}

// Module to find the sum of digits in a number
private static int FindSumOfDigits(int number)
{
int sum = 0;
while (number > 0)
{
sum += (number % 10);
number /= 10;
}
return sum;
}

// Module to check whether digits in the given number are in ascending order
private static bool IsDigitsInAscendingOrder(int number)
{
bool isDigitsInAscendingOrder = false;

// Getting the first digit
int firstDigit = number / 1000;

// Getting the second digit
number %= 1000;
int secondDigit = number / 100;

// Getting the third digit
number %= 100;
int thirdDigit = number / 10;

int fourthDigit = number % 10;

if (firstDigit < secondDigit && secondDigit < thirdDigit && thirdDigit < fourthDigit)
{
isDigitsInAscendingOrder = true;
}

return isDigitsInAscendingOrder;
}

static void Main(string[] args)
{
int[] exclusiveVehicleRegNos = GetExclusiveVehicleRegNos();
string t = "";
for (int i = 0; i < exclusiveVehicleRegNos.Length; i++)
{
// Printing those exclusive nos
Console.WriteLine(exclusiveVehicleRegNos[i]);
}

/********** Output *********************
1234
1279
1369
1378
1459
1468
1567
2359
2368
2458
2467
3457
4789
5689
****************************************/
}

}

}

```

1. 2. 3. 