loop puzzle - 1

Hello everybody, So, do you love solving puzzles? If yes, then before reading the rest of this article give it a go and try to write a loop that will generate the following pattern:

2020202020202020202020202020202020202020 
_19191919191919191919191919191919191919 
__181818181818181818181818181818181818
 ___1717171717171717171717171717171717
 ____16161616161616161616161616161616 
_____151515151515151515151515151515
 ______1414141414141414141414141414
 _______13131313131313131313131313
 ________121212121212121212121212 
_________1111111111111111111111
 __________10101010101010101010
___________999999999 
____________88888888 
_____________7777777 
______________666666 
_______________55555 
________________4444 
_________________333 
__________________22 
___________________1 

Assuming you gave it a go, let us examine how you can solve this puzzle. After the first glance on the pattern, you will realize three things:

1.  There are 20 rows, starting from 20 going down to 1 
2.  In each row, the number is repeated as many times as its value( e.g., number 9 is repeated 9 times) 
3.  From the second row we print an underscore once, then we increase the number of the printed underscores along the way to number 1 

lets kick off with the first point and actually, this is the easiest part. Since we have 20 rows then we will have a loop that will run 20 times.

(for int i = 20;  i >= 1; i—0)
{  
  Console.WriteLine(i);
}

This loop will print the numbers from 20 to 1 single time in each iteration. But what we want is to repeat the number according to its value. To do that, we will have an inner loop that will repeat the number i times.

(for int i = 20;  i >= 1; i—0)
{  
     for (int j = i; j >= 1; j--)
         Console.Write(i);
Console.WriteLine(); // just to print a new line character 
}

To here we achieved point 1 and 2. Lets do the third point which is tricky one. We want the printing of the underscore starts from the second iteration, so the simplest way is to check which iteration is this, if it is not the first iteration then print the underscore. So, our loop will be now like:

for (int i = 20; i >= 1; i--)
            {
                if (i < 20)
                {
                        Console.Write("_");
                }
                for (int j = i; j >= 1; j--)
                    Console.Write(i);
                Console.WriteLine();
            }

However, this will cause the loop to print the underscore one time in every single iteration. What we want is to increase the printing of the underscores. To get that we will apply the following:

•  Declare two integers: x and counter = 1
•  Inside the if statement put the following equation: x = i – counter 
•  Create a third inner loop inside the if statement that will take care of printing the underscores.

for (int k = 1; k <= i- x; k++)
         Console.Write("_");
So the final loop will look like this:
for (int i = 20; i >= 1; i--)
            {
                if (i < 20)
                {
                    x = i - counter;
                    for (int k = 1; k <= i- x; k++)
                        Console.Write("_");
                    counter++;
                }
                for (int j = i; j >= 1; j--)
                    Console.Write(i);

                Console.WriteLine();
            }

Lets analyze the loop a couple of times to understand how it work:

 In the first iteration we will get the number 20 twenty times

 In the second iteration the if block gets executed as: x = 19 – 1; // so x will be 18
 for (int k = 1; k <= i- x; k++) // the condition here is k <= 19 – 18 = 1
 Console.Write("_");
And this will cause the underscore loop to be executed 1 time. Then we increment counter by 1.

In the third execution: x = 18 – 2 // so x will be 16
 for (int k = 1; k <= i- x; k++) // the condition here is k <= 18 – 16 = 2
 Console.Write("_");
And this will cause the underscore loop to be executed 2 times. Then we increment counter by 1.

In the fourth execution: X = 17 – 3 // so x will be 14 for (int k = 1; k <= i- x; k++) // the condition here is k <= 17 – 14 = 3 Console.Write("_"); And this will cause the underscore loop to be executed 3 times. Then we increment counter by 1.

And so on.
That's it. You got the puzzle solved :).
For more convenience, we will replace the 20 number by an N number taken from the user.

Here is the full C# code:

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

namespace TestConsole
{

    class Program
    {
        static void Main(string[] args)
        {
            int n;
            int x = 0, counter = 1;
            Console.WriteLine("Enter the number of rows:");
            n = int.Parse(Console.ReadLine());
            for (int i = n; i >= 1; i--)
            {
                if (i < n)
                {
                    x = i - counter;
                    for (int k = 1; k <= i- x; k++)
                        Console.Write("_");
                    counter++;
                }
                for (int j = i; j >= 1; j--)
                    Console.Write(i);

                Console.WriteLine();
            }

            Console.ReadLine();
        }
    }
}

output: