Project Euler - Problem 28

Starting with the number 1 and moving to the right in a clockwise direction a 5 by 5 spiral is formed as follows:

21 22 23 24 25
20  7  8  9 10
19  6  1  2 11
18  5  4  3 12
17 16 15 14 13

It can be verified that the sum of the numbers on the diagonals is 101.
What is the sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way?


To solve this problem, I used VB.NET. Here are the design and the code.

Design:

It consists of 1 Textbox, 1 Label, and 1 Button.


Code:

Public Class Form1
    Dim x, y, z, a, b, c As Integer
    Dim num As Double
    Private Sub Button1_Click(ByVal sender As System.Object, ByVal e As System.EventArgs) Handles Button1.Click
        c = 1
        z = 1
        x = TextBox1.Text
        If x > 0 And x Mod 2 = 1 Then
            For a = 1 To x * 2 - 2
                y = 2 * c
                z = z + y
                num = num + z
                b = b + 1
                If b = 4 Then
                    c = c + 1
                    b = 0
                End If
            Next
        Else
            MsgBox("Spiral must be of odd size and has a minimum size of 1.")
            End
        End If
        Label1.Text = num + 1
    End Sub
End Class



Explanation:

The Textbox receives the size of the spiral.

Note that the size must be an odd number starting from the minimum of 1. 

The sum of the numbers on the diagonals will be shown in the Label. 

Answer to PROBLEM 28 of Project Euler :

The sum of the numbers on the diagonals in a 1001 by 1001 spiral formed in the same way is  669171001.

 

Happy Coding !

Cyber Frost