Grapics question checkerboard

I am working on a checkerboard in a winform. I have a fixed size board drawing in the form but want to make the checkerboard rescale itself whenever the window is resized. I have a drawBoard function that I am calling in my Paint event. I think I am just missing something easy but I can only get it to work right when I use specific coordinates.

Code:

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void Form1_Paint(object sender, PaintEventArgs e)
        {
            drawBoard(e.Graphics, this.ClientRectangle);
        }

private void drawBoard(Graphics g, Rectangle rectangle)
        {
            bool dark = true;
            for (int i = 0; i < 8; i++)
            {
                dark = !dark;
                for (int j = 0; j < 8; j++)
                {
                    dark = !dark;

                    Pen redPen = new Pen(Color.Red, 2);
                    SolidBrush brush;
                    if (dark)
                    {
                        brush = new SolidBrush(Color.DarkGray);
                    }
                    else
                    {
                        brush = new SolidBrush(Color.Red);
                    }

                    int x = 50 * i + 10;
                    int y = 50 * j + 10;
                    int width = 50;
                    int height = 50;
                    //Draw rectangle to screen.
                    g.DrawRectangle(redPen, x, y, width, height);
                    g.FillRectangle(brush, x, y, width, height);
                    //Invalidate (); // redraw the screen
                }
            }
        }

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What if you create an event handler for the form's Resize event?

Code:

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void Form1_Resize(object sender, ResizeEventArgs e)  // or whatever it is...
{
  Invalidate();  // Force the Paint event to trigger
}

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To illustrate:

Code:

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    public partial class Form1 : Form
    {
        public Form1()
        {
            InitializeComponent();
        }

        protected override void OnPaint(PaintEventArgs e)
        {
            base.OnPaint(e);

            using (Pen pen = new Pen(Color.Red))
                e.Graphics.DrawLine(pen, ClientRectangle.Left, ClientRectangle.Bottom, ClientRectangle.Right, ClientRectangle.Top);
        }

        protected override void OnResize(EventArgs e)
        {
            base.OnResize(e);

            Invalidate();  // Without this, it doesn't work correctly
        }
    }

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