Custom user control cannot be found in the solution?-Collection of common programming errors

I created a simple Sudoku application, where each 3×3 squares is a user control, with this skeleton code in CellBlock.Designer.cs and nothing but the automatically generated code in CellBlock.cs:

namespace Sudoku
{
    partial class CellBlock
    {

        private System.ComponentModel.IContainer components = null;

        protected override void Dispose(bool disposing)
        {
            if (disposing && (components != null))
            {
                components.Dispose();
            }
            base.Dispose(disposing);
        }


        private void InitializeComponent()
        {
            this.CellOne = new System.Windows.Forms.MaskedTextBox();
            this.CellFour = new System.Windows.Forms.MaskedTextBox();
            this.CellFive = new System.Windows.Forms.MaskedTextBox();
            this.CellSix = new System.Windows.Forms.MaskedTextBox();
            this.CellTwo = new System.Windows.Forms.MaskedTextBox();
            this.CellThree = new System.Windows.Forms.MaskedTextBox();
            this.CellSeven = new System.Windows.Forms.MaskedTextBox();
            this.CellEight = new System.Windows.Forms.MaskedTextBox();
            this.CellNine = new System.Windows.Forms.MaskedTextBox();
            this.SuspendLayout();
            // 
            // CellOne
            // 
            this.CellOne.BorderStyle = System.Windows.Forms.BorderStyle.FixedSingle;
            this.CellOne.Font = new System.Drawing.Font("Microsoft Sans Serif", 12F, System.Drawing.FontStyle.Regular, System.Drawing.GraphicsUnit.Point, ((byte)(0)));
            this.CellOne.Location = new System.Drawing.Point(8, 8);
            this.CellOne.Mask = "0";
            this.CellOne.Name = "CellOne";
            this.CellOne.PromptChar = ' ';
            this.CellOne.Size = new System.Drawing.Size(26, 26);
            this.CellOne.TabIndex = 0;
            this.CellOne.TextAlign = System.Windows.Forms.HorizontalAlignment.Center;

            //CellTwo through CellNine omitted for brevity

        // 
        // CellBlock
        // 
        this.AutoScaleDimensions = new System.Drawing.SizeF(6F, 13F);
        this.AutoScaleMode = System.Windows.Forms.AutoScaleMode.Font;
        this.BorderStyle = System.Windows.Forms.BorderStyle.FixedSingle;
        this.Controls.Add(this.CellNine);
        this.Controls.Add(this.CellEight);
        this.Controls.Add(this.CellSeven);
        this.Controls.Add(this.CellThree);
        this.Controls.Add(this.CellTwo);
        this.Controls.Add(this.CellSix);
        this.Controls.Add(this.CellFive);
        this.Controls.Add(this.CellFour);
        this.Controls.Add(this.CellOne);
        this.Name = "CellBlock";
        this.Size = new System.Drawing.Size(107, 107);
        this.ResumeLayout(false);
        this.PerformLayout();

    }

    private System.Windows.Forms.MaskedTextBox CellOne;
    private System.Windows.Forms.MaskedTextBox CellFour;
    private System.Windows.Forms.MaskedTextBox CellFive;
    private System.Windows.Forms.MaskedTextBox CellSix;
    private System.Windows.Forms.MaskedTextBox CellTwo;
    private System.Windows.Forms.MaskedTextBox CellThree;
    private System.Windows.Forms.MaskedTextBox CellSeven;
    private System.Windows.Forms.MaskedTextBox CellEight;
    private System.Windows.Forms.MaskedTextBox CellNine;
}

}

These files are in the same solution as Sudoku.cs, the main file. I simply added a user control to the solution through the project menu. This is the code in Sudoku.Designer.cs, once again, automatically generated by Visual Studio.

namespace Sudoku
{
    partial class Sudoku
    {

        private System.ComponentModel.IContainer components = null;

        protected override void Dispose(bool disposing)
        {
            if (disposing && (components != null))
            {
                components.Dispose();
            }
            base.Dispose(disposing);
        }

        private void InitializeComponent()
        {
            System.ComponentModel.ComponentResourceManager resources = new System.ComponentModel.ComponentResourceManager(typeof(Sudoku));
            this.cellBlock1 = new Sudoku.CellBlock();
            this.cellBlock2 = new Sudoku.CellBlock();
            this.cellBlock3 = new Sudoku.CellBlock();
            this.cellBlock4 = new Sudoku.CellBlock();
            this.cellBlock5 = new Sudoku.CellBlock();
            this.cellBlock6 = new Sudoku.CellBlock();
            this.cellBlock7 = new Sudoku.CellBlock();
            this.cellBlock8 = new Sudoku.CellBlock();
            this.cellBlock9 = new Sudoku.CellBlock(); //errors occur at these lines

}


        private CellBlock cellBlock1;
        private CellBlock cellBlock2;
        private CellBlock cellBlock3;
        private CellBlock cellBlock4;
        private CellBlock cellBlock5;
        private CellBlock cellBlock6;
        private CellBlock cellBlock7;
        private CellBlock cellBlock8;
        private CellBlock cellBlock9;

    }
}

I think that’s all correct, even though I’m omitting some of the automatically-generated code for the sake of brevity. When I build the solution, I get 9 errors like this: The type name ‘CellBlock’ does not exist in the type ‘Sudoku.Sudoku’

referencing the lines that read: this.cellBlock1 = new Sudoku.CellBlock();, etc. I thought that maybe I need to add a reference to CellBlock, even though it's within the same solution, but when I clickAdd Reference`, nothing is listed under project.