How do I reference multi-dimensional arrays?

Question

I'm trying to understand multi-dimensional arrays in Java, but I think it applies to any language. Please consider this snippet I found on the web:

          //************************************
            //     static array initialization
            //************************************
    byte[][] smallArray = { { 10, 11, 12, 13 },
    { 20, 21, 22, 23 },
    { 30, 31, 32, 33 },
    { 40, 41, 42, 43 }, };

    // Display the array element at row 2, column 3
    System.out.println(smallArray[1][2]); 
// Value is 21

Why is it 21? I thought it would be 22.

I looked this up because I am trying to figure out what length means in this context:

public class Pieces {
    int thePieces[][][];
    public Pieces(){

    }
    public int[][][] createPieces(){

        /* pieces in order below
                **** [0]

                **
                **

                *
                ****

                   *
                ****

                ***
                 *

                **
                 **

                 **
                ** [6]
         *
         *
         *
         */
       int myPieces [][][] =
       {
           {  //square
               {0,0},
               {1,0},
               {1,1},
               {0,1}

           },
           { //T
               {-1,0},
               {0,0},
               {0,1},
               {1,0}
           }

       };

       thePieces = myPieces;

    return thePieces;
    }

    public void printPieces(){

        System.out.println(thePieces[0][0].length);
    }

}

I am trying to learn java by creating a tetris clone. What I don't understand is why length is required to use [][]. It was the only way I could get to work. I tried thePieces[0][0][0].length but got an error that I did not understand?

Why don't I have to put [][][] to get the reference? I saw online where the first "level" of the array was referenced myArray.length instead of myArray[].length. What then am I saying with myArray[][].length (it seems 2nd,3rd levels but I'm not getting what I expect)?

I ran my piece code and got 2. I have no idea why it is two. Is it because I have two sets at the third level? I expected to get four because of the four sets of points.

Thank you for your helping me understand.

EDIT: I figured out why it is two. It is giving me my two points in the innermost set. If I wanted four I would use thePieces[0].length. But what about the first example? Is it a typo?

Answer 1

Why is it 21? I thought it would be 22.

22 is correct -- I ran the code to verify it.

The indexes refer to the array elements, from the outer ones to the inner ones. So,

myPieces[0] is { {0,0}, {1,0}, {1,1}, {0,1} } (an array containing arrays), myPieces[0][0] is {0,0} (an array containing ints), and myPieces[0][0][0] is 0 (an int).