Seems like you don't need to code using Apps Inventor ?

Just to drop by and ask this :

I went thru a few videos on the project covered by Apps Inventor.

It seems that there is no need coding at all doing the project and one just drag the puzzles and the thing will run.

Is that how it works ?

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Not quite. It depends what your definition of coding is. Yes you slide puzzle pieces, and if you do this right, your app will run as desired.
The big if is, that you still have to apply logic and this will be difficult sometimes.
Do some tutorials and find out. It is free and it will take you about an afternoon to find out whether you like it.
http://appinventor.mit.edu/explore/ai2/tutorials.html

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Can I know are we able to see the code behind after putting all the pieces of puzzle together?

Is there any way to see the puzzles logic code ?

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Download your project as an aia

Open up the aia with and Archive Manager / "unzip" type program

Open the src folder

View files therein with text editor

That said the logic should be right there in front of you in the blocks :)

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The blocks are the source code. Just like you do not want to see what is going on in the virtual machine for a Java program, or the compiled code for a C program, you do not want to know what there is behind the App Inventor blocks. Yes, there is XML zipped in he .aia file, but the logic is much clearer to see if you look at the blocks themselves.
In the last years a number of block-languages have emerged, besides App Inventora notable one is Scratch, also from MIT. See: https://scratch.mit.edu/

All block languages derive from Blockly, if you want to know more about it, then look here: https://developers.google.com/blockly/

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I thought if MIT can make the block open up and let us see the 'java code' (I am assuming it is written using Java) it would be good cos then people can learn Java from there.

Using block no doubt is good but it has limited libraries right, unlike a real java programming language.

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as Ghica already said, the blocks are the code

see also here what computer programming language is the app builder?

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