I've read ahead four or five chapters, so I know what's coming... I tell you this so you'll just pay attention to what you read in Chapter 15 and don't worry about modifying the circuit. You'll have plenty of chances ahead to improve this circuit and learn about reducing the number of chips you need. It's good stuff and as long as you examine and understand Charles' method for showing open/closed and 1/0 input and outputs... you shouldn't find Experiment 15 too troublesome.
If I had any issues with this circuit, it was dealing with these annoying little pushbuttons and the proper orientation for inserting into the breadboard. Insert them the wrong way, and they're basically always on (Closed or Pushed) and the LED stays lit. Once I figured out what was going on, I turned the buttons 90 degrees and everything was fine. (I used my multimeter and the continuity setting to check how the buttons worked and to verify I had the orientation wrong.)
As you can see from the photo, I'm once again back to 5V DC regulated. I used my meter to verify the voltage on the rails of the breadboard before moving forward with the experiment -- don't risk burning out your chips by applying to much voltage.
The video below pretty much speaks for itself and shows you how the circuit works (and how a player could cheat):