Circuit Design for 6 LEDs flashing in sequence
Getting 20 second timing with RCs is non-trivial. Consider looking at an HC4060, which is a VCO with built in divider, designed for long period timing.

Depending on what your son is supposed to achieve during 'his' design, you may then want to look at either a binary counter like HC161 + decoder like HC138, or look at a 'one-hot' coded state machine, built from D flops like HC74. I think the latter would be better suited to his needs.

You may also want to look up 'Johnson Counter', and shift registers like the HC164.

However, from experience, I can say that 'helping' your son with his tech homework by introducing him to stuff several levels above his ken is simply counterproductive. If you can point him at the data sheets, then stay the heck out, there's a better chance that he might learn somthing.