This is one of my favorite puzzles. You can use any number
of 'and' and 'or' gates, with any number of inputs each, but
only two 'not' gates. You must build a circuit that computes
for inputs A, B, and C, the three separate values not A, not B,
and not C.
Essentially, can you invert three signals, using two inverters
and any number of `and' and `or' gates?
Once you have solved that, the next question is, can you
use this circuit recursively to build 4, then 6, then 9, then
13, then 19, then 28, then 42, and so on, effective inverters?
In other words, can you say that any combinational circuit
can be constructed with just two inverters?