The input and inout (used as inpputs) pins are connected to 8 different logic gates, which lead to the outputs. Only one logic layer of combinatoric logic. Each input is hooked up to only one gate.
No clock, enable or reset is used. As this is just one layer of combinatoric logic, you can simply check against a precalculated truth table. To play, flip the inputs and observe the output until you recognise what it must be.
Connect 16 switches to the input and inout pins, the 8 outputs are hooked up to one LED each (or other display hardware of your choice).
The solution is:
SPOILER
out0 = in0 and in2
out1 = not in1
out2 = in5 and in7 and inA
out3 = in6 xor inC
out4 = in4 nand in9
out5 = in8 xnor B
out6 = inE nor inF
out7 = in3 or inD