Ah yes, the riddle from hell. It is not as bad as it seems though.

Click around a bit to understand what is happening. Clicking the gates changes their type. Clicking the pentagram simulates your created circuit using the input to the left. Your output is displayed with red x’s where it does not match the actual output to the far right. After a simulation of the circuit, the next click will generate a new random input sequence and a new random constellation of gates. Gate types remain the same.

For those completely unfamiliar with binary signals and logical gates, this riddle will require some googling. Learn what AND, OR, NAND, NOR-gates etc are. Some quick reading will get you up to speed.
By expirmentation you can determine the types of the gates. Check the input to a gate, set it to the first gate type and simulate to see what the output becomes. Do that for all inputs (0,0), (0,1) and (1,1), and you will have enough information to know what gate type it is (obviously you can’t choose the inputs, but just keep clicking that pentagram until you by chance get the desired input to a certain gate).
You will figure out that the gate types are:

Upper left – NAND
Top middle – XOR
Upper right – NOR
Bottom left – AND
Bottom middle – OR
Bottom right – NEXOR (sometines known as EXNOR)

When you know this, generate a new random input and gate constellation and set the gates so that the given input produces the given output (to the far right), then click the pentagram. This step is the larger part of the riddle. You only have one chance per circuit to get it right, since circuit resets upon simulation, so you gotta make sure that the gate types you have set will produce the correct output.

Good luck!