Sorry - I don't think I was clear after all.
So the sequence that is generated will be a known length which is decided before the game begins. And you/the agent can make as many guesses at the code as you would like - the challenge is to make an attempt as guessing the sequence AND the value of Z.
As a human I can come up with a number of heuristics that will try to achieve the goal in a lower number of steps than just random guessing.
For example lets say the generated sequence is 1100 and the generated Z is 2:
1111 - 'close'
0000 - 'close'
1100 - 'close'
1110 - 'not close' (now I know there is some sensitivity on the result on the third bit)
1101 - 'not close'
So as you can see one can build up a knowledge base of evidence given their historical guesses and the systems 'close'/'not close' outputs.
Essentially, the agent should be able to navigate this evidence till it has enough to make a guess on the sequence and Z.