This puzzle is adapted from Isaac Asimov's short story Little Lost Robot (1947). For anyone familiar with the story, you will note I have changed many details for sake of brevity (This also means the story's actual solution may not be the best fit).
Robots in Isaac Asimov stories have an artificial intelligence that is kept in check with three "laws" that are at the core of their programming:
- A robot may not injure a human being or, through inaction, allow a human being to come to harm
- A robot must obey the orders given it by human beings except where such orders would conflict with the First Law
- A robot must protect its own existence as long as such protection does not conflict with the First or Second Laws
There was a military research station that used a number of robots. The research involved gamma radiation. Given the strength of this radiation, it was decided that a human could be safely exposed to it for long as 30 minutes, but a robot's positronic brain would almost certainly be destroyed in less than a minute in that environment.
The robots, upon observing that a human had been in the contaminated zone for a while, would conclude that the human may be confused or complacent and may overstay their allotted 30 minute window. The first law outranks the third law, and so the nearby robots would run into the gamma radiation to try and "save" the human, even though they themselves almost certainly wouldn't survive the ordeal. Many robots were destroyed as a result, and no arguments would convince the robots to not take the risk. Even though the human risk was minute, they are more than willing to die protecting them. Not even commanding them to stay put could work, as the first law is above the second.
The lead researcher of the station decided to take a drastic step to correct this problem. He had the robot's programming modified such that the first law was now "A robot may not injure a human being" and omitting the inaction part. Now, in theory, the robots could ignore humans left in the radiation zone, even if they had been there for much longer than 30 minutes.
A few days later, a frustrated researcher told one of the (now modified) robots to "Get Lost!", not intending the robot to take the phrase literally. It became evident that the robot did interpret that as a command because after a search nobody could find it. The lead researcher, upon finding out, became concerned. If a robot, whose 1st law was modified, went out into the world and possibly let a human die through their inaction, it could be traced back to him and he would surely go to jail. The lead researcher ordered the station into lockdown and called the best team possible to help save his him from this problem.
This is where you, a robot detective, come in. Arriving at the research station, you looked for clues. Eventually, you found something. A cargo ship arrived the same day that the robot became lost (it was still docked because the whole facility was on lockdown). The cargo manifest was for 62 robots; all replacements for the ones lost earlier that week. There are, however, 63 robots in the cargo hold, all currently in sleep mode.
You switch the robots on one at a time and question them. All 63 claim to have been shipped direct from the factory and have no knowledge of this facility or which robot among them is the imposter. The "lost" robot has apparently chosen to follow the "Get Lost!" command above any command you could give.
The robots are physically identical, and the positronic brain is too complicated to analyze for differences. The "lost" robot is trying to not be found out, and will try to act exactly as though it is one of the newly built robots.
What can you do to identify the missing robot from the 63 robots?
Clarification Edit: The Asimov story has something of a reason for why the lost robot chooses to follow the "Get Lost" order above all other orders, but I skipped over it. From its perspective, it will do practically anything to not be caught. If you order the robot to do something, it will try to follow along in the spirit of being indistinguishable from the others. It is hiding "in plain sight" so to speak.