Smuggling yourself aboard the rogue submarine was the easy part. Hacking into the nuclear missile launch override was a little harder. However, now you have a problem: you don’t have the override code. You know you need the same two numbers that the agents of chaos just used to authorize the launch. But, one wrong answer will lock you out.
From your hiding spot, you’ve been able to learn the following information: The big boss didn’t trust any minion with the full information to launch nuclear missiles on their own. So, he gave one launch code to Minion A and the other to Minion B, and forbade them to share the numbers with each other. When the order came, each entered their own number and activated the countdown. That was 50 minutes ago, and there’s only 10 minutes left before the missiles launch.
Suddenly, the boss says, “Funny story— your launch codes were actually related. I chose a set of distinct positive integers with at least two elements, each less than 7, and told their sum to you, A, and their product to you, B.” After a moment of awkward silence, A says to B, “I don’t know whether you know my number.” B thinks this over, then responds, “I know your number, and now I know you know my number too.” That’s all you’ve got. What numbers do you enter to override the launch?
Ignorance-based puzzles like this are notoriously difficult to work through. The trick is to put yourself in the heads of both characters and narrow down the possibilities based on what they know or don’t know. So, let’s start with A’s first statement.
It means that B could conceivably have something with the potential to reveal A’s number, but isn’t guaranteed to. That doesn’t sound very definitive, but it can lead us to a major insight. The only scenarios where B could know A’s number are when there’s exactly one valid way to factor B’s number. Because the boss’s numbers must be less than 7, A’s list of B’s possibilities only has these 4 numbers.
Here’s where we can conclude a major clue. To think B could have these numbers, A’s number must be a sum of their factors— so 3, 4, 5, or 6. We’ll soon have to do something similar going from sums to products and back to sums.
Write a brief summary of the scenario in your own words. This will help you understand the problem better. Remember, you are trying to find the two launch codes that the minions used. What information do you have? What do you need to find out?
Try to put yourself in the shoes of Minion A and Minion B. What do they know? What don’t they know? Write down your thoughts. This will help you understand the problem from different perspectives.
Based on the information given, list down all the possible numbers that could be the launch codes. Remember, the numbers are distinct positive integers, each less than 7. What are the possible sums and products?
Based on the conversation between Minion A and Minion B, try to narrow down the possibilities. What can you infer from their conversation? Use this information to eliminate some of the possible numbers.
Now that you have narrowed down the possibilities, try to find the two numbers that are the launch codes. Remember, one wrong answer will lock you out. Be sure of your answer before you enter it.
