Criminals in space? That's not new. A quarter of a century ago we chased Carmen Sandiego across the Solar System, but this time our success depends on how good we are at solving riddles. A group of seven planets has become the refuge of the rebels, and they jump from one to another in their old ship following a specific pattern. The police only have ten attempts at their disposal, so what sequence guarantees capture regardless of the initial condition?
Needless to say, the riddle requires a much broader explanation, which is available in the video below with Spanish subtitles. The positions of the planets remind us of a flux capacitor turned upside down. The rebels are hidden on one of the seven planets, and obviously the police don't know which one. The jump from one planet to another takes an hour, but the authorities must capture the fugitives in ten hours or less, or they will receive reinforcements.
Now, there is a huge advantage in favor of the police: their ship jumps from one planet to another regardless of order, repetition, or distance, while the rebels' ship can only move between adjacent planets. To compensate, the rebels never stop. Each planet has been numbered, with 3 in the center, 2-4-6 in the inner ring, and 1-5-7 in the outer ring. This detail is very important, because being limited to adjacent planets in their jumps, the rebels always move from an even planet to an odd one, or vice versa.
Editor's note: Play the video before continuing if you want to solve it yourself.
Solution to the puzzle
If there were four planets instead of seven, the solution would be very simple: check planet 3 twice in a row. The adjacent movement would force the rebels to visit it, finding the police in the process. Everything becomes complicated with seven planets, but the DNA of the strategy is the same. The question is: do the rebels start their escape on an even planet or an odd one?
Let's suppose the planet is even, so the police visit one of those planets first, say 2. If they are not there, then the rebels started from 4 or 6, and can only move to 3, 5 or 7. The control of the center is important, and the police decide to jump to planet 3. If they are not there, they moved to 5 or 7, and their only options are planets 4 and 6.
So, 4 or 6? In the video example, the police choose 4. If they don't appear, it's because they were on planet 6, and their only alternatives are 3 and 7. In other words, they are cornered. The police travel to 3, and if the rebels are not there, they moved to 7. Their only move is 6, and that's where the patrol goes.
Case closed... or not? In reality, that sequence 2-3-4-3-6 only works when the rebels' starting planet is even. If after the fifth jump the police don't find the rebels, it's because they started from an odd planet, and the solution is simply to repeat the sequence again: 2-3-4-3-6-2-3-4-3-6. In ten jumps, they are captured.
Now comes the interesting part: there is more than one solution to this riddle.
