Outsmarting Interstellar Fugitives: A Planet-Hopping Puzzle

\Imagine you're an interstellar cop tasked with catching a group of rebels hiding among seven planets. These rebels are slippery, constantly moving to evade capture. Your cruiser has the advantage of warping between any two planets instantly, but the rebels can only jump to adjacent planets. With rebel reinforcements on their way, you have only ten warps to catch them. How do you devise a search strategy that guarantees their capture?

This is a classic problem-solving scenario that requires careful planning and a bit of clever thinking. Let's break down the steps to ensure those rebels don't escape justice.

The Challenge: Seven Planets, Ten Warps

The core challenge lies in the uncertainty. You don't know the rebels' starting location. They could be on any of the seven planets, and they're constantly on the move. To make things even more complicated, they relocate every chance they get.

Simplifying the Problem

When faced with a complex problem, it often helps to simplify it. Let's start by imagining only four planets arranged in a line. Planet three is key because it's adjacent to all the others. This means the rebels either start on planet three and move, or they start elsewhere and must move to planet three.

In this simplified scenario, checking planet three twice in a row guarantees capture.

Adding Complexity: The Outer Planets

Now, let's bring back the three outer planets. The same strategy applies: we need to find a way to corner the rebels. Here's where a crucial insight comes into play:

• The rebels always move from an even-numbered planet to an odd-numbered planet, or vice versa.

This allows us to divide the planets into two subsets and tackle each one separately.

The Winning Strategy: A Ten-Warp Sequence

Here's the sequence that guarantees capture in ten warps or less:

1. Two
2. Three
3. Four
4. Three
5. Six
6. Two
7. Three
8. Four
9. Three
10. Six

Why This Works

Let's break down why this sequence is so effective:

• Assumption 1: Rebels Start on an Even-Numbered Planet: If the rebels start on planet two, four, or six, this sequence will catch them within the first five warps.
• Assumption 2: Rebels Start on an Odd-Numbered Planet: If the rebels start on an odd-numbered planet, after five moves, they must be on an even-numbered planet. By repeating the sequence, we guarantee their capture in the second set of five warps.

The Logic Behind the Sequence

1. Start with Planet Two: If the rebels are there, you've caught them. If not, they must be on planet four or six.
2. Check Planet Three: This is a crucial point, as rebels from four or six can move to three, five, or seven. If they're not on three, they must be on five or seven.
3. Search Planet Four: Rebels from five or seven will move to four or six. If they're not on four, they must be on six.
4. Revisit Planet Three: Rebels on six can only flee to three or seven. If they're not on three, they're cornered on seven.
5. Final Check on Planet Six: Rebels on planet seven can only move to planet six, where you apprehend them.

By repeating this sequence, you cover all possible starting locations and movements, ensuring the rebels have nowhere to hide.

Mastering Deductive Reasoning

This planet-hopping puzzle demonstrates the power of deductive reasoning. By breaking down the problem, identifying key constraints, and systematically eliminating possibilities, you can devise a strategy that guarantees success. So, the next time you face a seemingly impossible challenge, remember the interstellar police squad and their ten-warp solution. With a little logic and planning, you can restore order to any galaxy – or at least solve a really cool riddle!