In a distant galaxy, your elite interstellar police squad is on a mission to capture a group of elusive rebels. These fugitives have taken refuge within a cluster of seven small planets, and time is of the essence. With their reinforcements just 10 hours away, you must act swiftly to apprehend them. However, the rebels are not ones to stay idle; they will attempt to evade capture by hopping from one planet to another. Fortunately, your advanced cruiser has the capability to warp between any two planets within an hour, whereas their outdated smuggling ship can only jump to adjacent planets in the same timeframe.
The rebels are determined to keep moving, making it challenging to pinpoint their location. Your scouts have informed you that the rebel fleet will arrive in 10 hours, leaving you with a limited window to capture them. The task is to devise a search strategy that guarantees their capture in 10 warps or less, regardless of their movements.
To tackle this complex problem, let’s simplify the scenario. Imagine the cluster consists of only four central planets, excluding the outermost ones. Although the rebels’ starting planet is unknown, there’s a crucial detail: the third planet is adjacent to all others. This means the rebels either start there and move elsewhere or begin on another planet and must eventually move to planet three. By checking planet three twice consecutively, you can effectively trap them.
Introducing the three outer planets adds complexity, but the core strategy remains. The goal is to search the planets in a sequence that will eventually corner the rebels. An important insight is that each hour, the rebels move from an even-numbered planet to an odd-numbered one, or vice versa. This allows us to divide the planets into two subsets and tackle each separately.
Assume the rebels start on an even-numbered planet: two, four, or six. Begin by searching planet two. If they are not there, they must have started on four or six, allowing them to move to three, five, or seven. Since planet three offers the most options for their next move, check there next. If they are not found, they must have been at planet five or seven, meaning their next move will be to four or six. Search planet four next. If they are not there, they must have moved to planet six and can only flee to three or seven. By searching planet three again, you can corner them at planet seven, where they can only move to planet six, allowing you to capture them on your fifth search.
This plan assumes the rebels started on an even-numbered planet. But what if they began on an odd-numbered one? In that case, their location will alternate between odd and even-numbered planets every hour. After five moves, they will be on an even-numbered planet. If the first five searches miss them due to the wrong initial assumption, simply repeat the sequence: two, three, four, three, six. This ensures the rebels have nowhere to run.
Thanks to your strategic reasoning, order is restored to the galaxy, and the rebels are finally captured.
Imagine you are part of the interstellar police squad. Create a board game where each of the seven planets is represented by a space on the board. Use game pieces to represent the rebels and the police cruiser. Take turns moving the rebels and the police cruiser according to the rules described in the article. Your goal is to capture the rebels within 10 moves. This activity will help you understand the strategy and movements involved in the pursuit.
Draw a map of the seven planets and use arrows to indicate possible movements of the rebels and the police cruiser. Label each planet with its number and use different colors for the rebels’ and police cruiser’s paths. This visual representation will help you grasp the concept of dividing the planets into subsets and planning the search sequence.
In groups, role-play the scenario where one student acts as the rebel and another as the police officer. The rebel can only move to adjacent planets, while the police officer can warp to any planet. Use a timer to simulate the 10-hour limit. This interactive activity will reinforce the importance of strategic thinking and quick decision-making.
Write down the sequence of moves for both the rebels and the police cruiser. Analyze the patterns and use mathematical reasoning to explain why the strategy guarantees capture within 10 moves. This activity will enhance your problem-solving skills and deepen your understanding of the underlying logic.
Write a short story from the perspective of the interstellar police squad or the rebels. Describe the chase, the strategies used, and the final capture. Include dialogues and emotions to make the story engaging. This creative exercise will help you internalize the concepts while practicing your writing skills.
Strategy – A plan of action designed to achieve a specific goal or solve a problem. – The students used a clever strategy to solve the complex math problem by breaking it down into smaller parts.
Planets – Celestial bodies orbiting a star, such as the Earth orbiting the Sun. – In science class, we learned about the different planets in our solar system and their unique characteristics.
Capture – To take or record information for analysis or understanding. – The teacher asked us to capture the data from our experiment in a table for easier comparison.
Rebels – Individuals who resist or defy authority or convention. – In the story problem, the rebels used their knowledge of geometry to design a secret hideout.
Search – The act of looking for information or a solution. – We had to search through the textbook to find the formula needed to solve the equation.
Even – A number divisible by two without a remainder. – The teacher asked us to list all the even numbers between 1 and 20.
Odd – A number not divisible by two, leaving a remainder of one. – During the game, we had to identify all the odd numbers on the board.
Movement – A change in position or location, often used in geometry to describe transformations. – The movement of the shape on the grid was a translation to the right by three units.
Problem – A question or situation that requires a solution or answer. – The math problem asked us to find the area of a triangle given its base and height.
Plan – A detailed proposal for achieving a specific goal or solving a problem. – Our plan to solve the puzzle involved dividing the tasks among team members to work more efficiently.
