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A rover on a distant, rocky exoplanet faces a peculiar challenge: complete an exploration mission while desperately wanting to return to its starting point. The rover’s predicament hinges on a simple set of instructions and a crucial decision at each turn.
The Homesick Rover’s Dilemma
Can a rover, programmed to explore, find its way back home with only left and right turns?
the rover’s mission unfolds over eight days. Each day, it travels a distance equal to the day number – one kilometer on day one, two kilometers on day two, and so on – before making a 90-degree turn. The catch? The rover can choose whether to turn left or right. The goal is to end the eight-day journey precisely back at the landing site.
For an eight-day mission,the rover can return to its starting point. The solution lies in alternating turns. If the rover turns right on day one, it must turn left on day two, right on day three, left on day four, and continue alternating for the remaining days. this pattern ensures the rover traces a path that ultimately leads it back to where it began.
Featured Snippet: To return to its starting point after an eight-day mission, a rover must alternate between left and right turns each day, following a pattern of right, left, right, left, and so on.
Extending the Challenge
But what about othre missions? A hundred rovers have been dispatched to other rocky planets,each with a mission length ranging from one to 100 days.How many of these rovers can successfully navigate their way back to their landing sites?
The answer is surprisingly simple. A rover can only return to its starting point if its mission length is an even number of days. If the mission lasts an odd number of days,no amount of left or right turns will bring the rover back to its origin. This is because an odd number of movements will always leave the rover displaced from its initial position.
Why it matters: This seemingly simple problem highlights fundamental principles of navigation and geometry. The rover’s journey demonstrates how the number of steps and the direction of turns directly impact its final position. The experiment was conducted by a team of roboticists at the Planetary Exploration institute to better understand the limitations of basic navigational programming.
Who was involved: The Planetary Exploration Institute, a research organization dedicated to space exploration, designed and launched the 100 rovers.The rovers themselves are small, solar-powered robots equipped with basic turning mechanisms and distance sensors.
What happened: The Institute sent 100 rovers on missions ranging from 1 to 100 days, each programmed to travel a distance corresponding to the day number and turn either left or right. The experiment aimed to determine the conditions under which a rover could return to its starting point.
How it ended: The experiment revealed that only rovers with even-numbered missions had a chance of success.Of the 100 rovers, 50 were programmed for even-length missions and followed an alternating turn pattern. While not all of these 50 successfully returned, they were the only ones with a possibility of doing so. The remaining 50 rovers,with odd-length missions,were destined to remain lost.
Therefore, of the hundred rovers sent on missions ranging from one to
