In the distance, on a large rocky exoplanet, a rover from Earth has just arrived on an exploration mission. But the poor guy doesn’t want to explore. As soon as he starts moving, he becomes homesick and just wants to return to the very place where he started. Unfortunately, he received very explicit instructions. On the first day, he must go one kilometer in a straight line, then turn 90 degrees. On the second day, he must travel two kilometers forward, then turn 90 degrees. On the third day, he must travel three kilometers forward, then turn 90 degrees. On the fourth day, he must travel four kilometers forward, then turn 90 degrees. And so on, for the duration of an eight-day mission.
The rover wants to return to the site where it landed. But he can only choose which direction to turn, left or right, at the end of each day. How can the rover complete the eight-day mission at its landing site?
PRIME: About 100 rovers with the same set of instructions were sent to other large rocky planets, each with a different mission duration, ranging from one day to 100 days.
How many of these rovers can complete their mission at their landing sites?
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