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Distant, on a big, rocky exoplanet, a rover from Earth has simply arrived on a mission of exploration. However the poor factor doesn’t need to discover. The second it begins transferring, it grows homesick and needs nothing greater than to return to the very spot the place it started. Sadly, it has obtained very express directions. The primary day, it should journey one kilometer ahead in a straight line, then flip 90 levels. The second day, it should journey two kilometers ahead, then flip 90 levels. The third day, it should journey three kilometers ahead, then flip 90 levels. The fourth day, it should journey 4 kilometers ahead, then flip 90 levels. And so forth, all through an eight-day mission.
The rover needs to return to the location the place it landed. However it could select solely which path to show, left or proper, on the finish of every day. How can the rover finish the eight-day mission again at its touchdown web site?
BONUS: 100 rovers with the identical set of directions have been despatched to different massive, rocky planets, every with a special mission size, starting from someday to 100 days.
What number of of those rovers can finish their missions again at their touchdown websites?
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