The puzzle presented at the 2017 International Mathematical Olympiad is slightly different than what was posted here.
The question on their website is after 109 rounds can the distance be at most 100
After reading the word problem, it appears that the computer moves in a radius of 1, then places the Contestant at or within a radius of 1 from the the computer's new position. The Contestant then moves a radius of 1 from the placement point. How friendly is this computer? How random is this computer? Does the computer learn (AI)?
I'll just pass, cuz even presuming an average error in distance of 1/e gets rather dynamic rather quickly. But I'll guess that it has something to do with the inverse Lambert function and squaring the result as an average radius of error.
JMHWAG of 86.4
Thanks for an interesting problem. Is the computer, perhaps using game theory, trying to get away or does it pick randomly. For instance if it moved to (1,0) and you moved to (-1,0) then it would move (possibly with some probability) to (2,0) and report something like (1.7,0.7) to try and send you in the wrong direction. It seems reasonable that your best move is to go towards the reported point by 1 unit, and the puzzle is can the computer get away.Quote: ThatDonGuy
....The computer moves to a new location...at the end of the 109th turn, [will] your location will always be distance 100...