A fugitive is surrounded by N police officers, with the nearest one at distance 1 away. The fugitive and the officers move alternatively.
- In a fugitive move, the fugitive can travel no more than a distance of d.
- In an officer move, the sum of distances travelled by all officers can be no more than d.
The fugitive is caught if their distance to some officer is 0 in finite moves, otherwise they escape.
Question: Given N, is there always some $d \gt 0$ for which the fugitive can escape, regardless of the officers' initial distribution?
Related: One king vs many. Can white force a draw? (discrete version dual problem)