Knop's game
A game discussed on SeqFans on 2025-05-21, attributed to Konstantin Knop:
You have an infinite row of cells numbered with the integers (open in both directions). In the starting position, you have N counters on cell 0. At each move, you pick a starting cell, and move K counters from that starting cell to the cell K steps either to the right or left. The object of the game is to finish with all N counters on cell 1 in the smallest possible number of moves.