Never Rush to Be First in Playing Nimbi
Aviezri S. Fraenkel, Hans Herda · Mathematics Magazine · 1980
Nimbi is a two-player board game invented by Piet Hein. Twelve tokens, placed on the twelve vertices of a hexagonal board numbered 1, 2,..., 9, T, E, D, constitute the initial position of Nimbi (see FIGURE 1). The board contains twelve rows: four horizontal rows, four diagonal rows in northeast to southwest direction and four diagonal rows in northwest to southeast direction. The two players play alternately. Each player at his turn can remove any contiguous portion from a single row. (Thus 159D may be removed in one move. But if 5 had been removed previously, then neither 19 nor ID nor 19D can be removed in a single move, though 1 or 9 or D or even 9D can.) In Piet Hein's version, the player making the last move is the loser, his opponent the winner. We call this version LPL-Nimbi. The other version, in which the player making the last move wins and his opponent loses, will be called LPW-Nimbi.