A dragon king is a shogi piece that moves any number of squares vertically or horizontally or one square diagonally but does not move through or jump over other pieces. We construct infinite families of solutions to the n + k dragon kings problem of placing k pawns and n + k mutually nonattacking dragon kings on an n+n board, including solutions symmetric with respect to quarter-turn or half-turn rotations, solutions symmetric with respect to one or two diagonal reflections, and solutions not symmetric with respect to any nontrivial rotation or reflection. We show that an n + k dragon kings solution exists whenever n > k + 5 and that, given some extra conditions, symmetric solutions exist for n > 2k + 5.
Recreational Mathematics Magazine, Vol. 5, No. 10, pp. 39–55.