Solve 1-million-queens puzzle in less than 1 second and 100-million-queens puzzle in less than 1 minute.
Local search and Queen Search 4 algorithm[1].
[1] Sosic, Rok, and Jun Gu. "3,000,000 queens in less than one minute." ACM SIGART Bulletin 2, no. 2 (1991): 22-24.