A solution using a minimal amount of time (which is units of time for soldiers), was first found by , but his solution used thousands of states. improved this to 16 states, and further improved it to eight states, while claiming to prove that no four-state solution exists. Peter Sanders later found that Balzer's search procedure was incomplete, but managed to reaffirm the four-state non-existence result through a corrected search procedure. The best currently known solution, using six states, was introduced by . It is still unknown whether a five-state solution exists.