15 Oct
2007
15 Oct
'07
4:59 p.m.
If I haven't made a mistake, the size 10 submarine problem can be solved in 19 time steps (with 18 shots). I don't know if this can be massaged down to 18 time steps. The following table gives the shots for my solution. The 10th shot (at time 09) is not needed and is shown as x. d 0 1 2 3 4 5 6 7 8 9 t = 00+d 8 2 0 6 0 0 0 4 0 x t = 10+d 9 7 1 1 3 5 5 9 7 I'll conjecture the size 2p problem for prime p can always be solved within 2p-1 steps. Note that if the goal was to minimize ammunition instead of max kill time, the size N problem only needs N shots -- shoot square 0 at time 0, 1 at time N, 2 at time 2N, ... Nice problem! - Scott