A puzzle
It’s the Cold War, and you command a missile station tasked with bombing an enemy submarine. Intelligence has provided you with these facts:
1) The submarine travels with some constant integer velocity, due either east or west (i.e., travels along the standard number line, either to the right or left).
2) At any integral time, the submarine’s position on the number line is an integer.
For example, it could be that at time 1, the sub is at position 5, at time 2 it’s at position 3, at time 3 it’s at position 1, at time 4 it’s at position -1, and so forth. In this case the constant integer velocity is -2.
Your missile station is able to fire one missile at each integral time value. So if in the above example you had tried the sequence of bombings (0,1,2,3) - the ordered numbers here representing positions on the number line - you would have missed every time. But if you just so happened to bomb the location -3 on the fifth try, you would have a lucky hit.
Unfortunately the above is just one of many possible situations, and Intelligence has supplied you no information about the submarine’s particular velocity and current location. Nevertheless, can you develop a bombing plan that will eventually find your target?
