SHOTS

gistfile1.java

public static void main(String args[]){

        final int startingShot = 1;
        ArrayList<Integer> startingList = new ArrayList<Integer>();

        // fill list with shots
        for(int i=0;i<1024;i++){
            startingList.add(i, i+1);
        }

        // find solution
        for (int solution=0;solution<=1024;solution++){
            // init
            int currentShotIndex = startingShot-1;
            ArrayList<Integer> shotsList = (ArrayList<Integer>)startingList.clone();

            // take shots until just 7 is left
            while(!allShotsBut7(shotsList)){
                // find next shot, Circle back around
                for(int i=0; i<solution; i++){
                    currentShotIndex = (currentShotIndex+1) % shotsList.size();
                }
                //shoot
                if (shotsList.get(currentShotIndex) == 7)break;
                shotsList.remove(currentShotIndex);
                // recover if we're now outside of the circle as a result of last shot
                if (currentShotIndex > shotsList.size()-1){
                    currentShotIndex = 0;
                }
            }
            if (allShotsBut7(shotsList)){
                System.out.println("Only shot 7 is left!  Solution found: " + solution);
            }
        }
    }

    public static boolean allShotsBut7(ArrayList<Integer> list){
        return (list.get(0) == 7 && list.size() == 1);
    }

There is an excellent writeup of this problem in Donald Knuth’s Concrete Mathematics (Chapter 1, Section 3), which gives a closed form solution and the intuition behind it.

https://blog.exodusintel.com/2015/04/27/exodus-adventure-ctf-2015/
https://en.wikipedia.org/wiki/Josephus_problem

https://www.youtube.com/watch?v=uCsD3ZGzMgE