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);
    }

Josephus takes out a tiny flag on a tiny stick and places it in the glass in
front of you and says:
Let's call this shot number 7, you must start at shot number 1. You pick a
number between 0 and 1024 and that is how many glasses you skip before taking
the next shot. Once you take a shot that glass is removed from the bar. You
continue around the bar skipping and drinking, over and over, until you have
consumed all the drinks except for number 7, then you can take the flag.
What number do you choose?

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