Hi! I’ve just started competitive programming, and I’m having some trouble understanding the solution to ‘Shell Game.’ Any help would be greatly appreciated.

Solution code (from usaco guide):

```
import java.io.*;
import java.util.*;
public class Shell {
public static void main(String[] args) throws IOException {
Kattio io = new Kattio("shell");
int n = io.nextInt();
// shellAtPos[i] stores the label of the shell located at position i
int[] shellAtPos = new int[3];
// Arbitrarily place the shells down
for (int i = 0; i < 3; i++) { shellAtPos[i] = i; }
// counter[i] stores the number of times the shell with label i was
// picked
int[] counter = new int[3];
for (int i = 0; i < n; i++) {
// Zero indexing: offset all positions by 1
int a = io.nextInt() - 1;
int b = io.nextInt() - 1;
int g = io.nextInt() - 1;
// Perform Bessie's swapping operation
int temp = shellAtPos[b];
shellAtPos[b] = shellAtPos[a];
shellAtPos[a] = temp;
// Count the number of times Elsie guesses each particular shell
counter[shellAtPos[g]]++;
}
io.println(Math.max(counter[0], Math.max(counter[1], counter[2])));
io.close();
}
//BeginCodeSnip{Kattio}
static class Kattio extends PrintWriter {
private BufferedReader r;
private StringTokenizer st;
// standard input
public Kattio() { this(System.in, System.out); }
public Kattio(InputStream i, OutputStream o) {
super(o);
r = new BufferedReader(new InputStreamReader(i));
}
// USACO-style file input
public Kattio(String problemName) throws IOException {
super(problemName + ".out");
r = new BufferedReader(new FileReader(problemName + ".in"));
}
// returns null if no more input
public String next() {
try {
while (st == null || !st.hasMoreTokens())
st = new StringTokenizer(r.readLine());
return st.nextToken();
} catch (Exception e) { }
return null;
}
public int nextInt() { return Integer.parseInt(next()); }
public double nextDouble() { return Double.parseDouble(next()); }
public long nextLong() { return Long.parseLong(next()); }
}
//EndCodeSnip
}
```

What I don’t understand about this solution is the ‘arbitrary’ ordering of the shells. When I read the problem, I understood that the order of the shells was unknown, and that you had to permute through all the possible orderings (012, 021, 102, 120, et cetera.) This solution stores the initial positions of the shells as 0, 1, and 2 (1, 2, and 3 with non-array indices.)

Wouldn’t this return an incorrect answer if you’re supposed to permute through ALL of the orderings?

Thank you!