Please take a look on the following pseudo-code:
boolean blocked[2];
int turn;
void P(int id) {
while(true) {
blocked[id] = true;
Mutual Exclusion is in this exemple not guaranteed because of the following:
We begin with the following situation:
blocked = {false, false};
turn = 0;
P1 is now executes, and skips
blocked[id] = false; // Not yet executed.
The situation is now:
blocked {false, true}
turn = 0;
Now P0 executes. It passes the second while loop, ready to execute the critical section. And when P1 executes, it sets turn to 1, and is also ready to execute the critical section.
Btw, this method was originally invented by Hyman. He sent it to Communications of the Acm in 1966