Maze Mania.

Maze Mania is a wooden fence maze that covers 2.5 acres in Garden City, South Carolina. Inside the maze are several open rooms which offer several exits.
Step up to the counter and check in with the cashier. You will see a posted time in which to get through the maze. Pick up your time card and punch in! Run through the maze to find the cheese and punch your card. Now you keep running through the maze until you find the finish. Once out of the maze you punch out at the counter. If you beat the posted time on your first try, you win a free t-shirt. -via J-Walk Blog

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The right turn technique will always get you out, but the maze is designed with a check point that moves each day, which may defeat this rule. The layout of the maze itself also changes through the use of different gates that are set each morning.
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"No, because there would still presumably be a right hand turn to get out of it."

Actually, the right-hand turn "rule" will fail if the person starts inside a disjointed island. In this case, you need something called a Pledge algorithm to solve this problem.
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"The trick would fail if for some reason you start in an “island” inside of the maze."

No, because there would still presumably be a right hand turn to get out of it. If the outside wall was just one big square it might fail, but I would wager that you would notice that you could see all the way from one corner to the next.
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