How to play the the Train game. At each turn, take the number of steps requiest. In this ample, enter below the number of steps you would care to take. The press the "Show me" button to see the march of that number of steps ; Press the "Show me" button again and again, to see the same number of steps. You may change the number of steps at any time.

What is the secret of the the Train game? What should I see? It's as simple as even and odd numbers. It the number of steps is even (i.e. 2, 4, 6, ...) and you start in a "blue" car, you will end in a "blue" car. Similarly, if you start in a "brown" car, you will end in a "brown car. If the number of steps is odd the result is reversed: start in a "blue" car and you will end in a "brown" car and vice versa. This is how the magician knows where you are. The game is set where you will begin in a blue car.

Exercises.

1. Find a strategy that forces the hiding traveler to be found in the mail car.
2. Find a strategy that forces the hiding traveler to be found in the engine. Can you do this in two moves?
3. Find a strategy that leaves the player unable to move and the magician unable to determine where he or she is?
4. What is the minimum number of steps needed to find the hiding traveler, given a starting point in either of the Club, Shower, Diner, or Mail cars?
5. Suppose the train cars are all arranged in a row, as shown below. Can we play the same kind of game apply? (Hint. Remember even-odd.)
6. Suppose the cars are arranged on a circle? Can we play the same kind of game?