Thanks for your question. According to the scenario in this game, a train makes five trips around a loop through five stations, P, Q, R, S, and T, in that order, stopping at exactly three of the stations on each trip. To help visualize this information, let's use the 5 trips as the base (1-5), with three "stacked" spaces above each trip (to represent the fact that the train stops at three of the stations on each trip:
- _ _ _ _ _
_ _ _ _ _
_ _ _ _ _
1 2 3 4 5
Now, let's take a look at the two rules in this game:
The train stops at any given station on exactly three
trips, but not on three consecutive trips.
In other words, we'll need to place the following 15 variables into our diagram, ensuring that no 3 variables of the same kind appear consecutively on it:
- P P P Q Q Q R R R S S S T T T
The train stops at any given station at least once in any two consecutive trips.
Essentially, we need to see all 5 variables appear in any two adjacent columns (remember - each column represents a separate one of the five consecutive trips). If you have difficulty understanding this rule, try a few hypotheticals to help clarify the patterns that result from its interaction with the previous rule. Let's say the train stops at P, Q, and R on the first trip. To ensure compliance with the second rule, the train must stop at S and T on the second trip, along with one of P, Q and R (let's say P). For its third trip, the train cannot stop at P (or else we'd be in violation of the first rule), but it must stop at Q and R (in compliance with the second rule). And so on.
For most test-takers, a hypothetical such as this is enough to ensure that they understand how the game works, and move on. A minority will be able to determine the patterns governing the three stations where the train stops on each trip.
The two rules produce the following set of five patterns that must appear in every solution of the game. Each pattern represents the sequence of stops at which each of the five trains must stop:
Pattern #1: 1-3-5
Pattern #2: 1-3-4
Pattern #3: 1-2-4
Pattern #4: 2-3-5
Pattern #5: 2-4-5
Detecting the patterns while setting up the game would make the questions significantly easier; nevertheless, the game can still be attacked successfully without ever understanding the patterns if you identify strongly with each individual rule. Coming up with a few hypothetical solutions before you delve into the questions is key in games of this type.
Hope this helps! Let me know.