How to Rotate Train Tracks to Change Their Orientation
How can you determine which buttons to push in order to get every track running East/West?
Your goal is to determine which buttons you should push in order to get every track running East/West. If there is not a way to do it, then explain how you know it cannot be done. If there is more than one way to do it, provide a second way; if there is not a second way to do it, explain how you know there cannot be another way. Please help! SAT solvers may be used.
Final answer:
To determine which buttons should be pushed in order to get every track running East/West, we can represent the track orientations as Boolean variables and use a SAT solver to find a satisfying assignment of variables that represents the desired track orientations.
Explanation: To solve this problem, we can represent the track orientations as Boolean variables. Let's denote the track orientations as follows:
R: Red track orientation
O: Orange track orientation
Y: Yellow track orientation
G: Green track orientation
B: Blue track orientation
I: Indigo track orientation
V: Violet track orientation
We can represent the given rotations as a set of constraints:
Button 1: Yellow, Indigo, Violet
Button 2: Red, Orange, Green
Button 3: Yellow, Blue, Violet
Button 4: Orange, Blue, Indigo
Button 5: Red, Blue, Indigo
Button 6: Red, Orange, Yellow
Button 7: Yellow, Green, Violet
Our goal is to find a satisfying assignment of variables that represents the desired track orientations. We can represent this as a Boolean formula:
(R = East/West) AND (O = East/West) AND (Y = East/West) AND (G = East/West) AND (B = East/West) AND (I = East/West) AND (V = East/West)
We can use a SAT solver to find a satisfying assignment of variables that satisfies this formula. If a satisfying assignment is found, it means that there is a way to get every track running East/West. If no satisfying assignment is found, it means that there is no way to get every track running East/West.