Daily Math Puzzle: 2026-06-06
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2026-06-06
You are at the entrance of 'Wonderland Park', which has a peculiar grid layout where all main paths are perfectly straight and intersect at right angles. You want to visit three attractions in a specific order: first the 'Mystic Maze', then the 'Sky-High Swing', and finally the 'River Rapids'. From the Entrance: - The Mystic Maze is 3 blocks North and 2 blocks East. - The Sky-High Swing is 1 block North and 4 blocks East. - The River Rapids is 4 blocks North and 1 block East. Here's the catch: When you start your journey at the Entrance, you are facing North. More importantly, after you exit *any* attraction, you *always* find yourself facing North again, regardless of how you entered or exited. To move to your next destination, you must first turn to face the correct direction before walking. Each turn (left, right, or about-face) counts as 1 'orientation adjustment'. Each block walked is a 'movement unit', but we are only interested in minimizing turns. What is the minimum total number of orientation adjustments needed to visit all three attractions in the specified order?
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Solution
4 — Let's map the locations, assuming the Entrance is at (0,0) on a grid where North is +Y and East is +X:
- Entrance (E): (0,0)
- Mystic Maze (MM): (2,3) (2 East, 3 North)
- Sky-High Swing (SHS): (4,1) (4 East, 1 North)
- River Rapids (RR): (1,4) (1 East, 4 North)
The key rule is that you start facing North, and you *always* face North after exiting an attraction.
**Leg 1: Entrance (0,0) -> Mystic Maze (2,3)**
- **Starting:** At (0,0), facing North.
- **Destination:** (2,3). This requires moving 2 blocks East and 3 blocks North.
- Since you are already facing North and need to move North, you can prioritize moving North first: Move 3 blocks North (0 turns). You are now at (0,3), still facing North.
- From (0,3), you need to move 2 blocks East. To move East from North: Turn Right (1 turn). Now facing East.
- Move 2 blocks East. Arrive at MM (2,3).
- **Orientation adjustments for this leg: 1 turn.**
- After exiting MM, you are at (2,3) and facing North.
**Leg 2: Mystic Maze (2,3) -> Sky-High Swing (4,1)**
- **Starting:** At (2,3), facing North.
- **Destination:** (4,1). This requires moving 2 blocks East and 2 blocks South.
- You are facing North. You need to go East and South. Neither of these directions is directly North, so you cannot take advantage of your current orientation for the first move.
- To move East from North: Turn Right (1 turn). Now facing East.
- Move 2 blocks East. You are now at (4,3), facing East.
- From (4,3), you need to move 2 blocks South. To move South from East: Turn Right (1 turn). Now facing South.
- Move 2 blocks South. Arrive at SHS (4,1).
- **Orientation adjustments for this leg: 2 turns.**
- After exiting SHS, you are at (4,1) and facing North.
**Leg 3: Sky-High Swing (4,1) -> River Rapids (1,4)**
- **Starting:** At (4,1), facing North.
- **Destination:** (1,4). This requires moving 3 blocks West and 3 blocks North.
- Since you are already facing North and need to move North, you can prioritize moving North first: Move 3 blocks North (0 turns). You are now at (4,4), still facing North.
- From (4,4), you need to move 3 blocks West. To move West from North: Turn Left (1 turn). Now facing West.
- Move 3 blocks West. Arrive at RR (1,4).
- **Orientation adjustments for this leg: 1 turn.**
**Total Orientation Adjustments:** 1 (Leg 1) + 2 (Leg 2) + 1 (Leg 3) = **4 turns.**
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