The (x, y) Conundrum
You find yourself in a coordinate system, at the origin, facing the +x direction (east). If you follow the following instructions, you'll find out how to leave.
- Move forward 1 unit. Mark your coordinates.
- Turn left 90 degrees. Mark your coordinates.
- Move right until your x coordinate is 2 digits. Mark your coordinates.
- Move forward 1 unit. Turn to the right 45 degrees. Mark your coordinates. Move left until your coordinates are the same.
- Move back a specific number of units, 3.5 in fact. Snap to the nearest integer coordinates. Mark your coordinates.
- Imagine, for a second, that you’re on a circle centered at the origin. Mark your coordinates. Having imagined the circle, move east until your x coordinate matches what it was at the end of step 3. Move east 3 more units.
- Move back until you hit the x axis. After that, mark your coordinates. Turn left 135 degrees.
- Move forward the index of the second step in which you moved east. Move right the same number of steps. Mark your coordinates. Turn right 1 degree.
- Until you reach the y axis, move forward. Snap to and mark the ceilings of your coordinates. Imagine, for another second, that you’re on a circle centered at the origin.
- Remember those circles you imagined? There are 2 points with nonnegative coordinates strictly between them. Move to my favorite one; you’ll figure it out. Mark your coordinates.
- What’s the index of the first step where you stopped facing east? Move back that many steps, then move west 1 step. Snap to the nearest integer coordinates and mark them.
- Move left until your coordinates are both integers again. You’re stumped? It’s impossible? Then turn right 3149 degrees. Repeat the first 4 sentences of this step 8 more times. Mark your coordinates.
- For playing around and spinning so wildly, you’re punished. Face (-1, -1). Go to (-1, -1). Go directly to (-1, -1). Do not cross (6, 0). Do not collect $200. Mark your coordinates. I hope you learned your lesson.
- Take the absolute value of and add 1 to each coordinate you marked so far, both the x’s and the y’s. Move back 3 units. Snap to the nearest integer coordinates. Mark your coordinates.
- Move back the index of this step. Nice self reference. Mark the floors of your coordinates. Snap to the nearest integer coordinates.
- It’s time for a walk! Face north. Move forward 7 units. Turn left 90 degrees. Move forward 1 unit. Repeat sentences 3-5 (inclusive) of this step. Turn right 90 degrees. Repeat sentences 3-6 (inclusive) of this step. Mark your coordinates. Add 1 to each coordinate you marked from the previous 2 steps.