# λy.2016

## --- Day 13: A Maze of Twisty Little Cubicles ---

You arrive at the first floor of this new building to discover a much less welcoming environment than the shiny atrium of the last one. Instead, you are in a maze of twisty little cubicles, all alike.

Every location in this area is addressed by a pair of non-negative integers (`x,y`). Each such coordinate is either a wall or an open space. You can't move diagonally. The cube maze starts at `0,0` and seems to extend infinitely toward positive `x` and `y`; negative values are invalid, as they represent a location outside the building. You are in a small waiting area at `1,1`.

While it seems chaotic, a nearby morale-boosting poster explains, the layout is actually quite logical. You can determine whether a given `x,y` coordinate will be a wall or an open space using a simple system:

• Find `x*x + 3*x + 2*x*y + y + y*y`.
• Find the binary representation of that sum; count the number of bits that are `1`.
• If the number of bits that are `1` is even, it's an open space.
• If the number of bits that are `1` is odd, it's a wall.

For example, if the office designer's favorite number were `10`, drawing walls as `#` and open spaces as `.`, the corner of the building containing `0,0` would look like this:

``````  0123456789
0 .#.####.##
1 ..#..#...#
2 #....##...
3 ###.#.###.
4 .##..#..#.
5 ..##....#.
6 #...##.###
``````

Now, suppose you wanted to reach `7,4`. The shortest route you could take is marked as `O`:

``````  0123456789
0 .#.####.##
1 .O#..#...#
2 #OOO.##...
3 ###O#.###.
4 .##OO#OO#.
5 ..##OOO.#.
6 #...##.###
``````

Thus, reaching `7,4` would take a minimum of `11` steps (starting from your current location, `1,1`).

What is the fewest number of steps required for you to reach `31,39`?

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