Source: Treetop Tree House

Part 1

Given a grid of numbers, count how many of these numbers have a direct path in any cardinal direction to the edge of the grid.

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Source: Fractal Art

Part 1: Start with an input image made of . and # pixels. For n iterations, break the image into blocks:

• If the current size is even, break the image into 2x2 chunks and replace each with a 3x3 chunk
• If the current size is odd, break the image into 3x3 chunks and replace each with a 4x4 chunk

The replacement rules will be specified in the following format (example is a 3x3 -> 4x4 rule):

.#./..#/### => #..#/..../..../#..#  

In that example, replace this:

.#.
..#
###

With this:

#..#
....
....
#..#

Any rotation or reflection of a chunk can be used to match the input of a replacement rule.

After n = 18 iterations, how many # pixels are there?

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Source: Particle Swarm

Part 1: Given the initial position, velocity, and acceleration of a large number of particles, which particle will stay the closet to the origin as the simulation runs to infinity?

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Source: Duet

Part 1: Create a virtual machine with the following instruction set:

• snd X plays a sound with a frequency equal to the value of X
• set X Y sets register X to Y
• add X Y set register X to X + Y
• mul X Y sets register X to X * Y
• mod X Y sets register X to X mod Y
• rcv X recovers the frequency of the last sound played, if X is not zero
• jgz X Y jumps with an offset of the value of Y, iff X is greater than zero

In most cases, X and Y can be either an integer value or a register.

What is the value recovered by rcv the first time X is non-zero?

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Source: Disk Defragmentation

Part 1: Create a 128x128 grid. Generate each row by taking the knot hash of salt-{index}. The bits of the hash represent if a tile in the grid is free (0) or used (1).

Given your salt as input, how many squares are used?

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Source: Digital Plumber

Part 1: A network of nodes is defined by a list of lines formatted as such:

2 <-> 0, 3, 4

> In this case, node `2` is connected to `0`, `3`, and `4` and vice versa.

> How many nodes are in the group that contains the node `0`?





First, load the data into an [[wiki:adjacency map]]():

```python
nodes = set()
neighbors = collections.defaultdict(set)

for line in lib.input():
    source, destinations = line.split('<->')
    source = int(source.strip())
    nodes.add(source)

    for destination in destinations.strip().split(','):
        destination = int(destination.strip())
        nodes.add(destination)

        neighbors[source].add(destination)
        neighbors[destination].add(source)

Then, write a function that can take a node and recursively expand until it finds all nodes in the same group:

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I’m a bit behind the times, but this post from Programming Praxis intrigued me enough that I kept it in my todo list for rather a while. So let’s get around to it.

I’ll just copy the description straight from the Programming Praxis website (although there are at least two previous version:[1][2]):

There is a monkey which can walk around on a planar grid. The monkey can move one space at a time left, right, up or down. That is, from (x, y) the monkey can go to (x+1, y), (x-1, y), (x, y+1), and (x, y-1). Points where the sum of the digits of the absolute value of the x coordinate plus the sum of the digits of the absolute value of the y coordinate are lesser than or equal to 19 are accessible to the monkey. For example, the point (59, 79) is inaccessible because 5 + 9 + 7 + 9 = 30, which is greater than 19. Another example: the point (-5, -7) is accessible because abs(-5) + abs(-7) = 5 + 7 = 12, which is less than 19. How many points can the monkey access if it starts at (0, 0), including (0, 0) itself?

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