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:

#..# …. …. #..#

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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: A Series of Tubes

Part 1: Take a network diagram of the following form:

|          
|  +--+    
A  |  C    

F—|–|-E—+ | | | D +B-+ +–+

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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: Spinlock¹

Part 1: Start with a circular buffer containing [0] and current_position = 0. For n from 1 up to 2017:

1. Step forward steps (puzzle input)
2. Input the next value for n, set current_position to n, increment n
3. Repeat

What is the value after 2017?

It’s a bit weird to describe, but the given example helps (assume steps = 3):

(0)
0 (1)
0 (2) 1
0  2 (3) 1
0  2 (4) 3  1
0 (5) 2  4  3  1
0  5  2  4  3 (6) 1
0  5 (7) 2  4  3  6  1
0  5  7  2  4  3 (8) 6  1
0 (9) 5  7  2  4  3  8  6  1

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Source: Permutation Promenade

Part 1: Running on the string a...p apply a series of the following commands:

• sX rotates the string right by X positions
• xX/Y swaps positions X and Y
• pA/B swaps the letters A and B no matter their positions

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Source: Dueling Generators

Part 1: Create a pair of generators A and B where:

• A_n = 16807 A_{n-1} \mod 2147483647
• B_n = 48271 B_{n-1} \mod 2147483647

How many of the first 40 million values have matching values for the low 16 bits of each generator?

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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: Packet Scanners

Part 1: Multiple layers are defined with rules of the form:

• {index}: {depth}

Each layer will start at position 0, then once per tick will advance towards depth. Once it hits depth-1, it will return to position 0, taking 2*depth-1 per full cycle.

Calculate the sum of index * depth for any scanners that are at position 0 when you pass through them given an initial starting time.

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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

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