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<html lang="en-us">
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<meta charset="utf-8" />
<title>Advent of Code 2022</title>
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<h1 class="title-global"><a href="https://adventofcode.com/2022" target="_blank">Advent of Code</a></h1>
<div class="user">John Dugan <span class="star-count">(AoC++) 50*</span></div>
</div>
<div>
<h1 class="title-event"> <span class="title-event-wrap">{year=></span><a href="https://adventofcode.com/2022" target="_blank">2022</a><span class="title-event-wrap">}</span></h1>
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<article class="day-desc">
<h2>--- Day 20: Grove Positioning System ---</h2>
<p>It's finally time to meet back up with the Elves. When you try to contact them, however, you get no reply. Perhaps you're out of range?</p>
<p>You know they're headed to the grove where the <em class="star">star</em> fruit grows, so if you can figure out where that is, you should be able to meet back up with them.</p>
<p>Fortunately, your handheld device has a file (your puzzle input) that contains the grove's coordinates! Unfortunately, the file is <em>encrypted</em> - just in case the device were to fall into the wrong hands.</p>
<p>Maybe you can <span title="You once again make a mental note to remind the Elves later not to invent their own cryptographic functions.">decrypt</span> it?</p>
<p>When you were still back at the camp, you overheard some Elves talking about coordinate file encryption. The main operation involved in decrypting the file is called <em>mixing</em>.</p>
<p>The encrypted file is a list of numbers. To <em>mix</em> the file, move each number forward or backward in the file a number of positions equal to the value of the number being moved. The list is <em>circular</em>, so moving a number off one
end of the list wraps back around to the other end as if the ends were connected.</p>
<p>For example, to move the <code>1</code> in a sequence like <code>4, 5, 6, <em>1</em>, 7, 8, 9</code>, the <code>1</code> moves one position forward: <code>4, 5, 6, 7, <em>1</em>, 8, 9</code>. To move the <code>-2</code> in a sequence like
<code>4, <em>-2</em>, 5, 6, 7, 8, 9</code>, the <code>-2</code> moves two positions backward, wrapping around: <code>4, 5, 6, 7, 8, <em>-2</em>, 9</code>.</p>
<p>The numbers should be moved <em>in the order they originally appear</em> in the encrypted file. Numbers moving around during the mixing process do not change the order in which the numbers are moved.</p>
<p>Consider this encrypted file:</p>
<pre><code>1
2
-3
3
-2
0
4
</code></pre>
<p>Mixing this file proceeds as follows:</p>
<pre><code>Initial arrangement:
1, 2, -3, 3, -2, 0, 4
1 moves between 2 and -3:
2, 1, -3, 3, -2, 0, 4
2 moves between -3 and 3:
1, -3, 2, 3, -2, 0, 4
-3 moves between -2 and 0:
1, 2, 3, -2, -3, 0, 4
3 moves between 0 and 4:
1, 2, -2, -3, 0, 3, 4
-2 moves between 4 and 1:
1, 2, -3, 0, 3, 4, -2
0 does not move:
1, 2, -3, 0, 3, 4, -2
4 moves between -3 and 0:
1, 2, -3, 4, 0, 3, -2
</code></pre>
<p>Then, the grove coordinates can be found by looking at the 1000th, 2000th, and 3000th numbers after the value <code>0</code>, wrapping around the list as necessary. In the above example, the 1000th number after <code>0</code> is
<code><em>4</em></code>, the 2000th is <code><em>-3</em></code>, and the 3000th is <code><em>2</em></code>; adding these together produces <code><em>3</em></code>.</p>
<p>Mix your encrypted file exactly once. <em>What is the sum of the three numbers that form the grove coordinates?</em></p>
</article>
<p>Your puzzle answer was <code>872</code>.</p>
<article class="day-desc">
<h2 id="part2">--- Part Two ---</h2>
<p>The grove coordinate values seem nonsensical. While you ponder the mysteries of Elf encryption, you suddenly remember the rest of the decryption routine you overheard back at camp.</p>
<p>First, you need to apply the <em>decryption key</em>, <code>811589153</code>. Multiply each number by the decryption key before you begin; this will produce the actual list of numbers to mix.</p>
<p>Second, you need to mix the list of numbers <em>ten times</em>. The order in which the numbers are mixed does not change during mixing; the numbers are still moved in the order they appeared in the original, pre-mixed list. (So, if -3
appears fourth in the original list of numbers to mix, -3 will be the fourth number to move during each round of mixing.)</p>
<p>Using the same example as above:</p>
<pre><code>Initial arrangement:
811589153, 1623178306, -2434767459, 2434767459, -1623178306, 0, 3246356612
After 1 round of mixing:
0, -2434767459, 3246356612, -1623178306, 2434767459, 1623178306, 811589153
After 2 rounds of mixing:
0, 2434767459, 1623178306, 3246356612, -2434767459, -1623178306, 811589153
After 3 rounds of mixing:
0, 811589153, 2434767459, 3246356612, 1623178306, -1623178306, -2434767459
After 4 rounds of mixing:
0, 1623178306, -2434767459, 811589153, 2434767459, 3246356612, -1623178306
After 5 rounds of mixing:
0, 811589153, -1623178306, 1623178306, -2434767459, 3246356612, 2434767459
After 6 rounds of mixing:
0, 811589153, -1623178306, 3246356612, -2434767459, 1623178306, 2434767459
After 7 rounds of mixing:
0, -2434767459, 2434767459, 1623178306, -1623178306, 811589153, 3246356612
After 8 rounds of mixing:
0, 1623178306, 3246356612, 811589153, -2434767459, 2434767459, -1623178306
After 9 rounds of mixing:
0, 811589153, 1623178306, -2434767459, 3246356612, 2434767459, -1623178306
After 10 rounds of mixing:
0, -2434767459, 1623178306, 3246356612, -1623178306, 2434767459, 811589153
</code></pre>
<p>The grove coordinates can still be found in the same way. Here, the 1000th number after <code>0</code> is <code><em>811589153</em></code>, the 2000th is <code><em>2434767459</em></code>, and the 3000th is <code><em>-1623178306</em></code>;
adding these together produces <code><em>1623178306</em></code>.</p>
<p>Apply the decryption key and mix your encrypted file ten times. <em>What is the sum of the three numbers that form the grove coordinates?</em></p>
</article>
<p>Your puzzle answer was <code>5382459262696</code>.</p>
<p class="day-success">Both parts of this puzzle are complete! They provide two gold stars: **</p>
<p>At this point, all that is left is for you to <a href="index.html">admire your Advent calendar</a>.</p>
<p>If you still want to see it, you can <a href="../data/day20/input.txt" target="_blank">get your puzzle input</a>.</p>
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