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  16 Oh, hello!  Funny seeing you here.
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  18 I appreciate your enthusiasm, but you aren't going to find much down here.
  19 There certainly aren't clues to any of the puzzles.  The best surprises don't
  20 even appear in the source until you unlock them for real.
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  22 Please be careful with automated requests; I'm not a massive company, and I can
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  25 If you're curious about how Advent of Code works, it's running on some custom
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  28 of the puzzles.
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  30 The puzzles are most of the work; preparing a new calendar and a new set of
  31 puzzles each year takes all of my free time for 4-5 months. A lot of effort
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  35 If you'd like to hang out, I'm @ericwastl on Twitter.
  36
  37 - Eric Wastl
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  90 <header><div><h1 class="title-global"><a href="/">Advent of Code</a></h1><nav><ul><li><a href="/2021/about">[About]</a></li><li><a href="/2021/events">[Events]</a></li><li><a href="https://teespring.com/stores/advent-of-code" target="_blank">[Shop]</a></li><li><a href="/2021/settings">[Settings]</a></li><li><a href="/2021/auth/logout">[Log Out]</a></li></ul></nav><div class="user">Neil Smith <a href="/2021/support" class="supporter-badge" title="Advent of Code Supporter">(AoC++)</a> <span class="star-count">24*</span></div></div><div><h1 class="title-event">&nbsp;&nbsp;<span class="title-event-wrap">0.0.0.0:</span><a href="/2021">2021</a><span class="title-event-wrap"></span></h1><nav><ul><li><a href="/2021">[Calendar]</a></li><li><a href="/2021/support">[AoC++]</a></li><li><a href="/2021/sponsors">[Sponsors]</a></li><li><a href="/2021/leaderboard">[Leaderboard]</a></li><li><a href="/2021/stats">[Stats]</a></li></ul></nav></div></header>
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  98 <article class="day-desc"><h2>--- Day 12: Passage Pathing ---</h2><p>With your <span title="Sublime.">submarine's subterranean subsystems subsisting suboptimally</span>, the only way you're getting out of this cave anytime soon is by finding a path yourself. Not just <em>a</em> path - the only way to know if you've found the <em>best</em> path is to find <em>all</em> of them.</p>
  99 <p>Fortunately, the sensors are still mostly working, and so you build a rough map of the remaining caves (your puzzle input). For example:</p>
 100 <pre><code>start-A
 101 start-b
 102 A-c
 103 A-b
 104 b-d
 105 A-end
 106 b-end
 107 </code></pre>
 108 <p>This is a list of how all of the caves are connected. You start in the cave named <code>start</code>, and your destination is the cave named <code>end</code>. An entry like <code>b-d</code> means that cave <code>b</code> is connected to cave <code>d</code> - that is, you can move between them.</p>
 109 <p>So, the above cave system looks roughly like this:</p>
 110 <pre><code>    start
 111     /   \
 112 c--A-----b--d
 113     \   /
 114      end
 115 </code></pre>
 116 <p>Your goal is to find the number of distinct <em>paths</em> that start at <code>start</code>, end at <code>end</code>, and don't visit small caves more than once. There are two types of caves: <em>big</em> caves (written in uppercase, like <code>A</code>) and <em>small</em> caves (written in lowercase, like <code>b</code>). It would be a waste of time to visit any small cave more than once, but big caves are large enough that it might be worth visiting them multiple times. So, all paths you find should <em>visit small caves at most once</em>, and can <em>visit big caves any number of times</em>.</p>
 117 <p>Given these rules, there are <code><em>10</em></code> paths through this example cave system:</p>
 118 <pre><code>start,A,b,A,c,A,end
 119 start,A,b,A,end
 120 start,A,b,end
 121 start,A,c,A,b,A,end
 122 start,A,c,A,b,end
 123 start,A,c,A,end
 124 start,A,end
 125 start,b,A,c,A,end
 126 start,b,A,end
 127 start,b,end
 128 </code></pre>
 129 <p>(Each line in the above list corresponds to a single path; the caves visited by that path are listed in the order they are visited and separated by commas.)</p>
 130 <p>Note that in this cave system, cave <code>d</code> is never visited by any path: to do so, cave <code>b</code> would need to be visited twice (once on the way to cave <code>d</code> and a second time when returning from cave <code>d</code>), and since cave <code>b</code> is small, this is not allowed.</p>
 131 <p>Here is a slightly larger example:</p>
 132 <pre><code>dc-end
 133 HN-start
 134 start-kj
 135 dc-start
 136 dc-HN
 137 LN-dc
 138 HN-end
 139 kj-sa
 140 kj-HN
 141 kj-dc
 142 </code></pre>
 143 <p>The <code>19</code> paths through it are as follows:</p>
 144 <pre><code>start,HN,dc,HN,end
 145 start,HN,dc,HN,kj,HN,end
 146 start,HN,dc,end
 147 start,HN,dc,kj,HN,end
 148 start,HN,end
 149 start,HN,kj,HN,dc,HN,end
 150 start,HN,kj,HN,dc,end
 151 start,HN,kj,HN,end
 152 start,HN,kj,dc,HN,end
 153 start,HN,kj,dc,end
 154 start,dc,HN,end
 155 start,dc,HN,kj,HN,end
 156 start,dc,end
 157 start,dc,kj,HN,end
 158 start,kj,HN,dc,HN,end
 159 start,kj,HN,dc,end
 160 start,kj,HN,end
 161 start,kj,dc,HN,end
 162 start,kj,dc,end
 163 </code></pre>
 164 <p>Finally, this even larger example has <code>226</code> paths through it:</p>
 165 <pre><code>fs-end
 166 he-DX
 167 fs-he
 168 start-DX
 169 pj-DX
 170 end-zg
 171 zg-sl
 172 zg-pj
 173 pj-he
 174 RW-he
 175 fs-DX
 176 pj-RW
 177 zg-RW
 178 start-pj
 179 he-WI
 180 zg-he
 181 pj-fs
 182 start-RW
 183 </code></pre>
 184 <p><em>How many paths through this cave system are there that visit small caves at most once?</em></p>
 185 </article>
 186 <p>Your puzzle answer was <code>4495</code>.</p><article class="day-desc"><h2 id="part2">--- Part Two ---</h2><p>After reviewing the available paths, you realize you might have time to visit a single small cave <em>twice</em>. Specifically, big caves can be visited any number of times, a single small cave can be visited at most twice, and the remaining small caves can be visited at most once. However, the caves named <code>start</code> and <code>end</code> can only be visited <em>exactly once each</em>: once you leave the <code>start</code> cave, you may not return to it, and once you reach the <code>end</code> cave, the path must end immediately.</p>
 187 <p>Now, the <code>36</code> possible paths through the first example above are:</p>
 188 <pre><code>start,A,b,A,b,A,c,A,end
 189 start,A,b,A,b,A,end
 190 start,A,b,A,b,end
 191 start,A,b,A,c,A,b,A,end
 192 start,A,b,A,c,A,b,end
 193 start,A,b,A,c,A,c,A,end
 194 start,A,b,A,c,A,end
 195 start,A,b,A,end
 196 start,A,b,d,b,A,c,A,end
 197 start,A,b,d,b,A,end
 198 start,A,b,d,b,end
 199 start,A,b,end
 200 start,A,c,A,b,A,b,A,end
 201 start,A,c,A,b,A,b,end
 202 start,A,c,A,b,A,c,A,end
 203 start,A,c,A,b,A,end
 204 start,A,c,A,b,d,b,A,end
 205 start,A,c,A,b,d,b,end
 206 start,A,c,A,b,end
 207 start,A,c,A,c,A,b,A,end
 208 start,A,c,A,c,A,b,end
 209 start,A,c,A,c,A,end
 210 start,A,c,A,end
 211 start,A,end
 212 start,b,A,b,A,c,A,end
 213 start,b,A,b,A,end
 214 start,b,A,b,end
 215 start,b,A,c,A,b,A,end
 216 start,b,A,c,A,b,end
 217 start,b,A,c,A,c,A,end
 218 start,b,A,c,A,end
 219 start,b,A,end
 220 start,b,d,b,A,c,A,end
 221 start,b,d,b,A,end
 222 start,b,d,b,end
 223 start,b,end
 224 </code></pre>
 225 <p>The slightly larger example above now has <code>103</code> paths through it, and the even larger example now has <code>3509</code> paths through it.</p>
 226 <p>Given these new rules, <em>how many paths through this cave system are there?</em></p>
 227 </article>
 228 <p>Your puzzle answer was <code>131254</code>.</p><p class="day-success">Both parts of this puzzle are complete! They provide two gold stars: **</p>
 229 <p>At this point, you should <a href="/2021">return to your Advent calendar</a> and try another puzzle.</p>
 230 <p>If you still want to see it, you can <a href="12/input" target="_blank">get your puzzle input</a>.</p>
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