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  34 Oh, hello!  Funny seeing you here.
  35
  36 I appreciate your enthusiasm, but you aren't going to find much down here.
  37 There certainly aren't clues to any of the puzzles.  The best surprises don=
  38 't
  39 even appear in the source until you unlock them for real.
  40
  41 Please be careful with automated requests; I'm not a massive company, and I=
  42  can
  43 only take so much traffic.  Please be considerate so that everyone gets to =
  44 play.
  45
  46 If you're curious about how Advent of Code works, it's running on some cust=
  47 om
  48 Perl code. Other than a few integrations (auth, analytics, ads, social medi=
  49 a),
  50 I built the whole thing myself, including the design, animations, prose, an=
  51 d
  52 all of the puzzles.
  53
  54 The puzzles are most of the work; preparing a new calendar and a new set of
  55 puzzles each year takes all of my free time for 4-5 months. A lot of effort
  56 went into building this thing - I hope you're enjoying playing it as much a=
  57 s I
  58 enjoyed making it for you!
  59
  60 If you'd like to hang out, I'm @ericwastl on Twitter.
  61
  62 - Eric Wastl
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 148 <main>
 149
 150 <article class=3D"day-desc"><h2>--- Day 12: The N-Body Problem ---</h2><p>T=
 151 he space near Jupiter is not a very safe place; you need to be careful of a=
 152  <a href=3D"https://en.wikipedia.org/wiki/Great_Red_Spot" rel=3D"noreferrer=
 153 " data-ss1576248183=3D"1">big distracting red spot</a>, extreme <a href=3D"=
 154 https://en.wikipedia.org/wiki/Magnetosphere_of_Jupiter" rel=3D"noreferrer" =
 155 data-ss1576248183=3D"1">radiation</a>, and a <a href=3D"https://en.wikipedi=
 156 a.org/wiki/Moons_of_Jupiter#List" rel=3D"noreferrer" data-ss1576248183=3D"1=
 157 ">whole lot of moons</a> swirling around.  You decide to start by tracking =
 158 the four largest moons: <em>Io</em>, <em>Europa</em>, <em>Ganymede</em>, an=
 159 d <em>Callisto</em>.</p>
 160 <p>After a brief scan, you calculate the <em>position of each moon</em> (yo=
 161 ur puzzle input). You just need to <em>simulate their motion</em> so you ca=
 162 n <span title=3D"Or you could just leave, but where's the fun in that?">avo=
 163 id them</span>.</p>
 164 <p>Each moon has a 3-dimensional position (<code>x</code>, <code>y</code>, =
 165 and <code>z</code>) and a 3-dimensional velocity.  The position of each moo=
 166 n is given in your scan; the <code>x</code>, <code>y</code>, and <code>z</c=
 167 ode> velocity of each moon starts at <code>0</code>.</p>
 168 <p>Simulate the motion of the moons in <em>time steps</em>. Within each tim=
 169 e step, first update the velocity of every moon by applying <em>gravity</em=
 170 >. Then, once all moons' velocities have been updated, update the position =
 171 of every moon by applying <em>velocity</em>. Time progresses by one step on=
 172 ce all of the positions are updated.</p>
 173 <p>To apply <em>gravity</em>, consider every <em>pair</em> of moons. On eac=
 174 h axis (<code>x</code>, <code>y</code>, and <code>z</code>), the velocity o=
 175 f each moon changes by <em>exactly +1 or -1</em> to pull the moons together=
 176 .  For example, if Ganymede has an <code>x</code> position of <code>3</code=
 177 >, and Callisto has a <code>x</code> position of <code>5</code>, then Ganym=
 178 ede's <code>x</code> velocity <em>changes by +1</em> (because <code>5 &gt; =
 179 3</code>) and Callisto's <code>x</code> velocity <em>changes by -1</em> (be=
 180 cause <code>3 &lt; 5</code>). However, if the positions on a given axis are=
 181  the same, the velocity on that axis <em>does not change</em> for that pair=
 182  of moons.</p>
 183 <p>Once all gravity has been applied, apply <em>velocity</em>: simply add t=
 184 he velocity of each moon to its own position. For example, if Europa has a =
 185 position of <code>x=3D1, y=3D2, z=3D3</code> and a velocity of <code>x=3D-2=
 186 , y=3D0,z=3D3</code>, then its new position would be <code>x=3D-1, y=3D2, z=
 187 =3D6</code>. This process does not modify the velocity of any moon.</p>
 188 <p>For example, suppose your scan reveals the following positions:</p>
 189 <pre><code>&lt;x=3D-1, y=3D0, z=3D2&gt;
 190 &lt;x=3D2, y=3D-10, z=3D-7&gt;
 191 &lt;x=3D4, y=3D-8, z=3D8&gt;
 192 &lt;x=3D3, y=3D5, z=3D-1&gt;
 193 </code></pre>
 194 <p>Simulating the motion of these moons would produce the following:</p>
 195 <pre><code>After 0 steps:
 196 pos=3D&lt;x=3D-1, y=3D  0, z=3D 2&gt;, vel=3D&lt;x=3D 0, y=3D 0, z=3D 0&gt;
 197 pos=3D&lt;x=3D 2, y=3D-10, z=3D-7&gt;, vel=3D&lt;x=3D 0, y=3D 0, z=3D 0&gt;
 198 pos=3D&lt;x=3D 4, y=3D -8, z=3D 8&gt;, vel=3D&lt;x=3D 0, y=3D 0, z=3D 0&gt;
 199 pos=3D&lt;x=3D 3, y=3D  5, z=3D-1&gt;, vel=3D&lt;x=3D 0, y=3D 0, z=3D 0&gt;
 200
 201 After 1 step:
 202 pos=3D&lt;x=3D 2, y=3D-1, z=3D 1&gt;, vel=3D&lt;x=3D 3, y=3D-1, z=3D-1&gt;
 203 pos=3D&lt;x=3D 3, y=3D-7, z=3D-4&gt;, vel=3D&lt;x=3D 1, y=3D 3, z=3D 3&gt;
 204 pos=3D&lt;x=3D 1, y=3D-7, z=3D 5&gt;, vel=3D&lt;x=3D-3, y=3D 1, z=3D-3&gt;
 205 pos=3D&lt;x=3D 2, y=3D 2, z=3D 0&gt;, vel=3D&lt;x=3D-1, y=3D-3, z=3D 1&gt;
 206
 207 After 2 steps:
 208 pos=3D&lt;x=3D 5, y=3D-3, z=3D-1&gt;, vel=3D&lt;x=3D 3, y=3D-2, z=3D-2&gt;
 209 pos=3D&lt;x=3D 1, y=3D-2, z=3D 2&gt;, vel=3D&lt;x=3D-2, y=3D 5, z=3D 6&gt;
 210 pos=3D&lt;x=3D 1, y=3D-4, z=3D-1&gt;, vel=3D&lt;x=3D 0, y=3D 3, z=3D-6&gt;
 211 pos=3D&lt;x=3D 1, y=3D-4, z=3D 2&gt;, vel=3D&lt;x=3D-1, y=3D-6, z=3D 2&gt;
 212
 213 After 3 steps:
 214 pos=3D&lt;x=3D 5, y=3D-6, z=3D-1&gt;, vel=3D&lt;x=3D 0, y=3D-3, z=3D 0&gt;
 215 pos=3D&lt;x=3D 0, y=3D 0, z=3D 6&gt;, vel=3D&lt;x=3D-1, y=3D 2, z=3D 4&gt;
 216 pos=3D&lt;x=3D 2, y=3D 1, z=3D-5&gt;, vel=3D&lt;x=3D 1, y=3D 5, z=3D-4&gt;
 217 pos=3D&lt;x=3D 1, y=3D-8, z=3D 2&gt;, vel=3D&lt;x=3D 0, y=3D-4, z=3D 0&gt;
 218
 219 After 4 steps:
 220 pos=3D&lt;x=3D 2, y=3D-8, z=3D 0&gt;, vel=3D&lt;x=3D-3, y=3D-2, z=3D 1&gt;
 221 pos=3D&lt;x=3D 2, y=3D 1, z=3D 7&gt;, vel=3D&lt;x=3D 2, y=3D 1, z=3D 1&gt;
 222 pos=3D&lt;x=3D 2, y=3D 3, z=3D-6&gt;, vel=3D&lt;x=3D 0, y=3D 2, z=3D-1&gt;
 223 pos=3D&lt;x=3D 2, y=3D-9, z=3D 1&gt;, vel=3D&lt;x=3D 1, y=3D-1, z=3D-1&gt;
 224
 225 After 5 steps:
 226 pos=3D&lt;x=3D-1, y=3D-9, z=3D 2&gt;, vel=3D&lt;x=3D-3, y=3D-1, z=3D 2&gt;
 227 pos=3D&lt;x=3D 4, y=3D 1, z=3D 5&gt;, vel=3D&lt;x=3D 2, y=3D 0, z=3D-2&gt;
 228 pos=3D&lt;x=3D 2, y=3D 2, z=3D-4&gt;, vel=3D&lt;x=3D 0, y=3D-1, z=3D 2&gt;
 229 pos=3D&lt;x=3D 3, y=3D-7, z=3D-1&gt;, vel=3D&lt;x=3D 1, y=3D 2, z=3D-2&gt;
 230
 231 After 6 steps:
 232 pos=3D&lt;x=3D-1, y=3D-7, z=3D 3&gt;, vel=3D&lt;x=3D 0, y=3D 2, z=3D 1&gt;
 233 pos=3D&lt;x=3D 3, y=3D 0, z=3D 0&gt;, vel=3D&lt;x=3D-1, y=3D-1, z=3D-5&gt;
 234 pos=3D&lt;x=3D 3, y=3D-2, z=3D 1&gt;, vel=3D&lt;x=3D 1, y=3D-4, z=3D 5&gt;
 235 pos=3D&lt;x=3D 3, y=3D-4, z=3D-2&gt;, vel=3D&lt;x=3D 0, y=3D 3, z=3D-1&gt;
 236
 237 After 7 steps:
 238 pos=3D&lt;x=3D 2, y=3D-2, z=3D 1&gt;, vel=3D&lt;x=3D 3, y=3D 5, z=3D-2&gt;
 239 pos=3D&lt;x=3D 1, y=3D-4, z=3D-4&gt;, vel=3D&lt;x=3D-2, y=3D-4, z=3D-4&gt;
 240 pos=3D&lt;x=3D 3, y=3D-7, z=3D 5&gt;, vel=3D&lt;x=3D 0, y=3D-5, z=3D 4&gt;
 241 pos=3D&lt;x=3D 2, y=3D 0, z=3D 0&gt;, vel=3D&lt;x=3D-1, y=3D 4, z=3D 2&gt;
 242
 243 After 8 steps:
 244 pos=3D&lt;x=3D 5, y=3D 2, z=3D-2&gt;, vel=3D&lt;x=3D 3, y=3D 4, z=3D-3&gt;
 245 pos=3D&lt;x=3D 2, y=3D-7, z=3D-5&gt;, vel=3D&lt;x=3D 1, y=3D-3, z=3D-1&gt;
 246 pos=3D&lt;x=3D 0, y=3D-9, z=3D 6&gt;, vel=3D&lt;x=3D-3, y=3D-2, z=3D 1&gt;
 247 pos=3D&lt;x=3D 1, y=3D 1, z=3D 3&gt;, vel=3D&lt;x=3D-1, y=3D 1, z=3D 3&gt;
 248
 249 After 9 steps:
 250 pos=3D&lt;x=3D 5, y=3D 3, z=3D-4&gt;, vel=3D&lt;x=3D 0, y=3D 1, z=3D-2&gt;
 251 pos=3D&lt;x=3D 2, y=3D-9, z=3D-3&gt;, vel=3D&lt;x=3D 0, y=3D-2, z=3D 2&gt;
 252 pos=3D&lt;x=3D 0, y=3D-8, z=3D 4&gt;, vel=3D&lt;x=3D 0, y=3D 1, z=3D-2&gt;
 253 pos=3D&lt;x=3D 1, y=3D 1, z=3D 5&gt;, vel=3D&lt;x=3D 0, y=3D 0, z=3D 2&gt;
 254
 255 After 10 steps:
 256 pos=3D&lt;x=3D 2, y=3D 1, z=3D-3&gt;, vel=3D&lt;x=3D-3, y=3D-2, z=3D 1&gt;
 257 pos=3D&lt;x=3D 1, y=3D-8, z=3D 0&gt;, vel=3D&lt;x=3D-1, y=3D 1, z=3D 3&gt;
 258 pos=3D&lt;x=3D 3, y=3D-6, z=3D 1&gt;, vel=3D&lt;x=3D 3, y=3D 2, z=3D-3&gt;
 259 pos=3D&lt;x=3D 2, y=3D 0, z=3D 4&gt;, vel=3D&lt;x=3D 1, y=3D-1, z=3D-1&gt;
 260 </code></pre>
 261 <p>Then, it might help to calculate the <em>total energy in the system</em>=
 262 . The total energy for a single moon is its <em>potential energy</em> multi=
 263 plied by its <em>kinetic energy</em>. A moon's <em>potential energy</em> is=
 264  the sum of the <a href=3D"https://en.wikipedia.org/wiki/Absolute_value" re=
 265 l=3D"noreferrer" data-ss1576248183=3D"1">absolute values</a> of its <code>x=
 266 </code>, <code>y</code>, and <code>z</code> position coordinates. A moon's =
 267 <em>kinetic energy</em> is the sum of the absolute values of its velocity c=
 268 oordinates.  Below, each line shows the calculations for a moon's potential=
 269  energy (<code>pot</code>), kinetic energy (<code>kin</code>), and total en=
 270 ergy:</p>
 271 <pre><code>Energy after 10 steps:
 272 pot: 2 + 1 + 3 =3D  6;   kin: 3 + 2 + 1 =3D 6;   total:  6 * 6 =3D 36
 273 pot: 1 + 8 + 0 =3D  9;   kin: 1 + 1 + 3 =3D 5;   total:  9 * 5 =3D 45
 274 pot: 3 + 6 + 1 =3D 10;   kin: 3 + 2 + 3 =3D 8;   total: 10 * 8 =3D 80
 275 pot: 2 + 0 + 4 =3D  6;   kin: 1 + 1 + 1 =3D 3;   total:  6 * 3 =3D 18
 276 Sum of total energy: 36 + 45 + 80 + 18 =3D <em>179</em>
 277 </code></pre>
 278 <p>In the above example, adding together the total energy for all moons aft=
 279 er 10 steps produces the total energy in the system, <code><em>179</em></co=
 280 de>.</p>
 281 <p>Here's a second example:</p>
 282 <pre><code>&lt;x=3D-8, y=3D-10, z=3D0&gt;
 283 &lt;x=3D5, y=3D5, z=3D10&gt;
 284 &lt;x=3D2, y=3D-7, z=3D3&gt;
 285 &lt;x=3D9, y=3D-8, z=3D-3&gt;
 286 </code></pre>
 287 <p>Every ten steps of simulation for 100 steps produces:</p>
 288 <pre><code>After 0 steps:
 289 pos=3D&lt;x=3D -8, y=3D-10, z=3D  0&gt;, vel=3D&lt;x=3D  0, y=3D  0, z=3D  =
 290 0&gt;
 291 pos=3D&lt;x=3D  5, y=3D  5, z=3D 10&gt;, vel=3D&lt;x=3D  0, y=3D  0, z=3D  =
 292 0&gt;
 293 pos=3D&lt;x=3D  2, y=3D -7, z=3D  3&gt;, vel=3D&lt;x=3D  0, y=3D  0, z=3D  =
 294 0&gt;
 295 pos=3D&lt;x=3D  9, y=3D -8, z=3D -3&gt;, vel=3D&lt;x=3D  0, y=3D  0, z=3D  =
 296 0&gt;
 297
 298 After 10 steps:
 299 pos=3D&lt;x=3D -9, y=3D-10, z=3D  1&gt;, vel=3D&lt;x=3D -2, y=3D -2, z=3D -=
 300 1&gt;
 301 pos=3D&lt;x=3D  4, y=3D 10, z=3D  9&gt;, vel=3D&lt;x=3D -3, y=3D  7, z=3D -=
 302 2&gt;
 303 pos=3D&lt;x=3D  8, y=3D-10, z=3D -3&gt;, vel=3D&lt;x=3D  5, y=3D -1, z=3D -=
 304 2&gt;
 305 pos=3D&lt;x=3D  5, y=3D-10, z=3D  3&gt;, vel=3D&lt;x=3D  0, y=3D -4, z=3D  =
 306 5&gt;
 307
 308 After 20 steps:
 309 pos=3D&lt;x=3D-10, y=3D  3, z=3D -4&gt;, vel=3D&lt;x=3D -5, y=3D  2, z=3D  =
 310 0&gt;
 311 pos=3D&lt;x=3D  5, y=3D-25, z=3D  6&gt;, vel=3D&lt;x=3D  1, y=3D  1, z=3D -=
 312 4&gt;
 313 pos=3D&lt;x=3D 13, y=3D  1, z=3D  1&gt;, vel=3D&lt;x=3D  5, y=3D -2, z=3D  =
 314 2&gt;
 315 pos=3D&lt;x=3D  0, y=3D  1, z=3D  7&gt;, vel=3D&lt;x=3D -1, y=3D -1, z=3D  =
 316 2&gt;
 317
 318 After 30 steps:
 319 pos=3D&lt;x=3D 15, y=3D -6, z=3D -9&gt;, vel=3D&lt;x=3D -5, y=3D  4, z=3D  =
 320 0&gt;
 321 pos=3D&lt;x=3D -4, y=3D-11, z=3D  3&gt;, vel=3D&lt;x=3D -3, y=3D-10, z=3D  =
 322 0&gt;
 323 pos=3D&lt;x=3D  0, y=3D -1, z=3D 11&gt;, vel=3D&lt;x=3D  7, y=3D  4, z=3D  =
 324 3&gt;
 325 pos=3D&lt;x=3D -3, y=3D -2, z=3D  5&gt;, vel=3D&lt;x=3D  1, y=3D  2, z=3D -=
 326 3&gt;
 327
 328 After 40 steps:
 329 pos=3D&lt;x=3D 14, y=3D-12, z=3D -4&gt;, vel=3D&lt;x=3D 11, y=3D  3, z=3D  =
 330 0&gt;
 331 pos=3D&lt;x=3D -1, y=3D 18, z=3D  8&gt;, vel=3D&lt;x=3D -5, y=3D  2, z=3D  =
 332 3&gt;
 333 pos=3D&lt;x=3D -5, y=3D-14, z=3D  8&gt;, vel=3D&lt;x=3D  1, y=3D -2, z=3D  =
 334 0&gt;
 335 pos=3D&lt;x=3D  0, y=3D-12, z=3D -2&gt;, vel=3D&lt;x=3D -7, y=3D -3, z=3D -=
 336 3&gt;
 337
 338 After 50 steps:
 339 pos=3D&lt;x=3D-23, y=3D  4, z=3D  1&gt;, vel=3D&lt;x=3D -7, y=3D -1, z=3D  =
 340 2&gt;
 341 pos=3D&lt;x=3D 20, y=3D-31, z=3D 13&gt;, vel=3D&lt;x=3D  5, y=3D  3, z=3D  =
 342 4&gt;
 343 pos=3D&lt;x=3D -4, y=3D  6, z=3D  1&gt;, vel=3D&lt;x=3D -1, y=3D  1, z=3D -=
 344 3&gt;
 345 pos=3D&lt;x=3D 15, y=3D  1, z=3D -5&gt;, vel=3D&lt;x=3D  3, y=3D -3, z=3D -=
 346 3&gt;
 347
 348 After 60 steps:
 349 pos=3D&lt;x=3D 36, y=3D-10, z=3D  6&gt;, vel=3D&lt;x=3D  5, y=3D  0, z=3D  =
 350 3&gt;
 351 pos=3D&lt;x=3D-18, y=3D 10, z=3D  9&gt;, vel=3D&lt;x=3D -3, y=3D -7, z=3D  =
 352 5&gt;
 353 pos=3D&lt;x=3D  8, y=3D-12, z=3D -3&gt;, vel=3D&lt;x=3D -2, y=3D  1, z=3D -=
 354 7&gt;
 355 pos=3D&lt;x=3D-18, y=3D -8, z=3D -2&gt;, vel=3D&lt;x=3D  0, y=3D  6, z=3D -=
 356 1&gt;
 357
 358 After 70 steps:
 359 pos=3D&lt;x=3D-33, y=3D -6, z=3D  5&gt;, vel=3D&lt;x=3D -5, y=3D -4, z=3D  =
 360 7&gt;
 361 pos=3D&lt;x=3D 13, y=3D -9, z=3D  2&gt;, vel=3D&lt;x=3D -2, y=3D 11, z=3D  =
 362 3&gt;
 363 pos=3D&lt;x=3D 11, y=3D -8, z=3D  2&gt;, vel=3D&lt;x=3D  8, y=3D -6, z=3D -=
 364 7&gt;
 365 pos=3D&lt;x=3D 17, y=3D  3, z=3D  1&gt;, vel=3D&lt;x=3D -1, y=3D -1, z=3D -=
 366 3&gt;
 367
 368 After 80 steps:
 369 pos=3D&lt;x=3D 30, y=3D -8, z=3D  3&gt;, vel=3D&lt;x=3D  3, y=3D  3, z=3D  =
 370 0&gt;
 371 pos=3D&lt;x=3D -2, y=3D -4, z=3D  0&gt;, vel=3D&lt;x=3D  4, y=3D-13, z=3D  =
 372 2&gt;
 373 pos=3D&lt;x=3D-18, y=3D -7, z=3D 15&gt;, vel=3D&lt;x=3D -8, y=3D  2, z=3D -=
 374 2&gt;
 375 pos=3D&lt;x=3D -2, y=3D -1, z=3D -8&gt;, vel=3D&lt;x=3D  1, y=3D  8, z=3D  =
 376 0&gt;
 377
 378 After 90 steps:
 379 pos=3D&lt;x=3D-25, y=3D -1, z=3D  4&gt;, vel=3D&lt;x=3D  1, y=3D -3, z=3D  =
 380 4&gt;
 381 pos=3D&lt;x=3D  2, y=3D -9, z=3D  0&gt;, vel=3D&lt;x=3D -3, y=3D 13, z=3D -=
 382 1&gt;
 383 pos=3D&lt;x=3D 32, y=3D -8, z=3D 14&gt;, vel=3D&lt;x=3D  5, y=3D -4, z=3D  =
 384 6&gt;
 385 pos=3D&lt;x=3D -1, y=3D -2, z=3D -8&gt;, vel=3D&lt;x=3D -3, y=3D -6, z=3D -=
 386 9&gt;
 387
 388 After 100 steps:
 389 pos=3D&lt;x=3D  8, y=3D-12, z=3D -9&gt;, vel=3D&lt;x=3D -7, y=3D  3, z=3D  =
 390 0&gt;
 391 pos=3D&lt;x=3D 13, y=3D 16, z=3D -3&gt;, vel=3D&lt;x=3D  3, y=3D-11, z=3D -=
 392 5&gt;
 393 pos=3D&lt;x=3D-29, y=3D-11, z=3D -1&gt;, vel=3D&lt;x=3D -3, y=3D  7, z=3D  =
 394 4&gt;
 395 pos=3D&lt;x=3D 16, y=3D-13, z=3D 23&gt;, vel=3D&lt;x=3D  7, y=3D  1, z=3D  =
 396 1&gt;
 397
 398 Energy after 100 steps:
 399 pot:  8 + 12 +  9 =3D 29;   kin: 7 +  3 + 0 =3D 10;   total: 29 * 10 =3D 29=
 400 0
 401 pot: 13 + 16 +  3 =3D 32;   kin: 3 + 11 + 5 =3D 19;   total: 32 * 19 =3D 60=
 402 8
 403 pot: 29 + 11 +  1 =3D 41;   kin: 3 +  7 + 4 =3D 14;   total: 41 * 14 =3D 57=
 404 4
 405 pot: 16 + 13 + 23 =3D 52;   kin: 7 +  1 + 1 =3D  9;   total: 52 *  9 =3D 46=
 406 8
 407 Sum of total energy: 290 + 608 + 574 + 468 =3D <em>1940</em>
 408 </code></pre>
 409 <p><em>What is the total energy in the system</em> after simulating the moo=
 410 ns given in your scan for <code>1000</code> steps?</p>
 411 </article>
 412 <p>Your puzzle answer was <code>6735</code>.</p><article class=3D"day-desc"=
 413 ><h2 id=3D"part2">--- Part Two ---</h2><p>All this drifting around in space=
 414  makes you wonder about the nature of the universe.  Does history really re=
 415 peat itself?  You're curious whether the moons will ever return to a previo=
 416 us state.</p>
 417 <p>Determine <em>the number of steps</em> that must occur before all of the=
 418  moons' <em>positions and velocities</em> exactly match a previous point in=
 419  time.</p>
 420 <p>For example, the first example above takes <code>2772</code> steps befor=
 421 e they exactly match a previous point in time; it eventually returns to the=
 422  initial state:</p>
 423 <pre><code>After 0 steps:
 424 pos=3D&lt;x=3D -1, y=3D  0, z=3D  2&gt;, vel=3D&lt;x=3D  0, y=3D  0, z=3D  =
 425 0&gt;
 426 pos=3D&lt;x=3D  2, y=3D-10, z=3D -7&gt;, vel=3D&lt;x=3D  0, y=3D  0, z=3D  =
 427 0&gt;
 428 pos=3D&lt;x=3D  4, y=3D -8, z=3D  8&gt;, vel=3D&lt;x=3D  0, y=3D  0, z=3D  =
 429 0&gt;
 430 pos=3D&lt;x=3D  3, y=3D  5, z=3D -1&gt;, vel=3D&lt;x=3D  0, y=3D  0, z=3D  =
 431 0&gt;
 432
 433 After 2770 steps:
 434 pos=3D&lt;x=3D  2, y=3D -1, z=3D  1&gt;, vel=3D&lt;x=3D -3, y=3D  2, z=3D  =
 435 2&gt;
 436 pos=3D&lt;x=3D  3, y=3D -7, z=3D -4&gt;, vel=3D&lt;x=3D  2, y=3D -5, z=3D -=
 437 6&gt;
 438 pos=3D&lt;x=3D  1, y=3D -7, z=3D  5&gt;, vel=3D&lt;x=3D  0, y=3D -3, z=3D  =
 439 6&gt;
 440 pos=3D&lt;x=3D  2, y=3D  2, z=3D  0&gt;, vel=3D&lt;x=3D  1, y=3D  6, z=3D -=
 441 2&gt;
 442
 443 After 2771 steps:
 444 pos=3D&lt;x=3D -1, y=3D  0, z=3D  2&gt;, vel=3D&lt;x=3D -3, y=3D  1, z=3D  =
 445 1&gt;
 446 pos=3D&lt;x=3D  2, y=3D-10, z=3D -7&gt;, vel=3D&lt;x=3D -1, y=3D -3, z=3D -=
 447 3&gt;
 448 pos=3D&lt;x=3D  4, y=3D -8, z=3D  8&gt;, vel=3D&lt;x=3D  3, y=3D -1, z=3D  =
 449 3&gt;
 450 pos=3D&lt;x=3D  3, y=3D  5, z=3D -1&gt;, vel=3D&lt;x=3D  1, y=3D  3, z=3D -=
 451 1&gt;
 452
 453 After 2772 steps:
 454 pos=3D&lt;x=3D -1, y=3D  0, z=3D  2&gt;, vel=3D&lt;x=3D  0, y=3D  0, z=3D  =
 455 0&gt;
 456 pos=3D&lt;x=3D  2, y=3D-10, z=3D -7&gt;, vel=3D&lt;x=3D  0, y=3D  0, z=3D  =
 457 0&gt;
 458 pos=3D&lt;x=3D  4, y=3D -8, z=3D  8&gt;, vel=3D&lt;x=3D  0, y=3D  0, z=3D  =
 459 0&gt;
 460 pos=3D&lt;x=3D  3, y=3D  5, z=3D -1&gt;, vel=3D&lt;x=3D  0, y=3D  0, z=3D  =
 461 0&gt;
 462 </code></pre>
 463 <p>Of course, the universe might last for a <em>very long time</em> before =
 464 repeating.  Here's a copy of the second example from above:</p>
 465 <pre><code>&lt;x=3D-8, y=3D-10, z=3D0&gt;
 466 &lt;x=3D5, y=3D5, z=3D10&gt;
 467 &lt;x=3D2, y=3D-7, z=3D3&gt;
 468 &lt;x=3D9, y=3D-8, z=3D-3&gt;
 469 </code></pre>
 470 <p>This set of initial positions takes <code>4686774924</code> steps before=
 471  it repeats a previous state! Clearly, you might need to <em>find a more ef=
 472 ficient way to simulate the universe</em>.</p>
 473 <p><em>How many steps does it take</em> to reach the first state that exact=
 474 ly matches a previous state?</p>
 475 </article>
 476 <p>Your puzzle answer was <code>326489627728984</code>.</p><p class=3D"day-=
 477 success">Both parts of this puzzle are complete! They provide two gold star=
 478 s: **</p>
 479 <p>At this point, you should <a href=3D"https://adventofcode.com/2019" data=
 480 -ss1576248183=3D"1">return to your Advent calendar</a> and try another puzz=
 481 le.</p>
 482 <p>If you still want to see it, you can <a href=3D"https://adventofcode.com=
 483 /2019/day/12/input" target=3D"_blank" data-ss1576248183=3D"1">get your puzz=
 484 le input</a>.</p>
 485 <p>You can also <span class=3D"share">[Share<span class=3D"share-content">o=
 486 n
 487   <a href=3D"https://twitter.com/intent/tweet?text=3DI%27ve+completed+%22Th=
 488 e+N%2DBody+Problem%22+%2D+Day+12+%2D+Advent+of+Code+2019&amp;url=3Dhttps%3A=
 489 %2F%2Fadventofcode%2Ecom%2F2019%2Fday%2F12&amp;related=3Dericwastl&amp;hash=
 490 tags=3DAdventOfCode" target=3D"_blank" rel=3D"noreferrer" data-ss1576248183=
 491 =3D"1">Twitter</a>
 492   <a target=3D"_blank" rel=3D"noreferrer" data-ss1576248183=3D"1">Mastodon<=
 493 /a></span>]</span> this puzzle.</p>
 494 </main>
 495
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1185 5px; }
1186   100% { color: rgb(204, 204, 204); text-shadow: transparent 0px 0px 5px; }
1187 }
1188
1189 .stats > span, .stats > span .stats-firstonly, .stats > span .stats-both { =
1190 color: rgb(102, 102, 102); }
1191
1192 .stats > a { color: rgb(204, 204, 204); min-width: 35em; display: inline-bl=
1193 ock; }
1194
1195 .stats > a:hover, .stats > a:focus { background-color: rgb(30, 30, 70); }
1196
1197 .stats-firstonly { color: rgb(153, 153, 204); }
1198
1199 .stats-both { color: rgb(255, 255, 102); }
1200
1201 .leaderboard-daylinks { cursor: default; }
1202
1203 .leaderboard-daylinks-selected { color: rgb(255, 255, 255); text-shadow: rg=
1204 b(255, 255, 255) 0px 0px 5px; }
1205
1206 .leaderboard-daydesc-first { color: rgb(153, 153, 204); }
1207
1208 .leaderboard-daydesc-both { color: rgb(255, 255, 102); }
1209
1210 .leaderboard-entry { white-space: pre; }
1211
1212 .leaderboard-entry .leaderboard-totalscore { color: rgb(255, 255, 255); }
1213
1214 .leaderboard-anon { opacity: 0.6; }
1215
1216 .leaderboard-userphoto { display: inline-block; height: 20px; width: 20px; =
1217 margin: 0px 0.5em; text-align: center; }
1218
1219 .leaderboard-userphoto img { height: 20px; max-width: 20px; vertical-align:=
1220  middle; position: relative; top: -2px; }
1221
1222 .leaderboard-time { opacity: 0.5; }
1223
1224 .privboard-row { white-space: pre; }
1225
1226 .privboard-row .star-count { color: rgb(255, 255, 102); }
1227
1228 .privboard-name { vertical-align: text-bottom; }
1229
1230 .privboard-days > span { display: inline-block; color: rgb(51, 51, 51); }
1231
1232 .privboard-days > a { display: inline-block; }
1233
1234 .privboard-star-locked { visibility: hidden; }
1235
1236 .privboard-star-unlocked { color: rgb(51, 51, 51); }
1237
1238 .privboard-star-firstonly { color: rgb(153, 153, 204); }
1239
1240 .privboard-star-both { color: rgb(255, 255, 102); }
1241
1242 .privboard-delbtn { opacity: 0.33; }
1243
1244 .privboard-row:hover .privboard-delbtn { opacity: 1; }
1245
1246 .sponsors { width: 46em; }
1247
1248 .sponsor { margin: 1em 0px; }
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1251 Content-Transfer-Encoding: quoted-printable
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1253
1254 @charset "utf-8";
1255
1256 * { background: white !important; color: black !important; text-shadow: non=
1257 e !important; }
1258
1259 a { color: rgb(0, 0, 255) !important; text-decoration: underline !important=
1260 ; }
1261
1262 em { font-weight: 900 !important; }
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