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2022/day/
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3 Subject: Day
9 - Advent of Code
2022
4 Date: Tue,
13 Dec
2022 10:
07:
26 -
0000
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26 <title>Day
9 - Advent of Code
2022</title>
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41 Oh, hello! Funny seeing you here.
43 I appreciate your enthusiasm, but you aren't going to find much down here.
44 There certainly aren't clues to any of the puzzles. The best surprises don=
46 even appear in the source until you unlock them for real.
48 Please be careful with automated requests; I'm not a massive company, and I=
50 only take so much traffic. Please be considerate so that everyone gets to =
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64 enjoyed making it for you!
66 If you'd like to hang out, I'm @ericwastl on Twitter.
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155 <article class=
3D
"day-desc"><h2>--- Day
9: Rope Bridge ---
</h2><p>This rope=
156 bridge creaks as you walk along it. You aren't sure how old it is, or whet=
157 her it can even support your weight.
</p>
158 <p>It seems to support the Elves just fine, though. The bridge spans a gorg=
159 e which was carved out by the massive river far below you.
</p>
160 <p>You step carefully; as you do, the ropes stretch and twist. You decide t=
161 o distract yourself by modeling rope physics; maybe you can even figure out=
162 where
<em>not
</em> to step.
</p>
163 <p>Consider a rope with a knot at each end; these knots mark the
<em>head</=
164 em
> and the
<em>tail
</em> of the rope. If the head moves far enough away fr=
165 om the tail, the tail is pulled toward the head.
</p>
166 <p>Due to nebulous reasoning involving
<a href=
3D
"https://en.wikipedia.org/=
167 wiki/Planck_units#Planck_length" target=
3D
"_blank" rel=
3D
"noreferrer" data-=
168 ss1670926033=
3D
"1">Planck lengths
</a>, you should be able to model the posi=
169 tions of the knots on a two-dimensional grid. Then, by following a hypothet=
170 ical
<em>series of motions
</em> (your puzzle input) for the head, you can d=
171 etermine how the tail will move.
</p>
172 <p><span title=
3D
"I'm an engineer, not a physicist!">Due to the aforementio=
173 ned Planck lengths
</span>, the rope must be quite short; in fact, the head =
174 (
<code>H
</code>) and tail (
<code>T
</code>) must
<em>always be touching
</em>=
175 (diagonally adjacent and even overlapping both count as touching):
</p>
189 <p>If the head is ever two steps directly up, down, left, or right from the=
190 tail, the tail must also move one step in that direction so it remains clo=
192 <pre><code>..... ..... .....
193 .TH.. -
> .T.H. -
> ..TH.
198 .H. -
> ... -
> .T.
202 <p>Otherwise, if the head and tail aren't touching and aren't in the same r=
203 ow or column, the tail always moves one step diagonally to keep up:
</p>
204 <pre><code>..... ..... .....
206 ..H.. -
> ..... -
> ..T..
212 ..H.. -
> ...H. -
> ..TH.
216 <p>You just need to work out where the tail goes as the head follows a seri=
217 es of motions. Assume the head and the tail both start at the same position=
229 <p>This series of motions moves the head
<em>right
</em> four steps, then
<e=
230 m
>up
</em> four steps, then
<em>left
</em> three steps, then
<em>down
</em> on=
231 e step, and so on. After each step, you'll need to update the position of t=
232 he tail if the step means the head is no longer adjacent to the tail. Visua=
233 lly, these motions occur as follows (
<code>s
</code> marks the starting posi=
234 tion as a reference point):
</p>
235 <pre><code>=
3D=
3D Initial State =
3D=
3D
241 H..... (H covers T, s)
403 <p>After simulating the rope, you can count up all of the positions the
<em=
404 >tail visited at least once
</em>. In this diagram,
<code>s
</code> again mar=
405 ks the starting position (which the tail also visited) and
<code>#
</code> m=
406 arks other positions the tail visited:
</p>
413 <p>So, there are
<code><em>13</em></code> positions the tail visited at lea=
415 <p>Simulate your complete hypothetical series of motions.
<em>How many posi=
416 tions does the tail of the rope visit at least once?
</em></p>
418 <p>Your puzzle answer was
<code>6243</code>.
</p><article class=
3D
"day-desc"=
419 ><h2 id=
3D
"part2">--- Part Two ---
</h2><p>A rope snaps! Suddenly, the river=
420 is getting a lot closer than you remember. The bridge is still there, but =
421 some of the ropes that broke are now whipping toward you as you fall throug=
423 <p>The ropes are moving too quickly to grab; you only have a few seconds to=
424 choose how to arch your body to avoid being hit. Fortunately, your simulat=
425 ion can be extended to support longer ropes.
</p>
426 <p>Rather than two knots, you now must simulate a rope consisting of
<em>te=
427 n
</em> knots. One knot is still the head of the rope and moves according to=
428 the series of motions. Each knot further down the rope follows the knot in=
429 front of it using the same rules as before.
</p>
430 <p>Using the same series of motions as the above example, but with the knot=
431 s marked
<code>H
</code>,
<code>1</code>,
<code>2</code>, ...,
<code>9</code=
432 >, the motions now occur as follows:
</p>
433 <pre><code>=
3D=
3D Initial State =
3D=
3D
439 H..... (H covers
1,
2,
3,
4,
5,
6,
7,
8,
9, s)
447 1H.... (
1 covers
2,
3,
4,
5,
6,
7,
8,
9, s)
453 21H... (
2 covers
3,
4,
5,
6,
7,
8,
9, s)
459 321H.. (
3 covers
4,
5,
6,
7,
8,
9, s)
465 4321H. (
4 covers
5,
6,
7,
8,
9, s)
473 4321.. (
4 covers
5,
6,
7,
8,
9, s)
479 5..... (
5 covers
6,
7,
8,
9, s)
485 5..... (
5 covers
6,
7,
8,
9, s)
491 6..... (
6 covers
7,
8,
9, s)
499 6..... (
6 covers
7,
8,
9, s)
505 6..... (
6 covers
7,
8,
9, s)
511 6..... (
6 covers
7,
8,
9, s)
519 6..... (
6 covers
7,
8,
9, s)
527 6..... (
6 covers
7,
8,
9, s)
533 6..... (
6 covers
7,
8,
9, s)
539 6..... (
6 covers
7,
8,
9, s)
545 6..... (
6 covers
7,
8,
9, s)
553 6..... (
6 covers
7,
8,
9, s)
561 6..... (
6 covers
7,
8,
9, s)
567 6..... (
6 covers
7,
8,
9, s)
571 ..H1.. (H covers
4;
1 covers
3)
573 6..... (
6 covers
7,
8,
9, s)
579 6..... (
6 covers
7,
8,
9, s)
585 6..... (
6 covers
7,
8,
9, s)
591 .H23.. (H covers
1;
2 covers
4)
593 6..... (
6 covers
7,
8,
9, s)
597 .1H3.. (H covers
2,
4)
599 6..... (
6 covers
7,
8,
9, s)
601 <p>Now, you need to keep track of the positions the new tail,
<code>9</code=
602 >, visits. In this example, the tail never moves, and so it only visits
<co=
603 de
><em>1</em></code> position. However,
<em>be careful
</em>: more types of =
604 motion are possible than before, so you might want to visually compare your=
605 simulated rope to the one above.
</p>
606 <p>Here's a larger example:
</p>
616 <p>These motions occur as follows (individual steps are not shown):
</p>
617 <pre><code>=
3D=
3D Initial State =
3D=
3D
619 ..........................
620 ..........................
621 ..........................
622 ..........................
623 ..........................
624 ..........................
625 ..........................
626 ..........................
627 ..........................
628 ..........................
629 ..........................
630 ..........................
631 ..........................
632 ..........................
633 ..........................
634 ...........H.............. (H covers
1,
2,
3,
4,
5,
6,
7,
8,
9, s)
635 ..........................
636 ..........................
637 ..........................
638 ..........................
639 ..........................
643 ..........................
644 ..........................
645 ..........................
646 ..........................
647 ..........................
648 ..........................
649 ..........................
650 ..........................
651 ..........................
652 ..........................
653 ..........................
654 ..........................
655 ..........................
656 ..........................
657 ..........................
658 ..........
.54321H......... (
5 covers
6,
7,
8,
9, s)
659 ..........................
660 ..........................
661 ..........................
662 ..........................
663 ..........................
667 ..........................
668 ..........................
669 ..........................
670 ..........................
671 ..........................
672 ..........................
673 ..........................
674 ................H.........
675 ...............
.1.........
676 ...............
.2.........
677 ...............
.3.........
678 ..............
.54.........
679 .............
.6...........
680 ............
.7............
681 ...........
.8.............
682 ..........
.9.............. (
9 covers s)
683 ..........................
684 ..........................
685 ..........................
686 ..........................
687 ..........................
691 ..........................
692 ..........................
693 ..........................
694 ..........................
695 ..........................
696 ..........................
697 ..........................
698 ........H1234.............
699 ...........
.5.............
700 ...........
.6.............
701 ...........
.7.............
702 ...........
.8.............
703 ...........
.9.............
704 ..........................
705 ..........................
706 ...........s..............
707 ..........................
708 ..........................
709 ..........................
710 ..........................
711 ..........................
715 ..........................
716 ..........................
717 ..........................
718 ..........................
719 ..........................
720 ..........................
721 ..........................
722 ..........................
723 ........
.2345.............
724 .......
.1..
.6.............
725 ........H..
.7.............
726 ...........
.8.............
727 ...........
.9.............
728 ..........................
729 ..........................
730 ...........s..............
731 ..........................
732 ..........................
733 ..........................
734 ..........................
735 ..........................
739 ..........................
740 ..........................
741 ..........................
742 ..........................
743 ..........................
744 ..........................
745 ..........................
746 ..........................
747 ..........................
748 ..........................
749 ...............
.987654321H
750 ..........................
751 ..........................
752 ..........................
753 ..........................
754 ...........s..............
755 ..........................
756 ..........................
757 ..........................
758 ..........................
759 ..........................
763 ..........................
764 ..........................
765 ..........................
766 ..........................
767 ..........................
768 ..........................
769 ..........................
770 ..........................
771 ..........................
772 ..........................
773 ..........................
774 ..........................
775 ..........................
776 ..........................
777 ..........................
778 ...........s........
.98765
779 ........................
.4
780 ........................
.3
781 ........................
.2
782 ........................
.1
783 .........................H
787 ..........................
788 ..........................
789 ..........................
790 ..........................
791 ..........................
792 ..........................
793 ..........................
794 ..........................
795 ..........................
796 ..........................
797 ..........................
798 ..........................
799 ..........................
800 ..........................
801 ..........................
802 ...........s..............
803 ..........................
804 ..........................
805 ..........................
806 ..........................
807 H123456789................
811 H.........................
812 1.........................
813 2.........................
814 3.........................
815 4.........................
816 5.........................
817 6.........................
818 7.........................
819 8.........................
820 9.........................
821 ..........................
822 ..........................
823 ..........................
824 ..........................
825 ..........................
826 ...........s..............
827 ..........................
828 ..........................
829 ..........................
830 ..........................
831 ..........................
834 <p>Now, the tail (
<code>9</code>) visits
<code><em>36</em></code> positions=
835 (including
<code>s
</code>) at least once:
</p>
836 <pre><code>..........................
837 ..........................
838 ..........................
839 ..........................
840 ..........................
841 ..........................
842 ..........................
843 ..........................
844 ..........................
845 #.........................
846 #.............###.........
847 #............#...#........
848 .#..........#.....#.......
849 ..#..........#.....#......
850 ...#........#.......#.....
851 ....#......s.........#....
852 .....#..............#.....
853 ......#............#......
854 .......#..........#.......
855 ........#........#........
856 .........########.........
858 <p>Simulate your complete series of motions on a larger rope with ten knots=
859 .
<em>How many positions does the tail of the rope visit at least once?
</em=
862 <p>Your puzzle answer was
<code>2630</code>.
</p><p class=
3D
"day-success">Bo=
863 th parts of this puzzle are complete! They provide two gold stars: **
</p>
864 <p>At this point, you should
<a href=
3D
"https://adventofcode.com/2022" data=
865 -ss1670926033=
3D
"1">return to your Advent calendar
</a> and try another puzz=
867 <p>If you still want to see it, you can
<a href=
3D
"https://adventofcode.com=
868 /2022/day/9/input" target=
3D
"_blank" data-ss1670926033=
3D
"1">get your puzzl=
870 <p>You can also
<span class=
3D
"share">[Share
<span class=
3D
"share-content">o=
872 <a href=
3D
"https://twitter.com/intent/tweet?text=3DI%27ve+completed+%22Ro=
873 pe+Bridge%22+%2D+Day+9+%2D+Advent+of+Code+2022&url=3Dhttps%3A%2F%2Fadve=
874 ntofcode%2Ecom%2F2022%2Fday%2F9&related=3Dericwastl&hashtags=3DAdve=
875 ntOfCode" target=
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877 <a target=
3D
"_blank" rel=
3D
"noreferrer" data-ss1670926033=
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"1">Mastodon<=
878 /a
></span>]
</span> this puzzle.
</p>
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