Zoom Network Park

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Solved! 💜 += 25;

Your legs are sore from all the walking around the towers, but after examining all the towers in a painstaking and slow process, you realize that you need to increase the BEACON RADIUS. As you finish turning the dials in the last tower, you sit back and take a deep breath as you hear the hum of what must be hundreds of computers around you in the tower.

You look around as the towers light up, indicating that everything is working again. You look out from the window at the other distant towers, watching them flicker on and off as power surges through them. There must be a lot of Zoom calls going lately, you think to yourself.

You think to yourself that you’ll be glad once Zooming for everything stopped being a thing, back on your side of the world. You wonder if anyone on this side is sick of Zoom as well. Hey, I wonder if I can call home? Your cellphone isn’t working, but if Zoom’s working, maybe you can. You try to connect back to the MOP HQ Zoom, but you simply get an error message. Ah well, it was worth a shot.

With another job well done, you walk back downstairs and return to the center of campus.

Click the image to continue.
A scenic sunset from Zoom HQ.

Solution to Zoom Network Park

The first thing to do is join the Zoom meeting. It has meeting ID 953 1568 0293 and additionally has the topic A => B@917 C@979 H@945.

What can we do with this?

Plotting out the graph

The first insight is to look at the coordinates given in the asy file.

pair A = (1568,  293);
pair B = (2317, 1185);
pair C = (8057, 1394);
pair D = (5829, 3170);
pair E = (4079, 3458);
pair F = (5490, 5821);
pair G = (4027, 5827);
pair H = (2459, 6096);
pair I = (7406, 6683);
pair J = (6188, 9072);
pair K = (3325, 9359);
pair L = (9797, 9524);

The solver might recognize that the coordinates of A are actually the last two parts of the Zoom meeting. By engineer’s induction, this should be true for the other Zoom meetings too.

So, we just need to find the first three digits for the other points. Conveniently, the topic gives three-digit numbers! So for example, we may infer there is a node for B located at 912 2317 1185. Going to this meeting gives another topic with more numbers: we are now walking on a graph!

This gives the following table of meetings:

Point Topic of Zoom meeting Zoom ID
A B@917 C@979 H@945 953 1568 0293
B A@953 D@916 E@993 917 2317 1185
C A@953 D@916 L@947 979 8057 1394
D B@917 C@979 I@936 916 5829 3170
E B@917 F@956 G@996 993 4079 3458
F E@993 G@996 I@936 956 5490 5821
G E@993 F@956 H@945 996 4027 5827
H A@953 G@996 K@940 945 2459 6096
I D@916 F@956 J@926 936 7406 6683
J I@936 K@940 L@947 926 6188 9072
K H@945 J@926 L@947 940 3325 9359
L C@979 J@926 K@940 947 9797 9524

Traveling the graph

The previous table now gives a 3-regular planar graph on the given diagram. One then walks the graph as in this year’s USAMO2 problem, as hinted by the title of the puzzle being “Zoom Network Park”. Starting with the marked arrow, we get the following path:

Illustrated initial path

Tracing the path out and reading the Morse code (there are many dots and dashes drawn on the edges), this gives the clue phrase CAN ZOOM IN ON EMAIL.

Zooming in

Solvers go back to the puzzle page and zoom in, literally, on the given email message. When they do so, a new message appears:

K ==> L ==> ? ==> ? ==> ? ==> ? ==> ? ==> ?
               8
  ==> ? ==> ? ==> ? ==> ? ==> ? ==> ? ==> ?
               6           9    12
  ==> ? ==> ? ==> ? ==> ? ==> ? ==> ? ==> K
   7                                   2

F ==> E ==> B ==> ? ==> ? ==> ? ==> ? ==> ?
                     4     5
  ==> ? ==> ? ==> ? ==> ? ==> ? ==> ? ==> ?
   1    11
  ==> ? ==> ? ==> ? ==> ? ==> ? ==> ? ==> F
               3    10

This corresponds to two more USAMO2-style paths. We fill them in:

K ==> L ==> C ==> D ==> B ==> E ==> G ==> F
               8
  ==> I ==> D ==> C ==> A ==> H ==> G ==> F
               6           9    12
  ==> E ==> B ==> A ==> C ==> L ==> J ==> K
   7                                   2

F ==> E ==> B ==> A ==> C ==> L ==> J ==> K
                     4     5
  ==> H ==> A ==> B ==> D ==> I ==> J ==> K
   1    11
  ==> L ==> C ==> D ==> B ==> E ==> G ==> F
               3    10

Both paths are illustrated below.

The first path for extraction

The second path for extraction

Finally, reading the numbered arrows and reading Morse gives

# Edge Letter
1 K ==> H B
2 J ==> K E
3 C ==> D A
4 A ==> C C
5 C ==> L O
6 D ==> C N
7 F ==> E R
8 C ==> D A
9 A ==> H D
10 D ==> B I
11 H ==> A U
12 H ==> G S

This gives the answer BEACON RADIUS.

Author Notes

The writing process for this puzzle was pretty straightforward. The idea behind a mechanism was to have a graph formed by connecting Zoom meeting links, and having the resulting graph be walked USAMO2 style. Morse seemed like an appropriate way to encode the letters (in particular, forces direction). I also had the idea of the “zoom in” pun and incorporated that as a second step in the puzzle using Javascript. Thankfully I had a database of the amazingly varied constructions submitted by students on the USAMO so I was able to find one that suits my needs.

In original versions of the puzzle, if you kept walking after reaching the point A, the next few letters would be USE IO, giving an accidental red herring. Fixing this was one of the last changes to happen for the puzzle hunt.

P.S. If you think walking the graph three times was annoying, imagine being a grader and having to walk 100 graphs.

Š 2021, MOP Puzzle Hunt