LXXIII. Uncovered.

2 years ago

20-06-2022

—

8 min read

1541 words

Contents Inspiration

Shout outs (solvers)
    Testimonials
Puzzle Solutions
    Puzzle #1.1
    Puzzle #1.2
    Puzzle #1.3
    Puzzle #2
    Puzzle #3
    Puzzle #4

“Deep in the human unconscious is a pervasive need for a logical universe that makes sense. But the real universe is always one step beyond logic.”
― Frank Herbert, Dune

✨ Inspiration

If you did not already know, LXXIII was heavily inspired by Cicada 3301 and if you are unfamiliar with this puzzle, I would highly recommend that you check out the video below 👇

📣 Shout outs (solvers)

I would like to briefly thank everyone who attempted LXXIII. The response I got from everyone was mindblowing and I hope you enjoyed solving the puzzle as much as I did creating it.

Testimonials

"LXXIII is a masterpiece of a scavenger hunt. It's one of the most creative projects I've received in my career!"
- Christian Gonzalez (Princeton High School Faculty)

"Very well done and an interesting ARG. The 6th puzzle was so hard! Thanks for the opportunity. :D"
- Zee Arrr

"LXXIII was challenging, but super fun! You can tell a lot of effort went into its creation, and it really paid off. LXXIII is a really cool puzzle!! :D"
- Sanjana

📖 Puzzle Solutions

Below I have explained the solutions of each puzzle in consecutive order. If you still wish to visit the website you can do so with the following link: https://lxxiii-old.vercel.app.

The website is static. The views will still be updated in the database but no solvers will be added.

As always, if you have any questions you can always contact me here

Puzzle #1.1

The scavenger hunt begins with the following clue:

?v=azo5Gjj9qMw

Solution

Although not immediately obvious, we observe that this is the videoID of a YouTube video. Take for example the link of the youtube video below:

https://www.youtube.com/watch?v=dQw4w9WgXcQ

the portion requesting ?v=dQw4w9WgXcQ is the video ID. Therefore, in our case the video link will be given as such:

https://www.youtube.com/watch?v=azo5Gjj9qMw

Puzzle #1.2

Following with the prior, we are led to this video:

Solution

From here we can extract quite a few clues.

Video Title

The title of the video is encrypted in binary, once decoded leaves us with the following message:

<!--Binary Cipher-->

01010011 01101000 01100001 01101011 01100101 01110011 01110000 01100101 01100001 01110010 01100101

<!--Decrypted Plain Text-->

Shakespeare

Video Description

The description of the video contains yet another encoded message in hexadecimal, once decoded leaves us with the following message

<!--Hexadecimal Cipher-->

68 74 74 70 73 3A 2F 2F 77 77 77 2E 79 6F 75 74 75 62 65 2E 63 6F 6D 2F 63 68 61 6E 6E 65 6C 2F 55 43 42 51 54 63 43 68 41 31 74 6D 62 4C 53 5A 5F 7A 53 6B 36 39 53 67 2F 61 62 6F 75 74

<!--Decrypted Plain Text-->

https://www.youtube.com/channel/UCBQTcChA1tmbLSZ_zSk69Sg/about

Channel About Page

The last cipher leads us to the about page of the channel which has the following encrypted description in binary:

<!--Binary Cipher-->

01101000 01110100 01110100 01110000 01110011 00111010 00101111 00101111 01101100 01111000 01111000 01101001 01101001 01101001 00101110 01110110 01100101 01110010 01100011 01100101 01101100 00101110 01100001 01110000 01110000 00101111 01001010 01010101 01100100 01001110 01010010 00110001 01000011 01100010 01111001 01001110 00111001 01101111 01101100 01010111 01101100 01001011 01110110 01100101 00111000 01011000 00101111 01000110 01111010 01001000 01100011 01101101 00110000 01101011 00110001 01001001 01111001 01100011 01101101 01101111 01001110 01011010 01111010 01111000 01100100 01101110 01101011

<!--Decrypted Plain Text-->

https://lxxiii.vercel.app/JUdNR1CbyN9olWlKve8X/FzHcm0k1IycmoNZzxdnk

If you are following along, you should use this link https://lxxiii-old.vercel.app/JUdNR1CbyN9olWlKve8X/FzHcm0k1IycmoNZzxdnk

Puzzle #1.3

The link in the about page leads us back to the initial puzzle page but with two additional questions:

In the video, there is a famous quote and composition. Could you find it?
- Composer
- Quote

Solution

If we look at the video subtitles closely, the starting of each letter form a hidden message:

<!--Message Cipher-->

All never dying souls over hells end. Playing long and yet so happy. Illustrators seeking pragmatic aims rest today.

<!--Decrypted Plain Text-->

And so he plays his part

And if we listen closely, we can hear faint ragtime music in the background. The song in question is:

<!--Composition-->

The Entertainer

<!--Composer-->

Scott Joplin

Using these answers we can proceed to the next puzzle.

Puzzle #2

The page has a QR code, which once scanned reveals leads us to the following image:

Math :) Math :)

What do all these symbols mean?! (Mathematical deduction)

Let's take things one line at a time.

Line 1

The first half defines a set of numbers $\mathbb{P}$ such that, each number $\alpha$ that is an element of $\mathbb{P}$ folllows the rule:

\prod_{i=1}^{\alpha-1}i\equiv -1 \pmod{\alpha}

Okay, still confusing. The product on the left hand side simplifies to:

(\alpha-1)!\equiv -1 \pmod{\alpha}

Aha! This is a restatement of Wilson's Theorem. From here we can see that $\mathbb{P}$ is simply the set of all prime numbers.

Line 2

The equation doesn't make much sense at first, but if we try substituting a few values, we quickly notice a interesting pattern

\begin{align*} n=1 &\implies \alpha_1 = 2 \\ n=2 &\implies \alpha_2 = 3 \\ n=3 &\implies \alpha_3 = 5 \\ n=4 &\implies \alpha_4 = 7 \\ n=5 &\implies \alpha_5 = 11 \\ &\quad\vdots \end{align*}

We conclude that $\alpha_n$ is a formula for the $n^\text{th}$ prime number.

The conlusion is not mathematically rigorous, if you want a more general solution you can look here

Line 3

This one quite straight forward. It is simply saying that $x^\prime$ is the digits reversed of a two digit number. For exmaple:

x = 73 \implies x^\prime = 37

Line 4, 5, 6

From the previous lines, we can now understand the problem statement. The question is asking for a two-digit prime number $\lambda$ such that when the digits are reversed, the order of the number in the set $\mathbb{P}$ is also reveresed. Moreover, we are given that the prime number $\lambda$ in base-two (binary) is a palindrome.

With all these clues we can deduce that the only two-digit prime satisfying all these conditions is:

\boxed{\lambda = 73}

Solution (The easy way)

One may notice that the name of the puzzle LXXIII is in roman numerals. This simply translates to $73$ .

Puzzle #3

Solving the previous puzzle redirects towards a blank page with a tuple of numbers

40.35778817139876, -74.65557806304463

Solution

These are geo decimal coordinates, and if we travel to the location we find something interesting.

The original photo The original photo

The QR code leads us to the final stage of the puzzle.

If you are following along, you should use this link https://lxxiii-old.vercel.app/GkCserScp7YExh4dKGE2/PWGkpkMELQ7tX4HUrfXv

Puzzle #4

The final puzzle is given below

Solution

ELA

The message in the image can be retrieved using the technique Error Level Analysis. Check out the interactive demo!

Message visibility The message is still quite difficult to read so we can increase

the brightness, contrast to seperate out the desired selection. Check out the interactive demo!

If you are following along, you should use this link https://lxxiii-old.vercel.app/KLRBnBYCtt