An Odd New Technology

Question

Since it's Friday, and I'm really looking forward to the weekend, I've created yet another riddle for everyone to try and solve.

The Puzzle

I was in my chemistry class the other day, and I noticed something rather odd about the periodic table.

I couldn't place my finger on it, yet I could see it clear as day. The professor stated that it was a new technology that he had created and it disproved a lot of the fundamental teachings for math and science. He stated that with the fundamentals of his technology, a basic math equation such as $4 + 6 = 10$ was now wrong. I asked how this could be, and he simply responded:

The very fabric of our knowledge is built on a lie that was established thousands of years ago.

How, seriously, how can this be correct? The lie that he speaks of has been proven over the course of these thousands of years.

Well, I decided to dive further into his periodic table, and couldn't find any of the essential building blocks such as hydrogen or helium. No matter how I did the math, I just couldn't do it. However, I was able to prove the following formulas true:

$4 + 20 = 61$

$13c + 6 = 36$

$15 + 4 = 12$

I was told there is another accurate formula that supports the professor's claims in his thesis, and that to find it I would have to solve a nested riddle which has also proven quite difficult.

The proof that you seek, is hidden in code; then scrambled again, the message unknown.

The key that you'll need, is hidden as well; seventy-seven minus all will tell.

Built on three, plus four you will see; the message that's hidden, not given, not free.

He gave me a piece of paper with a message scribbled on it; and told me to visit this website. He said that I shouldn't change the available mode options, but that the riddle above will tell me what to do. Here is the text:

K561YMuzen679PIISrSAYz2EQK+3uEPK7hrW7jKhlJH2FUCCWS63EZPolPvcygAcWIIKKiEMv11v+Cmy00TnOn/R/iwOvAOYq8wrk4EuCFLbXEZke3cPj7g8qzG9Fwq+B0g5T4ZgtBkPJfQ6411/V/JWq+bbLpBzTNo65EPG7LXyPzqnVuq4QVS51MOy8c7Jzf9I8Zy4YzfyizmGfRXdvHgDbW7AdIkNZPha/UlHup91KQxiWcWCl6/ayjzfvk9E0bNny8A5dysanBtDNbkkJ2+WMCxgdhSHlHgMP+ErTzpfr6IZo0DNj6VzdjM6JOE=

He also said that he found another formula quite useful on his journey to creating this new technology, and said that it might prove to be useful to me:

$PL - P$

I'm not really sure what to make of it; hopefully you guys can help me out here. What is the professor's thesis, and what is the final formula that supports it? Also, what’s up with the weird expression he said would help?

Notes and Hints

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I updated the message to be more fitting to a proper answer. For those who haven’t managed to decrypt yet, the unencrypted portions of the puzzle still apply. Just the encrypted portions have changed. I didn’t like the original answer as I thought it didn’t do the puzzle justice. The old version is still available in the edit history if you so choose.

Encryption Hint: The encryption method is difficult to figure out based on the minimal information given; however, once you find it you'll have one of those "ohhhhhhh okay" moments.

The message encrypted, electrical ties; would you like McChicken, or a burger with fries?

Key Hint: The key, similar to the encryption method is also difficult to find due to the nature of the riddle. I can tell you it is all lower case, and is more than one word!

The key you all need, is trapped within space; where it can seem hard, to keep up your pace.

Final Hint: Since there is already an answer that has made it to the final stages, I've decided to give one last hint to really help everyone.

The paragraphs start, after the art; include everything but math.

Clarifications

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• @user477343's comment in Rot13 is correct, also brought up this post.
  • The linked puzzle has no relation to this one.
• @Hugh wondered if the duplication of elements was significant.
  • In response, the only significance is that one provides a correct answer, where the other does not. I used duplicated elements to throw people off.
• @SteveV pointed out the duplication of column headers 3 and 10 being IIIA.
  • This is purely coincidence and has no significance. Also, great reference to 32, 18, and 17. I thought about using those in my puzzle but decided against it.
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If you have any questions along your journey, feel free to ask; and as always, if you down-vote, please explain in a comment how I can improve my post.

Answer 1

I think that

The Professor's theory is a lie

I got there by decrypting the code with these settings

Encryption Method: Arcfour (Arc from electricity, four from 4)
Encryption Key: zero gravity

This reveals a new challenge

Wkh sxccoh frqwdlqv wkh dqvzhuv, orrn ehbrqg wkh fkduw; wklv whfkqrorjb lv qrw frqwdlqhg, zlwklq wkh zrun ri duw. Vhyhudo qxpehuv jlyhq, wkh zrugv fdq vxuhob whoo; frxqw wkh vwduv, wklv surihvvru lvq’w zhoo.
1a16
5a12
5a16
4a5
6a4&9
T11

Which can be solved by

A caesar cypher. PL (playdoh 42) - P (plaque 19) = 23, which is the cypher key

This reveals the final puzzle:

the puzzle contains the answers, look beyond the chart; this technology is not contained, within the work of art. several numbers given, the words can surely tell; count the stars, this professor isn’t well.
1x16
5x12
5x16
4x5
6x4&9
q11

You can use these clues to

Get the 16th word of the first paragraph, 12th word of the 5th paragraph, etc.

Which reveals

The professor's thesis is a lie

Unless I messed up that last part, which is very likely

Answer 2

A very cool puzzle.

Obviously the starting formulas are shown as a logic example: we can combine elements referenced by numbers to get other elements (numbers). Also now we know for sure that fire+air does not result in stains :)

Encryption method:

3+4, or electricity plus fire - since gravity is a hint for the key, could be Sun (or Star) After seeing another hint, "electrical ties" could also mean nuclear bond (wut). McChiken or a burger with fries could hint to fat(46), meat(48), crisps(23) or fire(4). UPD1: Arcfour = Arc(electricity)+four(fire). Its the encryption method. UPD2: not sure if accidental, but CBC(Cypher block chaining) looks just like chicken bacon and crisps.

Encryption key:

Gravity ( minus all?). After seeing the second hint, it only strengthens my suspicion of space bodies or processes involved here. UPD2: key = zero gravity... (tried a hundred more complicated keys, meh)

Another hint:

Not sure what it means, but possibly: Pl - P = Plastic (or Playdoh) - Paint = 56(or 42) - 28 = 28 (or 14, which is papier mache) UPD2: the encrypted message was also scrambled. Tested rot14, then noticed that P is also plague(19): 42-19= rot23, which unscrambled the message.

The last part:

"The puzzle contains the answers, look beyond the chart; Several numbers given, the words can surely tell" - ok, that seems to mean that we have to get words from paragraphs, starting from the paragraph right after the chart. Tried different paragraphs and ideas, but the only sensible result is "The professor's thesis (dive) (a)"... so there is something wrong with this approach. Also tried including the paragraph with formulas (4 + 20 = 61... etc), no luck so far. An interesting part is "count the stars, this professor isn’t well". The third paragraph has "hydrogen or helium", and there are other hints to stars in the puzzle. The whole theme is space, after all. Also, 11th word in the encrypted message is "technology".

Answer 3

Partial Thoughts:

I have figured out the formulas you proved-

4+20=61 is Fire + Sand = Glass

13c+6=36 is Cold Water + Air = Snow

15+4=12 is Tobacco + Fire = Smoke

Also Built on 3 + 4 is built on fire and electricity.