enigmatic puzzle - You'll need Thomas Jefferson more than you'd expect - Clue Twelve

_{<---Previous clue}

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"[redacted]," you say aloud, following the instructions. And then a light shines through a crack in the wall, spreading until it shows an outline of a door. Then it swings open.

As the door opens, you get the light right in the face. As you squeeze your eyes shut, you hear the screech of a microphone, and a booming voice says:

"You've done well so far. Good job. So now we have another Clue for you. Pay attention here. Use the Clues you have gotten so far. Doubtlessly you remember them. Every word here is important. Understand the power of two. More than you might expect you will need Thomas Jefferson. I know these sentences have been cryptic. It all adds up."

It's a good thing you have your phone always recording, so you play it back and listen again. The obvious place to start is with your list of existing clues: (this is the list of answers to the previous 11 clues)

1. honey


2. hydrogen


3. silver


4. pepper


5. mercury


6. wormwood


7. barley


8. quartz


9. king cobra venom


10. magnesium



11. uranium

Hint 1:

There are two puzzles hidden in the text which have to be used together.

Hint 2:

How many sentences are there?

Hint 3:

Thomas Jefferson is both code and key.

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_{Next clue--->}

Answer

The clue about Thomas Jefferson tells us that the solution must involve

the Jefferson disc encryption method.

We also notice, as suggested by Hint 2, that

the number of sentences in the message is 11, exactly the same as the number of solutions found so far. This suggests that each sentence corresponds to one of these previous solutions.

Putting these two ideas together, I think we're going to need

an 11-disc Jefferson encryption.

So we still need three things in order to find the plaintext.

• 
  

  The ciphertext.

  
  

  
  

  This is probably hidden within the 11-sentence message somewhere, and an obvious guess is to take the first letter of every sentence: YGSPUDEUMII.

  
  

  
  


• 
  

  The key (i.e. the ordering of the discs).

  
  
  

  
  

  I.e. the ordering of the discs. According to Hint 3 this is "Jefferson", but I'm not sure how to turn that 9-letter word into an ordering of 11 discs. Jefferson was the 3rd president of the USA, but that only gives us an ordering of the 3rd disc, not all 11.

  
  

  
  


• 
  

  The discs themselves.

  
  

  
  

  We still need to know how the alphabet is actually scrambled on each disc! My guess is that we use the previous solutions: e.g. "hydrogen" gives the alphabet as HYDROGENABCFIJKLMPQSTUVWXZ or "wormwood" gives it as WORMDABCEFGHIJKLNPQSTUVXYZ.

  
  

  
  

  Or, following the OP's hint that "it might not be a standard Jefferson wheel", let's use the words themselves, to get the following 'discs':

  
  
  

  
  

  HONEY
HYDROGEN
SILVER
PEPPER
MERCURY
WORMWOOD
BARLEY
QUARTZ
KINGCOBRAVENOM

MAGNESIUM
URANIUM

  
  

  
  

Ignore the key for the moment, since the letters YGSPUDEUMII already appear in exactly the right words in the right order. Arranging the wheels to the right position, we get:

         HONEY
      ENHYDROG
        ILVERS

        EPPERP
       RYMERCU
      WORMWOOD
        YBARLE
        ARTZQU
KINGCOBRAVENOM
     UMMAGNESI
       UMURANI

Then we decrypt using a step size of 3 (since Jefferson was the 3rd president), i.e. shifting 3 letters backwards on each wheel, to get the 'plaintext'

ODVPMWATENR.

At some point we'll also need to use powers of 2 and everything adding up, as suggested by the hints in the message. And at the end of the day, the final answer is likely to be

WATER

as discovered by dcfyj.

So we'd like to be able to pick the 6th, 7th, 8th, 9th, and 11th letters from the 'plaintext' we now have, but I couldn't see where the motivation comes from to do so.

After getting help in chat, I realised what the justification is meant to be for the final step:

in the 11-sentence message, "Every word here is important" and "It all adds up" tells us to count the total number of words in that message: 61. Then "Understand the power of two" tells us to put that 61 into binary representation as 00000111101. Pick only the letters corresponding to 1's, and we get the final solution WATER as expected.

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Feedback section

Next time, please make the required steps a little clearer :-) There's a lot to do in this puzzle, with absolutely no confirmation (other than hints received from the OP) until the very last step. I wouldn't have got this at all if I hadn't known (thanks to dcfyj) what the solution was going to be; nor would I have been able to justify the final step if I hadn't got some help in chat. The ideal multi-layer puzzle has some sort of confirmation at each step that the solver is on the right track; I realise this isn't always possible, but it's at least something to strive for.