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The following cipher appears on the box of a puzzle called "Fire" from Pyro Puzzles:

Cipher comprising number triplets, text-only transcription available below

I know nothing about decryption, so I was hoping one of you would be able to help decrypt it. Thanks in advance.

Text-only transcription:

494 264 979 716 314 419 979 939 323 494 264 979 419 338 097 097 338 716 846 937 979 582 097 939 716 338 097 582 939 846 979 582 582 338 937 288 979 628 265 939 716 494 314 265 494 419 979, 327 939 264 716 781 314 494 097 939 716, 314 494:

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    $\begingroup$ This is a simple substitution cipher. The numbers do not appear to be significant. $\endgroup$ May 3, 2023 at 19:53
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    $\begingroup$ If this is a simple substitution cipher where there is exactly one number for each letter and vice versa, you don't have to make sense of how the letter can be derived from the number. You can try to find the key by looking at common words and usual leter frequencies. For example, 494 264 979 occurs twice, once at the beginning, so it is probably a common word like THE or YOU. $\endgroup$
    – M Oehm
    May 3, 2023 at 19:53
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    $\begingroup$ For those with lazyitis $\endgroup$
    – Daniel S
    May 3, 2023 at 20:06
  • $\begingroup$ Is the color important? Also, I upvoted your question. $\endgroup$ May 3, 2023 at 21:41

2 Answers 2

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As M Oehm suggests in comments I guessed that

the first four words were THE ___E OF THE

Then

the fifth to last word is _O_T__T which could be either SOFTEST or CONTACT. Since the next word is _E, I went with CONTACT ME

Then it fills in relatively easy to this point:

THE NAME OF THE MISSING PERSON IS ROGER RIP_E_ CONTACT ME, _O_N _ATSON, AT:

At that point I was reduced to guessing the remaining letters. Although one of the three digit patterns struck me as familiar while solving, I forgot about it until codewarrior0 pointed it out in the comments.

It turns out that

each letter is represented by three digits of pi, A being the first three, B being the second three and so on.

Using that we can solve the rest of the message:

THE NAME OF THE MISSING PERSON IS ROGER RIPLEY CONTACT ME, JOHN WATSON, AT:

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    $\begingroup$ The key is derived from a famous numerical constant. Can you recover the key and find out how it is derived? Knowing the key and how it was created will make you that much more confident in your decipherment. $\endgroup$ May 4, 2023 at 1:01
  • $\begingroup$ @codewarrior0 thank you, one of those three digit numbers did strike me as familiar but i forgot to pursue it. $\endgroup$
    – caPNCApn
    May 4, 2023 at 3:39
  • $\begingroup$ Great job. Thanks! $\endgroup$
    – Jade
    May 4, 2023 at 15:38
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Using this frequency table from wikipedia for the English language:

enter image description here

We can fine-tune the lookups to decode the message:

enter image description here

enter image description here

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