111 221 241 151

222 543 421

233 161

166 222 331 353 444

The problem is to translate this into a sentence.


  • 111, could also be 166, or 121
  • It is a Homophonic Substitution Cipher
  • The code he gave me before this was:
    • &!! "/ (?, }<€ \>!<* :~"& }?@! translates to
    • see if you can break this code
  • It is for an interview for an assistant trader position in Chicago.
  • $\begingroup$ Does each set of numbers represent a letter or a word? $\endgroup$ Mar 25 '15 at 23:28
  • 1
    $\begingroup$ Is there any hint in how these numbers were given to you and by whom ? And potentially, for what - or rather in what context ? $\endgroup$
    – BmyGuest
    Apr 26 '15 at 10:25
  • 1
    $\begingroup$ oh, and one last thing: the OQ's prior use of symbols instead of letters in what is still a basic substitution cipher is the sort of over-clever thing I'd be looking for here, too. You could read it as two transforms if you wanted (one to substitute, one to turn it into symbols) -- OP just didn't have to figure out the second one that lives inside OQ's head. Might be something like that here, too. $\endgroup$
    – lorimer
    May 5 '15 at 17:04
  • 1
    $\begingroup$ @Len: if he has taken this long to solve it (and come to the conclusion with an obviously immense amount of outside assistance) would you really still hire him for the job? $\endgroup$ May 6 '15 at 1:50
  • 1
    $\begingroup$ @user224980 if you think you're going to solve this by brute force, you're going to have a bad time. In a small (~6000 words) dictionary of most common words, after eliminating words that have a duplicate letter, there would be about 253,000,000 potential combinations of the correct lengths. Of those, about 68,000 combinations (272,000 words) have their only duplicate letters in the correct places. For reference, that word count would be somewhere between Paradise Lost and Ulysses in length, but full of nonsense like "mild use to punch" or "tidy cow be scrap." Good luck not going crazy. $\endgroup$
    – ajpolt
    May 6 '15 at 16:47
  • Although this code looks similar to a Polybius cipher, I don't think it is one. Groups of 3 digits would use a 3x3x3 grid and the numbers would be from 1 to 3. Numbers from 1 to 6 would use a 6x6 grid with groups of 2 digits. If a 6x6x6 grid was used, it would be impossible to decode.

  • It is notable that the code contains a majority of 1's and 2's with no 0's, 7's, 8's, or 9's. Perhaps the code is based on a system of 3 digit numbers from the "real world" like bus routes or office numbers or pages of a training manual.

  • As you suggest, we could try finding 4 words that fit the ABCD EFG HI JEKLM pattern. An example is "john was by twice" but it seems quite difficult to make a sensible sentence.

  • As noted by JLee, this code resembles a book cipher but the name of a book (or some written document) is required to decode.

  • Several 3 digit codes are in common use including the US ZIP code prefixes and the Dewey Decimal system (North American area codes do not use 100 series numbers). The following table shows the meaning of each 3 digit code, however this does not help with decoding the cipher.


  • 2
    $\begingroup$ That is the exact thing I got, with mod 26, but I saw the gibberish and thought I was barking up the wrong tree. Thanks for the quipquip link. I didn't know about it. $\endgroup$
    – JLee
    Mar 26 '15 at 21:32
  • $\begingroup$ Wouldn't it be more accurate to do mod-26 + 1, since the alphabet is not zero-indexed? We're getting a range of [0,25] here. I don't know if that changes what gets output by quipquip. $\endgroup$ Mar 26 '15 at 23:12
  • $\begingroup$ i dont quite understand how to apply mode-26 how could 111 and 241 both represent the same letter? $\endgroup$
    – user224980
    Mar 26 '15 at 23:36
  • $\begingroup$ the last one i was sent translated to "see if you can break this code" it might be something clever like that $\endgroup$
    – user224980
    Mar 26 '15 at 23:37
  • $\begingroup$ i dont see how it could be a book cipher though if this was all that i was given with no mention of any books $\endgroup$
    – user224980
    Mar 26 '15 at 23:38

The answer is:

THIS   111 221 241 151  
ONE    222 543 421  
IS     233 161  
TOUGH  166 222 331 353 444

User224980 explanation (from comment) - What it ended up coming down to was a lot of guess and check. Obviously the letters were represented by more than one number. Like I said before, you were going to know if you got the answer. Another clever one!

Len's summary of other comments below - This answer does seem most appropriate but it is disappointing because there should still be an explanation for associating the numbers in the question with the letters in the answer.

  • 5
    $\begingroup$ Please do go into greater detail. $\endgroup$ May 7 '15 at 7:04
  • 5
    $\begingroup$ If the solution was just trial and error, I don't think anything's really been solved -- we need more detail on how you got from 'a' to 'b'. While there is only one repeated 'character' in the ciphertext, there are 5 different repeated ones in the plaintext. In fact, there are only four letters in the plaintext that aren't duplicated, E G N U; all of H I S T O are repeated once. $\endgroup$
    – lorimer
    May 7 '15 at 12:26
  • 2
    $\begingroup$ 1) Was this 4-word sentence really long enough to allow the cipher to be solved? . 2) Was this a "guess what I am thinking" type of puzzle? . 3) Are you and your friend the same person? . 4) "Clever" means "mentally bright" but "cleaver" means "a heavy, broad-bladed knife" $\endgroup$
    – JLee
    May 7 '15 at 13:12
  • 6
    $\begingroup$ How do you know it's this and not "THAT ONE IS TOUGH" instead? Or for that matter, "THIS ONE IS TOAST," "SMUG MAN IS SMART," or "STEP TWO IS STUDY?" But let's assume you're right, because it does make sense. If you were handed another ciphertext encoded in the same way, with the same key, would you be able to find it any faster? If not, you haven't solved it at all. Is this guy supposed to be impressed at your guessing skills? I'd be pretty disappointed if someone solved my interview puzzle and then told me they basically just guessed, especially if it took them over a month to do it. $\endgroup$
    – ajpolt
    May 7 '15 at 17:54
  • 2
    $\begingroup$ @user224980 So for an interview question the solution was to randomly plug in letters for a homophonic substitution cipher? That's completely absurd. The numbers may as well have been hieroglyphics, making the 1-6 range and three digits meaningless. If somehow that actually was an interview question and that was how you were supposed to solve it, I'd run away. Fast. $\endgroup$
    – Quark
    May 10 '15 at 0:17

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