PUBLICSERVANT
DFGHJKMOQWXYZ

The letters below the 13-letter phrase are the other 13 letters of the alphabet, in alphabetic order.

Any given message can be encoded or decoded by finding each given letter among the 26 on the chart, and replacing it with the letter above or below it.

A different 13-letter phrase has been used in forming the key to encyphering a sentence, below. Again, of course that key phrase has no repeating letters.

The message:

THE QUICK BROWN FOX JUMPS OVER THE LAZY DOG

is, in this code:

PQS HGCIJ LXMZF NMR KGOTE MDSX PQS BYWA VMU

As was to be expected the replacements are mutual: for example, N codes F and F codes N.

What was the 13-letter phrase used in forming the key to this code?

Well, that was a fun problem.

1) By inspection, the letter pairs are
    AY
    BL
    CI
    DV
    ES
    FN
    GU
    HQ
    JK
    MO
    PT
    RX
    WZ
    
 2) I initially guessed that all the vowels were 
    in the phrase (which can't be far wrong).  
    Then, they would be in the following sequence:
 
    ..I..U..O..E..A..
    ..C..G..M..S..Y..
    
 3) Note the pair WZ.  It must be immediately before 
    or after the A, and along with A these would be 
    the last two letters in the phrase.  I guess 
    that the phrase ends in AW, not ZA, making it 
 
    ..I..U..O..E..AW
    ..C..G..M..S..YZ 
    
 3) Note the pair RX.  It must be pretty close to the 
    end, also, either immediately before the A or the E.
    Noting the PT pair, I guess before the A, because 
    a phrase ending in TXEAW or XEPAW seems wrong.  
    This makes it
 
    ..I..U..O..E..RAW
    ..C..G..M..S..XYZ
    
 4) I note pair DV next.  If V is in the bottom, the 
    phrase ends in DRAW, which is a word.  Next guess:
 
    ..I..U..O..E..DRAW
    ..C..G..M..S..VXYZ 
    
 5) Maybe the U is not in the phrase?  That would make 
    the letters before DRAW either TEG  or EPG.  
    I don't like either.
 
 6) How about the TP pair?  Is it ..EPDRAW or T..EDRAW?  
    The latter, because the H fits between T and E.  
    Still guessing, but feeling more confident that it is
 
    ..I..U..O..THEDRAW
    ..C..G..M..PQSVXYZ
    
  7) The next highest letter we haven't accounted for is 
     N, and that comes with and F.  
     If N is on the bottom, then we have
 
    ..I..U..OFTHEDRAW
    ..C..G..MNPQSVXYZ 
    
  8) And this is enough for me to recognize the phrase.  
     The I is on the bottom, not the top.
     
     LUCKOFTHEDRAW
     BGIJMNPQSVXYZ
     
  Final answer

Edited on May 16, 2013, 7:20 pm

Posted by Steve Herman on 2013-05-16 19:18:33