A simple replacement code can be created by using a 13-letter phrase with no repeated letters, such as the following:

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?

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From the 2013 Mensa 365 Brain Puzzlers for 2013 calendar, puzzle for May 1, by Mark Danna and Fraser Simpson, Workman Publishing, New York, NY.

After pairing the sentence with its encoding:
THE QUICK BROWN FOX JUMPS OVER  THE  LAZY   DOG
PQS HGCIJ  LXMZF  NMR KGOTE MDSX PQS BYWA VMU
I created an alphabetical string of the sentence coupled with is pairings below. After removing the second duplicate pairings I was left with the following table:
A B C D E F G H  J M P R W
Y  L  I V S N U Q K O T X  Z.

A phrase beginning "A LIVE .." seemed possible but some awkward combinations seemed to remain.

The letters FGH and LI seemed interesting.  Even accepting "A FLIGHT" some awkward pairings remained:
D E J M R W
V S K O X Z
After a bit of thought "WORKED" emerged.

In consideration of the fox, "A FLIGHT that WORKED" seems in keeping with the sense of the sentence and so I present as the 13-letter pairing key:
A F L I G H T W O R K E D
Y NBC U QP  Z M X  J S V.

Posted by brianjn on 2013-05-16 21:29:27