27 September 2006

9/27 cryptogram solution

Here is yesterday's cryptogram:
NGRORQLXN XMN XRON ENXBNNQ XMN RPNL LQP XMN LIX, LQP ASFU PUNLOH BRGG ENISON UNLGRXRNH. – ZNLQ-ZLITFNH USFHHNLF
Where to start? How about the same methods we used yesterday: frequency analysis, common two and three-letter words, and common double letters.

We have three three-letter words: XMN, LQP, and LIX. Two of these (XMN and LQP) are used twice which lends us to believe both of them are probably very common (Most likely the, the most commonly appearing word in the English language).

The letter N is used 18 times, almost twice as often as the next (L is used 10 times). Does N represent e? Combined with our knowledge that either XMN or LQP is probably the, and N probably presents e, let's start off with the assumption that XMN is the. So X represents t (X appears 8 times, or third most, while frequency analysis tells us t is the second most common, so this passes our common sense test); M represents h, and N represents e:
eGRORQLte the tROe EetBeeQ the RPeL LQP the LIt, LQP ASFU PUeLOH BRGG EeISOe UeLGRtReH. – ZeLQ-ZLITFeH USFHHeLF
The next thing that seems pretty obvious to me is that EetBeeQ is between; thus E represents b, B represents w, and Q represents n:
eGRORnLte the tROe between the RPeL LnP the LIt, LnP ASFU PUeLOH wRGG beISOe UeLGRtReH. – ZeLn-ZLITFeH USFHHeLF
We still have another three letter word left partially unsolved: LnP. Coming before the, could it be and? L appears 10 times (second most common), and a is the third most common according to frequency analysis. P appears 4 times which is the frequency we would expect to see from d. Thus L represents a and P represents d:

eGRORnate the tROe between the Rdea and the aIt, and ASFU dUeaOH wRGG beISOe UeaGRtReH. – Zean-ZaITFeH USFHHeaF

Yesterday I admitted I had never heard of Saki and thus that part of the cryptogram was a mystery to me to the end. Today, the reverse is true: I know see enough of it to make a good guess that Zean-ZaITFeH USFHHeaF is jean-jacques rousseau. Thus Z represents j, I represents c (again, consistent with frequency analysis), T represents q (uncommon enough to only appear once), F represents u, H represents s, U represents r, and S represents o:
eGRORnate the tROe between the Rdea and the act, and Aour dreaOs wRGG becoOe reaGRtRes. – jean-jacques rousseau
Almost done: Rdea is idea (R represents i), Aour is your (A represents y), dreaOs is dreams (O represents m), wRGG is will (G represents the common ll). This solves all of our remaining letters, G, R, O and A. Here is our final solution (with capitalization added):
Eliminate the time between the idea and the act, and your dreams will become realities. – Jean-Jacques Rousseau
What I think is interesting about this particular cryptogram is that while we used some of the same methods as yesterday, we also used a new method. Being able to indentify the author of the quotation at such an early point, we found the answers to seven of our 19 total letters (the seven remaining letters were unused).

Here is the frequency analysis matchup:

ETAOINSHRDLC
EATISNULMDRC

Once again, we see that even short quotations are reasonably faithful to frequency analysis. Only U and M were more common than expected (U is sometimes seen as the twelfth most common letter instead of C; either way, U and M are the 13th and 14th most common).

Pretty cool, eh?
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