Cracking the Level 10    by Mike Neumeier

 

I used skills similar to those one learns in solving the syndicated Crypto-Quip found in newspapers.  I paid most attention to the phrase, knowing it was a simple-substitution cypher.  Once you solve a phrase, typically a grid solve quickly follows.

 

An important solver's advantage is that letter guesses in the phrase are readily realized as more- or less-likely candidates based on how they fare in the grid.  A solving disadvantage (not a negative... a challenge!) is that phrases are typically brief, so it's important to be aware of how the phrase and grid relate.  This reduces solving time.

 

I used a back-and-forth trial-and-error method: phrase to grid to phrase to grid, until ideas emerged.  At times one might cast aside a correct guess, only later to return.  Overall knowledge of the problem is continually improving as the solve progresses.  Increasingly, improbable guesses are cast aside.  Thus, wild goose chases should not be considered as futile, as each is really training sights on the solution (by process of elimination). 

 

I looked first at Level 10's grid for the likely homes for QU.  (Q without U is extremely rare in the English language.)  In higher level grids, the possible places are often more numerous for QU's since there are fewer letters revealed in the diagram.  It's worth the time to stow away likely QU places, because once the word it's in is solved, very often you trip an 'avalanche'.

 

I spent roughly 30 minutes solving, and about two thirds of that was making inroads to the phrase.  My first "hit" came as I was repeatedly guessing at places for commonly occurring letters in English.  This is not a 100% foolproof method since authors can throw phrases at you that use less common letters.  Still, you can put trust in written English, as to how it looks (and feels), even when it is presented to you as numbers instead of letters.  Students of cryptanalysis know that the most commonly occurring letters in English, in order, are E T A O N I S, etc.  If you search the web for "frequency alphabet", you will find this sequence.

 

So, I set to work guessing the most populous unknown of the phrase, 5=?, which occurred three times.  After toying with 5=E and 5=S for a while (silent E or a plural S on the end of the first phrase word seemed plausible), I soon tried 5=T.  This gave me a strong feeling after noting that in the first phrase word, a 5=T would be preceded by a 4, which was represented in the grid in an intersection square (important clue!), which told me that 4 was a very strong candidate masquerading for a vowel. 

 

I guessed through vowels (4 = A E I O U) in conjunction with the 5=T.  I saw that the second T in the second phrase word had three letters following it.  I note there exists a plethora of words ending with T-vowel-vowel-consonant, such as -TION, -TIER, -TAIN, -TIAN, -TIAL and -TIUM, to name a few.

 

I remember having strong hopes first trying -TION.  I had seen earlier the downward P? in the grid, which had to be either PI or PA.  Being a man of mathematics, I got lucky and tried PI first, which presently limited word ending considerations to -TI?? combinations.  Fortunately, my second try after -TION was -TIAL, but this was not by accident!  Lightly penciling in 4=A in both the phrase and grid, I saw ?AP as an across-word in the grid.  Authors of very economical problems like this have to find a place to put Z's, and this seemed to be it -- ZAP!

 

From here, bells and whistles started going off.  I remember having looked at the downward ?A?? and realized this is probably going to be consonant-vowel-consonant-consonant, since I knew vowels needed to be used sparingly in this high-level grid.  Imagining this word ?A?? to be another site for dumping less commons, I considered words like WALK, PARK, JABS and CAMP here.  As I imagined each, I took the last letter (6=?) and in mind's eye placed it in the incomplete second phrase word, 6?T??TIAL.  Of course, I cast out WALK since I realized L was already being used in my guessed phrase word.

 

When CAMP came along, 6=P was tried and I was staring at P?T??TIAL.  Boom!  Any avid viewer of Wheel of Fortune would look at this and see the word POTENTIAL.

 

After filling 7=O (vowel at an intersection square!), 3=E (another intersection vowel!), 8=N (N likes being at the end of lots of words) and 4=A (my 'key' intersection vowel), the flood gates were blown wide open.  Soon, I corrected CAMP to VAMP (great dumping site for a V, which when not at the beginning of a word usually needs to be surrounded by a vowel on both sides; but I knew vowels were not cheap in this Level 10).  Seeing the first theme word now as ??EAT POTENTIAL, I put my Wheel of Fortune hat on again and landed on GREAT POTENTIAL!

 

So then, the G and R will filled in.  Also, the QU home was now very easy to spot since I looked downways at ??OTE?, which must be QUOTE? of course!  I believe RABID was the last word I filled in to complete the mystery.

 

In closing, I should mention that trust in the frequency alphabet paid dividends.  Note that the three most populous letters in the phrase were T (three times), E (twice), A (twice).  Now T E A or T A E is pretty darn close to that E T A, the first three of the frequency alphabet.  And so, this particular Level 10 was doomed for a reasonably quick cracking owing to its adherence to statistical likelihood present in written English.