Rats.  I just solved this puzzle after half an hour of
looking at the letter connection graph, then came to mail
you the solution and noticed you just posted the answer.
But, my solution is slightly different than the ones
posted, so I'll mail it anyhow.

 Q
FLU
YIA
STN
SEL
GIL

              -Dan Hennessy
[Ed -- I mistakenly had "qualify test" in one spot.]              
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There's probably more than one way of doing this. The one I found was:

   Q
U  L  F
A  I  Y
N  T  S
G  E  S
I  L  L

Cheers

Andrew Lord
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A few minutes running on my computer came up with this. I did stop and 
start it a few times as it went on for ages, and then an AHAH momement. 
I choose QUALIFYING TEST as the starting letters and 3 minutes later 
this answer.

Jim Eadie

*Q*
ULF
AIY
NTS
GES
ILL
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Hi Ed,

Interesting problem.

 q
ulf
aiy
nts
ges
ill

In case you aren't inundated with solutions, here' the steps I took,
including some false steps:

1) Listed the 12 letters.
2) Added an extra "l" and "s" to address the doubles.
3) Found all the letter pairs that appear in the words and phrases,
remembering to distinguish between the two l's and s's.
4) Created a graph (simple and undirected) from the pairs (letters as
the nodes, edges between paired letters).  By starting with "i", a
planar graph can be created of by excluding the letter "e".  "E" can
then be added into the graph with only 4 crossed edges.
5) Unsuccessfully mapped the graph onto the grid.
6) Created a second graph by removing the pairs unique to
"intelligentsia"
7) Successfully mapped the second graph into the grid.
8) Created a third graph for the pairs of "intelligentsia".
9) Used the third graph to finish the solution.


-Ron Zeno
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This does not qualify as a solution if a king-type move is required to move
from one phrase to the next, but independently, each word and phrase can be
formed. I wasn't sure what the problem demanded. In any case, here is what I
came up with. By the way, neat web site.

R1:   Q
R2: U L F
R3: A I Y
R4: N T S
R5: G E S
R6: I L L

Tim Treloar
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Attached is a picture of my solution.  Consider grid to be
labeled A-C (left to right) and 1-6 (bottom to top).  Moves are as follows:

   Quintessential
      B6-A5-B4-A3-B3-B2-(C2 or C3)-(C3 or C2)-B2-A3-B3-B4-A4-B5
   Intelligentsia
      B4-A3-B3-B2-C1-B1-A1-A2-B2-A3-B3-C3-B4-A4
   Qualifying Test
      B6-A5-A4-B5-B4-C5-C4-B4-A3-A2-B3-B2-(C2 or C3)-B3
   Final Analysis
      C5-B4-A3-A4-B5-A4-A3-A4-B5-C4-C3-B4-C3
      
Clint Weaver
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