I'm not sure if you don't understand the example puzzle, or if you don't understand how to find the solution. I'll explain both, just in case.
The example takes a word/phrase that is 13 letters long with no repeated letters. That means it contains exactly half of the letters in the alphabet (26 total). Then the 13 remaining letters are written below, in alphabetical order.
P U B L I C S E R V A N T
D F G H J K M O Q W X Y Z
To encrypt a word/phrase (like
GROVEL in the example), find the first letter in your grid, and take the letter directly above/below it.
G is below
B, so our first encrypted letter is
B. Next is
R. It is above
Q, so the next encrypted letter is
Continuing in this way, we encrypt
The puzzle creators have done the same thing with a different 13-letter phrase, and then have encrypted 3 words with it:
QUARTZ. They show you the encrypted version of these three words, and they want you to work backwards and find the 13-letter phrase they used to create their grid.
The key to solving this is to realize that the letters at the end of the alphabet are not very common, so many of them will not be included in most 13-letter phrases. That means they would be used to "fill in" the bottom row of the grid, which means they would remain in alphabetical order (much like
W X Y Z in the given example).
We start constructing our grid from the bottom right. According to the example words given,
Z matches with
If we write this into our grid, we have
. . . . . . . . . A P E S
. . . . . . . . . W X Y Z
That looks promising! The letters on the top look like they could be part of a common English word or phrase! Let's keep going.
. . . . . . G I R A P E S
. . . . . . T U V W X Y Z
This still looks promising. We need to skip
P, because they are already accounted for in the grid. A few more:
. . . J M F G I R A P E S
. . . N O Q T U V W X Y Z
This doesn't look too good! There is no English word with
JMFG in it!
O are way more common letters than
M, so they're more likely to be in the original phrase. What if we swap those around, so
O are on the top? Then the letters on the bottom are still in alphabetical order, as required, but we have something a little more sensible:
. . . N O F G I R A P E S
. . . J M Q T U V W X Y Z
Now I'm starting to see a pattern. Maybe the
I/U pair doesn't belong there. We can flip it over and insert it at the appropriate point (to keep the bottom row in alphabetical order):
. . . U N O F G R A P E S
. . . I J M Q T V W X Y Z
Now there are only 3 letter pairs unaccounted-for:
There aren't that many ways they can be added, since we need to keep everything on the bottom row in alphabetical order, so a little trial and error (or guessing at the phrase) yields:
B U N C H O F G R A P E S
D I J K L M Q T V W X Y Z
Thus the solution is
BUNCH OF GRAPES.