5.7: Cross-Check (Solution)

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```Author: Kiran Kedlaya and David Savitt

Hint 1: Start writing out some of the clue answers without putting them into
the grid.
Hint 2: Now try to fit as many as you can into the grid, maybe starting with a
long entry.
Hint 3: Try writing the ones that don't fit in another color, or on another
grid.
Hint 4: Do you notice any patterns between the words that do and don't fit?
(Hint 4a: No, the letters don't necessarily interchange.)
Hint 0: Read the introduction.
Hint 5: What long answers do you have? Do they suggest anything?

Once they realize that the relationship is that of a cryptogram,
but don't know how to get the answer:
Hint 0: Read the introduction.
Hint 5: What long answers do you have? Do they suggest anything?
Hint 6: It may help to make a table of what encrypts to what.

If they come up with the answer TRIM:
Hint 0: Read the introduction.

Solution:

If you start trying to solve the crossword, you quickly discover
lots of incompatible crossing letters. Moreover, you may notice
that the same letters seem to put into conflict repeatedly. One
way to proceed without losing too much of your sanity is to sort
the clues into two compatible sets, solved on separate grids, as
follows:

DONExCAPOxxNAGS     L..Ax..FUxxS..D
ALEXxOBELIxTUNA     E..Zx..AN.xT..E
FIXEDPOINTx.DA.     G..AL..IS.xALES
.OT..Yx..Ax.IR.     OUTLAWxRUExTIRE
xxx..IAxLLCOOLJ     xxxERIExN..U..X
SAMEASBEFORExxx     .EMAE...G..Axxx
AWEx.TUVxxT..N.     .BAxSTOPxxTRYST
G..DxSTEWSxBUOY     CARLx....DxYO.W
E..IDxxRA.QxFLU     ANVILxxREEKxG.O
xxxSUBSTITUTION     xxx.O....T.TI.S
M.GE.RAxLAIRxxx     MACABREx.E.Rxxx
...AxACTx.T..F.     ABLEx...xSTOPGO
...SxCRYPTOGRAM     TOADx....T.CR.M
ACNExTUKO.x..Z.     EVS.xTOQUExHAJI
BANDxxMEI.xABET     YES.xxMAIDxEY.T

Two of the long answers are "substitution" and "cryptogram". This
suggests that the answers can be squeezed into one grid if you
encrypt one set of answers by a suitable substitution cipher and
overlay it on the other (it doesn't matter which side you choose
to encrypt and which to leave as is). The Wizard's first comment
is an additional hint for this step.

How does this lead to the answer? The other two long answers are
"fixed point" and "same as before". This suggests picking out
those letters which are the same before and after encryption.
Dorothy's comment is an additional hint for this step.

Fortunately, there is enough overlap between the two sets of clues to
determine how 25 of the letters encrypt. Of those, the letters that don't
change are T, R, I, M. However, one must also include H, which by
elimination encrypts to itself. The Wizard's second comment is an
additional hint for this step.

The five unchanged letters spell the answer: MIRTH. The word
"glee" in the introduction is an additional hint for this step.

In case you were wondering, the full cipher table (assuming you
put the long answers in plaintext and not in cipher) is as follows:

PLAIN   ABCDEFGHIJKLMNOPQRSTUVWXYZ
CIPHER  EWGSAPFHIZQDMLUVKRNTOCYJBX

And the completed grid is as follows:
DONExCAPOxxNAGS
ALEX.OBELIxTUNA
FIXEDPOINTxEDAN
UOTDEYxROAxTIRA
xxxARIAxLLCOOLJ
SAMEASBEFORExxx
AWExNTUVxxTRBNT
GERDxSTEWSxBUOY
ELCIDxxRAAQxFLU
xxxSUBSTITUTION
MEGEWRAxLAIRxxx
EWDAxACTxNTUVFU
TUESxCRYPTOGRAM
ACNExTUKOAxHEZI
BANDxxMEISxABET

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