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Solving a transposition cipher involves a good deal of ingenuity, otherwise known as trial and error. Supposing that we received the following message and wanted to crack it.
ciphertext: THSOA INRRK YEEEG MLTAO NWRHI EETTE EVHHN AEERE OERYW BREEA
The first thing you should notice about the ciphertext are the high amounts of the common letters (etoan-irsh). This indicates that the letters in the ciphertext actually represent what they say they are representing, which indicates the cipher must be a transposition. The next step is to count the letters of the message. It turns out that there are 50.
If one was going to encipher 50 letters using a grid, there only two options: 25 by 2 or 5 by 10. And since most prefer more squarish grids, the 5 by 10 is probably the right guess. Of course, we can never be sure. Perhaps the sender is trying to trick us and the message is actually 48 characters with two nulls. Furthermore, would the sender be so absentminded not to even split the word groups up from their original column height? Perhaps. And it's too tempting not to try this very simple solution.
So, our first attack will assume that the system is a geometric route cipher with a 5 by 10 grid. The only problems know are the inscription and ciphertext routes used. And the only way to find these is trial and error. So, we create the 5 by 10 grid and place the text into it with the different methods that we know. The figures below illustrate the different attempts.

Unfortunatly, it appears that none of the routes used above were used by the sender. We know this simply because the plaintext still remains hidden, meaning that we either didn't use the right route or we're on the wrong track completely. We'll try a few more routes before moving on to column transposition.

The attempt above, using the fairly non-traditional spiral and zig zag, yield nothing useful, either. Of course there are the variants of those, too, such as starting the spiral at different corners or zig zagging from the bottom corner.
And, finally, we've hit it! Look at the diagonal variant inscription above and if we look down the first column, the word 'thing' is clear. The rest of the message follows going down the each column. In the end, the final message appears.
ciphertext: THSOA INRRK YEEEG MLTAO NWRHI EETTE EVHHN AEERE OERYW BREEA
plaintext: things are more like they are now than they ever were before - Dwight D. Eisenhower
  
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